Reply
 
Thread Tools Display Modes
  #41   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message

Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase. Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.

This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)




I think what you are saying is: the efficiency of a quad array is
higher, (at low frequencies) because the Zma (radiation impedance) is
higher.


Ok, that's another way of looking at it.

For pratical reasons, four separate drivers must have some physical
distance between them. Maybe 3 cm, edge to edge? That separation would
make the Zma a little lower.


Yes, but if we assume that the frequency is low the difference is
neglectible. It is never the distance in itself that is important, but
the distance compared to the wavelength.

Have you made a measurement of the actual efficiency of single driver

and of an array of those drivers?


I must confess, no. But it is basic acoustics.
  #42   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message

. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.


Sorry, Dick, I think you are wrong here. The efficiency is

actually

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers. The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)
  #43   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message

. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.


Sorry, Dick, I think you are wrong here. The efficiency is

actually

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers. The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)
  #44   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

ow (Goofball_star_dot_etal) wrote in message ...
On Sat, 29 Nov 2003 13:27:44 -0600, "Rusty Boudreaux"
wrote:

"Svante" wrote in message
. com...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is

actually

Nope, Mr. Pierce is quite correct and you are wrong.

Since the impedance is the same and the drive level is the same
the total output is the same.

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.



The question was about sensitivity which includes such things as
efficiency and directivity.


Errhh... Yes, you are right, but I don't see how this helps. I think
the easy way of understanding it is to think about low frequencies,
where directivity is zero, and sensitivity and efficiency is the same
(given that you measure sensitivity in dB at X watts (rather than dB
at Y volts)). Maybe it did help...
  #45   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

ow (Goofball_star_dot_etal) wrote in message ...
On Sat, 29 Nov 2003 13:27:44 -0600, "Rusty Boudreaux"
wrote:

"Svante" wrote in message
. com...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is

actually

Nope, Mr. Pierce is quite correct and you are wrong.

Since the impedance is the same and the drive level is the same
the total output is the same.

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.



The question was about sensitivity which includes such things as
efficiency and directivity.


Errhh... Yes, you are right, but I don't see how this helps. I think
the easy way of understanding it is to think about low frequencies,
where directivity is zero, and sensitivity and efficiency is the same
(given that you measure sensitivity in dB at X watts (rather than dB
at Y volts)). Maybe it did help...


  #46   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On Sun, 30 Nov 2003 09:47:42 +0000, Don Pearce
wrote:


No, you haven't understood.


Fine, I will wait until the mechanic returns from lunch. There is no
point in us oily rags arguing amongst ourselves..
  #47   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On Sun, 30 Nov 2003 09:47:42 +0000, Don Pearce
wrote:


No, you haven't understood.


Fine, I will wait until the mechanic returns from lunch. There is no
point in us oily rags arguing amongst ourselves..
  #48   Report Post  
Bob-Stanton
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Svante) wrote in message


Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase.


Hi:

In an array of four, each driver will see 1/2 the current of a single
driver. The force a voice coil exerts is directly proportional to the
current in the voice coil. The sound pressure caused by the driver is
directly proportional to the force exerted by the voice-coil/diaphram.
For 1/2 the voice-coil current, the sound pressure will be 1/2.

If each driver exerts 1/2 the force of a single driver than:
P = 20*log(0.5) = -6.02 dB. (Power output for each driver in array.)
4 drivers * -6.02 = 0 dB = No change in power output (or efficiency).




Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.




P = F * x/t

If current in each driver is 1/2, than F is 1/2.
F/2 means the displacement (for time T) will be x/2.

P = (F/2) * (x/2) = -6.02 dB

4 drivers * -6.02 = 0 dB = No increase in power output (or
efficiency).


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


The power output of an array (relative to a single driver) does not
change with frequency. At high frequencies, energy beams out in many
lobes. The sound pressure, on axis will change, but that is not the
same thing as efficiency changing.

Bob Stanton
  #49   Report Post  
Bob-Stanton
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Svante) wrote in message


Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase.


Hi:

In an array of four, each driver will see 1/2 the current of a single
driver. The force a voice coil exerts is directly proportional to the
current in the voice coil. The sound pressure caused by the driver is
directly proportional to the force exerted by the voice-coil/diaphram.
For 1/2 the voice-coil current, the sound pressure will be 1/2.

If each driver exerts 1/2 the force of a single driver than:
P = 20*log(0.5) = -6.02 dB. (Power output for each driver in array.)
4 drivers * -6.02 = 0 dB = No change in power output (or efficiency).




Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.




P = F * x/t

If current in each driver is 1/2, than F is 1/2.
F/2 means the displacement (for time T) will be x/2.

P = (F/2) * (x/2) = -6.02 dB

4 drivers * -6.02 = 0 dB = No increase in power output (or
efficiency).


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


The power output of an array (relative to a single driver) does not
change with frequency. At high frequencies, energy beams out in many
lobes. The sound pressure, on axis will change, but that is not the
same thing as efficiency changing.

Bob Stanton
  #50   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On 30 Nov 2003 05:10:31 -0800, (Bob-Stanton)
wrote:

(Svante) wrote in message


Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase.


Hi:

In an array of four, each driver will see 1/2 the current of a single
driver. The force a voice coil exerts is directly proportional to the
current in the voice coil. The sound pressure caused by the driver is
directly proportional to the force exerted by the voice-coil/diaphram.
For 1/2 the voice-coil current, the sound pressure will be 1/2.

If each driver exerts 1/2 the force of a single driver than:
P = 20*log(0.5) = -6.02 dB. (Power output for each driver in array.)
4 drivers * -6.02 = 0 dB = No change in power output (or efficiency).


You have to sum the pressures first. You are not adding power, you are
adding pressures and/or displacements in phase and the squaring to
get power. Just like if you double voltage or current Power =V^2/R =
I^2*R.





Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.




P = F * x/t

If current in each driver is 1/2, than F is 1/2.
F/2 means the displacement (for time T) will be x/2.

P = (F/2) * (x/2) = -6.02 dB

4 drivers * -6.02 = 0 dB = No increase in power output (or
efficiency).


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


The power output of an array (relative to a single driver) does not
change with frequency. At high frequencies, energy beams out in many
lobes. The sound pressure, on axis will change, but that is not the
same thing as efficiency changing.

Bob Stanton




  #51   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On 30 Nov 2003 05:10:31 -0800, (Bob-Stanton)
wrote:

(Svante) wrote in message


Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase.


Hi:

In an array of four, each driver will see 1/2 the current of a single
driver. The force a voice coil exerts is directly proportional to the
current in the voice coil. The sound pressure caused by the driver is
directly proportional to the force exerted by the voice-coil/diaphram.
For 1/2 the voice-coil current, the sound pressure will be 1/2.

If each driver exerts 1/2 the force of a single driver than:
P = 20*log(0.5) = -6.02 dB. (Power output for each driver in array.)
4 drivers * -6.02 = 0 dB = No change in power output (or efficiency).


You have to sum the pressures first. You are not adding power, you are
adding pressures and/or displacements in phase and the squaring to
get power. Just like if you double voltage or current Power =V^2/R =
I^2*R.





Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.




P = F * x/t

If current in each driver is 1/2, than F is 1/2.
F/2 means the displacement (for time T) will be x/2.

P = (F/2) * (x/2) = -6.02 dB

4 drivers * -6.02 = 0 dB = No increase in power output (or
efficiency).


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


The power output of an array (relative to a single driver) does not
change with frequency. At high frequencies, energy beams out in many
lobes. The sound pressure, on axis will change, but that is not the
same thing as efficiency changing.

Bob Stanton


  #52   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

"Rusty Boudreaux" wrote in message ...

Take identical drivers each with a sensitivity of n:
Put two in parallel you get 2n.
Put two in series you get n/2.
Put two in parallel and series with another two in parallel: You
get (2n*2n)/(2n+2n)=4n^2/4n=n (i.e. the same as a single driver).


This is exactly what is wrong. It does not take into account what
happens on the acoustic side of the speaker.

If we go back to the (two-in-series) in parallel with
(two-in-series)ie four speakers connected such that the impedance is
the same as for one speaker the following will happen:
-Each speaker will receive 1/4 of the power.
-The system will receive the same power.
-Each speaker will receive 1/2 of the voltage.
-Each speaker will displace 1/2 the amount of air (displacement is
proportional to the voltage at a given frequency, assuming linearity
and that the pressure from the other speakers does not affect the
motion (both are reasonable assumptions))
-The system will displace twice the amount of air.
-The acoustic output power will quadruple (acoustic power is
proportional to the volume displacement squared)

Net:
Input power is the same, output power is quadrupled, efficiency has
quadrupled (for low frequencies). So has sensitivity, since the
electrical impedance is the same and the directivity pattern is
spherical (for low frequencies).

Dick was right.


Nope. I wish Dick could think this through again and tell us if he
stands by his original statement. Dick?
  #53   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

"Rusty Boudreaux" wrote in message ...

Take identical drivers each with a sensitivity of n:
Put two in parallel you get 2n.
Put two in series you get n/2.
Put two in parallel and series with another two in parallel: You
get (2n*2n)/(2n+2n)=4n^2/4n=n (i.e. the same as a single driver).


This is exactly what is wrong. It does not take into account what
happens on the acoustic side of the speaker.

If we go back to the (two-in-series) in parallel with
(two-in-series)ie four speakers connected such that the impedance is
the same as for one speaker the following will happen:
-Each speaker will receive 1/4 of the power.
-The system will receive the same power.
-Each speaker will receive 1/2 of the voltage.
-Each speaker will displace 1/2 the amount of air (displacement is
proportional to the voltage at a given frequency, assuming linearity
and that the pressure from the other speakers does not affect the
motion (both are reasonable assumptions))
-The system will displace twice the amount of air.
-The acoustic output power will quadruple (acoustic power is
proportional to the volume displacement squared)

Net:
Input power is the same, output power is quadrupled, efficiency has
quadrupled (for low frequencies). So has sensitivity, since the
electrical impedance is the same and the directivity pattern is
spherical (for low frequencies).

Dick was right.


Nope. I wish Dick could think this through again and tell us if he
stands by his original statement. Dick?
  #54   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

Don Pearce wrote in message . ..
On 30 Nov 2003 02:06:41 -0800, (Svante)
wrote:

Don Pearce wrote in message . ..
On 29 Nov 2003 10:45:12 -0800,
(Svante)
wrote:

Stager wrote in message ...
I'm still not too clear on the answer. I'm not actually
looking for a simple answer but a way to calculate the
efficiency given the individual sensitivity and the number
of drivers in a cluster.

OK, the answer is really simple; If the efficiency is measured on
linear scale (%), the efficiency is proportional to the number of
drivers. So, if a single speaker has an efficiency of 0.1% a system
made of two such speakers would have an efficiency of 0.2%, three
0.3%, four 0.4% etc.
On a log scale (dB) each doubling of the number of speakers would give
you 3 dB a increase in efficiency. So, if a single speaker gives 90 dB
@ 1W a system made of two such speakers would give you 93 dB, four 96
dB, eight 99 dB etc.

The above holds for low frequencies (such that the dimensions of the
system is smaller than the wavelength) and for a reasonable number of
drivers. Obviously, the efficiency can never go above 100%.

None of this changes the efficiency, these apparent gains are in fact
increases in directivity. Move off axis and the result of multiple
speakers is actually reduced, not increased volume. Seen this way, it
is clear that there is actually no theoretical limit to the amount of
"gain" available from multiple speakers. Of course the increased level
is purely a far-field phenomenon, and the distance from the speakers
you need to reach the far field goes up with each added driver.


Sorry, you're wrong. For HIGH frequencies (averaged over directions
and frequencies), yes, but for low frequencies the decreased level off
axis that you describe will never occur. The contributions from the
speakers will be in phase, and thus add up to a pressure corresponding
to n*p1 (n = number of speakers, p1 being the sound pressure from one
speaker).
Input power will be multiplied by n, but output power by n^2, since
acoustic power is proportional to sound pressure squared. Thus
efficiency increases linearly with the number of speakers, (n^2)/n.


Please read my comment about the far field. That covers everything you
have said here. But I will repeat for clarity "EFFICIENCY IS NOT
INCREASED BY ADDING DRIVERS".


I understand what you mean, and it is all based on that there is
directivity. At low frequencies there is no directivity. The increased
level will occur at all directions. I will also repeat for clarity:
"EFFICIENCY IS INCREASED BY ADDING DRIVERS".
  #55   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

Don Pearce wrote in message . ..
On 30 Nov 2003 02:06:41 -0800, (Svante)
wrote:

Don Pearce wrote in message . ..
On 29 Nov 2003 10:45:12 -0800,
(Svante)
wrote:

Stager wrote in message ...
I'm still not too clear on the answer. I'm not actually
looking for a simple answer but a way to calculate the
efficiency given the individual sensitivity and the number
of drivers in a cluster.

OK, the answer is really simple; If the efficiency is measured on
linear scale (%), the efficiency is proportional to the number of
drivers. So, if a single speaker has an efficiency of 0.1% a system
made of two such speakers would have an efficiency of 0.2%, three
0.3%, four 0.4% etc.
On a log scale (dB) each doubling of the number of speakers would give
you 3 dB a increase in efficiency. So, if a single speaker gives 90 dB
@ 1W a system made of two such speakers would give you 93 dB, four 96
dB, eight 99 dB etc.

The above holds for low frequencies (such that the dimensions of the
system is smaller than the wavelength) and for a reasonable number of
drivers. Obviously, the efficiency can never go above 100%.

None of this changes the efficiency, these apparent gains are in fact
increases in directivity. Move off axis and the result of multiple
speakers is actually reduced, not increased volume. Seen this way, it
is clear that there is actually no theoretical limit to the amount of
"gain" available from multiple speakers. Of course the increased level
is purely a far-field phenomenon, and the distance from the speakers
you need to reach the far field goes up with each added driver.


Sorry, you're wrong. For HIGH frequencies (averaged over directions
and frequencies), yes, but for low frequencies the decreased level off
axis that you describe will never occur. The contributions from the
speakers will be in phase, and thus add up to a pressure corresponding
to n*p1 (n = number of speakers, p1 being the sound pressure from one
speaker).
Input power will be multiplied by n, but output power by n^2, since
acoustic power is proportional to sound pressure squared. Thus
efficiency increases linearly with the number of speakers, (n^2)/n.


Please read my comment about the far field. That covers everything you
have said here. But I will repeat for clarity "EFFICIENCY IS NOT
INCREASED BY ADDING DRIVERS".


I understand what you mean, and it is all based on that there is
directivity. At low frequencies there is no directivity. The increased
level will occur at all directions. I will also repeat for clarity:
"EFFICIENCY IS INCREASED BY ADDING DRIVERS".


  #56   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

ow (Goofball_star_dot_etal) wrote in message ...

2 2 2
p0 B l Sd
n0 = ------ * ---- * -------
2 pi c Re Mms^2

where
n0 is the reference efficiency of the driver
p0 is the densiy of air = 1.18 kilograms per cubic meter
pi is 3.1415926535...
c is the velocity of sound in air =~ 342 meters per second
B is the flux density of the magnetic field in the voice coil
gap
in Tesla (1 T = 10,000 Gauss)
l is the length of the voice coil wire in the magnet field B in
meters
Re is the DC resistance of the voice coil in Ohms
Sd is the area of the cone in square meters
Mms is the moving mass of the cone in kilograms

Phew!


End quote

It is not obvious how this relates to multiple drivers but it is clear
that the acoustic output power is proportional to the volume
displacement squared.


Thanks for sticking with me here, nobody seems to understand us... :-)

I think the equation gives us right, at least for speakers connected
in series. Take two speakers in series: B will remain, l will double
Re will double Sd will double and Mms will double. Net: a factor two.
(on EFFICIENCY nb)

It works for speakers in parallel as well, if you realise that Re is
halved and l remains the same (not doubled). (See the two wires
running beside oneanother in an ocean of magnetic field. The ends are
connected. The current is divided in two between the wires.
Understanding this is is clear that we may bundle these two wires
together and nothing will change. The equivalent wire thus has the
same length as the single speaker.) Net: a factor two. (also on
EFFICIENCY)
  #57   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

ow (Goofball_star_dot_etal) wrote in message ...

2 2 2
p0 B l Sd
n0 = ------ * ---- * -------
2 pi c Re Mms^2

where
n0 is the reference efficiency of the driver
p0 is the densiy of air = 1.18 kilograms per cubic meter
pi is 3.1415926535...
c is the velocity of sound in air =~ 342 meters per second
B is the flux density of the magnetic field in the voice coil
gap
in Tesla (1 T = 10,000 Gauss)
l is the length of the voice coil wire in the magnet field B in
meters
Re is the DC resistance of the voice coil in Ohms
Sd is the area of the cone in square meters
Mms is the moving mass of the cone in kilograms

Phew!


End quote

It is not obvious how this relates to multiple drivers but it is clear
that the acoustic output power is proportional to the volume
displacement squared.


Thanks for sticking with me here, nobody seems to understand us... :-)

I think the equation gives us right, at least for speakers connected
in series. Take two speakers in series: B will remain, l will double
Re will double Sd will double and Mms will double. Net: a factor two.
(on EFFICIENCY nb)

It works for speakers in parallel as well, if you realise that Re is
halved and l remains the same (not doubled). (See the two wires
running beside oneanother in an ocean of magnetic field. The ends are
connected. The current is divided in two between the wires.
Understanding this is is clear that we may bundle these two wires
together and nothing will change. The equivalent wire thus has the
same length as the single speaker.) Net: a factor two. (also on
EFFICIENCY)
  #60   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase.


Hi:

In an array of four, each driver will see 1/2 the current of a single
driver. The force a voice coil exerts is directly proportional to the
current in the voice coil. The sound pressure caused by the driver is
directly proportional to the force exerted by the voice-coil/diaphram.
For 1/2 the voice-coil current, the sound pressure will be 1/2.

If each driver exerts 1/2 the force of a single driver than:
P = 20*log(0.5) = -6.02 dB. (Power output for each driver in array.)
4 drivers * -6.02 = 0 dB = No change in power output (or efficiency).


You cannot sum the powers. You have to sum the sound pressures. The
sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
dB) for the same input power.

Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.




P = F * x/t

If current in each driver is 1/2, than F is 1/2.
F/2 means the displacement (for time T) will be x/2.

P = (F/2) * (x/2) = -6.02 dB

4 drivers * -6.02 = 0 dB = No increase in power output (or
efficiency).


No, again you cannot sum the individual powers. For the system, total
displacement will be x*2. This is acheived with the the same input
power. This corresponds to an increased efficiency of +6.02 dB.

This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


The power output of an array (relative to a single driver) does not
change with frequency. At high frequencies, energy beams out in many
lobes. The sound pressure, on axis will change, but that is not the
same thing as efficiency changing.


No. Given an ideal piston driven to an acceleration corresponding to
the signal, the level EXACTLY straight in front of and far away from
the piston does NOT vary with frequency. To the sides it does. To the
sides the level will vary towards higher frequencies due to
interference from the different parts of the piston. This will cause
on-axis level to be constant (vs frequency), but efficiency to drop
towards higher frequencies. Thus, the efficiency gain I have described
in this thread is only acheived in the low-frequency region.


  #61   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Bob-Stanton) wrote in message . com...
(Svante) wrote in message


Sorry, Dick, I think you are wrong here. The efficiency is actually
quadrupled in this case leading to a 10*log(4)=6dB increase in
efficiency. I know this seems terribly wrong, but is true, at least
for low frequencies. It is easiest to understand like this; 4 sources
gives 4 times the sound pressure, which leads to a 20*log(4)=12dB
increase of the SPL compared to the single driver. However, this
example assumes that each of the drivers received the same amount of
power as the single driver, which is 10*log(4)=6 dB more. The net gain
is 6 dB, which is an efficiency increase.


Hi:

In an array of four, each driver will see 1/2 the current of a single
driver. The force a voice coil exerts is directly proportional to the
current in the voice coil. The sound pressure caused by the driver is
directly proportional to the force exerted by the voice-coil/diaphram.
For 1/2 the voice-coil current, the sound pressure will be 1/2.

If each driver exerts 1/2 the force of a single driver than:
P = 20*log(0.5) = -6.02 dB. (Power output for each driver in array.)
4 drivers * -6.02 = 0 dB = No change in power output (or efficiency).


You cannot sum the powers. You have to sum the sound pressures. The
sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
dB) for the same input power.

Another way of looking at it
is to calculate the power produced by the motion of the cone, which
should be the F*x/t, F being the force from the air as sensed by the
cone, x being the displacement and t the time. If there is a sound
pressure from another driver, this will increase the output power of
the driver, and thus increase the efficiency.




P = F * x/t

If current in each driver is 1/2, than F is 1/2.
F/2 means the displacement (for time T) will be x/2.

P = (F/2) * (x/2) = -6.02 dB

4 drivers * -6.02 = 0 dB = No increase in power output (or
efficiency).


No, again you cannot sum the individual powers. For the system, total
displacement will be x*2. This is acheived with the the same input
power. This corresponds to an increased efficiency of +6.02 dB.

This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)


The power output of an array (relative to a single driver) does not
change with frequency. At high frequencies, energy beams out in many
lobes. The sound pressure, on axis will change, but that is not the
same thing as efficiency changing.


No. Given an ideal piston driven to an acceleration corresponding to
the signal, the level EXACTLY straight in front of and far away from
the piston does NOT vary with frequency. To the sides it does. To the
sides the level will vary towards higher frequencies due to
interference from the different parts of the piston. This will cause
on-axis level to be constant (vs frequency), but efficiency to drop
towards higher frequencies. Thus, the efficiency gain I have described
in this thread is only acheived in the low-frequency region.
  #62   Report Post  
Dick Pierce
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Svante) wrote in message ...
"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is

actually


Sorry, Mr. Svante, you can't read what I wrote and you chose
to omit the crucial piece of text that I EXPLICITLY wrote.

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers.


You apparently did not read or chose to ignore what I wrote
in my original replay. I said the following, QUITE clearly:

"Ignoring acoustic effects, and just concentrating on the
electrical properties, you essentially examine what the
total impedance of the array is, and then examine how it
is divided amongst the drivers."

Do you see how I EXPLICITLY chose to NOT talk about the acoustical
effects? The reason being is precisely BECAUSE of the complex
depednecny on frequency.

Now, within the context that I had writtenm as I have just reiterated,
would you care to show where my error was?


The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)

  #63   Report Post  
Dick Pierce
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Svante) wrote in message ...
"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is

actually


Sorry, Mr. Svante, you can't read what I wrote and you chose
to omit the crucial piece of text that I EXPLICITLY wrote.

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers.


You apparently did not read or chose to ignore what I wrote
in my original replay. I said the following, QUITE clearly:

"Ignoring acoustic effects, and just concentrating on the
electrical properties, you essentially examine what the
total impedance of the array is, and then examine how it
is divided amongst the drivers."

Do you see how I EXPLICITLY chose to NOT talk about the acoustical
effects? The reason being is precisely BECAUSE of the complex
depednecny on frequency.

Now, within the context that I had writtenm as I have just reiterated,
would you care to show where my error was?


The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)

  #68   Report Post  
Don Pearce
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On Mon, 01 Dec 2003 02:41:17 GMT, (gregs)
wrote:

In article ,
(Svante) wrote:
Don Pearce wrote in message
. ..
On 30 Nov 2003 02:06:41 -0800,
(Svante)
wrote:



I understand what you mean, and it is all based on that there is
directivity. At low frequencies there is no directivity. The increased
level will occur at all directions. I will also repeat for clarity:
"EFFICIENCY IS INCREASED BY ADDING DRIVERS".


Forget directivity. At low frequencies there is plenty phase shifting.
It doesn't take much to vary the phases. Many repeat having the need to closly space drivers.
Well this help control the phasing, especially if multiple drivers are directed
into a channel or common waveguide. I was trying to remember the term, but EV used a common
chamber for some of their LF PA boxes. I tried an experiment in the backyard afew years ago.
To speakers about 16 feet apart. At the exact center, the sound was 6 dBhigher over one speaker.
Even at my low test frequency of perhaps 40 Hz, it only took inches either direction with the SLM
toget significant change in SPL. So its basically true, if the wavefronts are combined at the
source, it helps maintain high constant SPL when you move around.

Yes, efficiency is increased by adding drivers.

greg


You've just given us a perfect description of an experiment
demonstrating directivity - and you draw the conclusion that it isn't
so, and efficiency has been increased.

I'm stunned.

d

_____________________________

http://www.pearce.uk.com
  #69   Report Post  
Don Pearce
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On Mon, 01 Dec 2003 02:41:17 GMT, (gregs)
wrote:

In article ,
(Svante) wrote:
Don Pearce wrote in message
. ..
On 30 Nov 2003 02:06:41 -0800,
(Svante)
wrote:



I understand what you mean, and it is all based on that there is
directivity. At low frequencies there is no directivity. The increased
level will occur at all directions. I will also repeat for clarity:
"EFFICIENCY IS INCREASED BY ADDING DRIVERS".


Forget directivity. At low frequencies there is plenty phase shifting.
It doesn't take much to vary the phases. Many repeat having the need to closly space drivers.
Well this help control the phasing, especially if multiple drivers are directed
into a channel or common waveguide. I was trying to remember the term, but EV used a common
chamber for some of their LF PA boxes. I tried an experiment in the backyard afew years ago.
To speakers about 16 feet apart. At the exact center, the sound was 6 dBhigher over one speaker.
Even at my low test frequency of perhaps 40 Hz, it only took inches either direction with the SLM
toget significant change in SPL. So its basically true, if the wavefronts are combined at the
source, it helps maintain high constant SPL when you move around.

Yes, efficiency is increased by adding drivers.

greg


You've just given us a perfect description of an experiment
demonstrating directivity - and you draw the conclusion that it isn't
so, and efficiency has been increased.

I'm stunned.

d

_____________________________

http://www.pearce.uk.com
  #70   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

Don Pearce wrote in message . ..
On Mon, 01 Dec 2003 02:41:17 GMT, (gregs)
wrote:

In article ,
(Svante) wrote:
Don Pearce wrote in message
. ..
On 30 Nov 2003 02:06:41 -0800,
(Svante)
wrote:



I understand what you mean, and it is all based on that there is
directivity. At low frequencies there is no directivity. The increased
level will occur at all directions. I will also repeat for clarity:
"EFFICIENCY IS INCREASED BY ADDING DRIVERS".


Forget directivity. At low frequencies there is plenty phase shifting.
It doesn't take much to vary the phases. Many repeat having the need to closly space drivers.
Well this help control the phasing, especially if multiple drivers are directed
into a channel or common waveguide. I was trying to remember the term, but EV used a common
chamber for some of their LF PA boxes. I tried an experiment in the backyard afew years ago.
To speakers about 16 feet apart. At the exact center, the sound was 6 dBhigher over one speaker.
Even at my low test frequency of perhaps 40 Hz, it only took inches either direction with the SLM
toget significant change in SPL. So its basically true, if the wavefronts are combined at the
source, it helps maintain high constant SPL when you move around.

Yes, efficiency is increased by adding drivers.

greg


You've just given us a perfect description of an experiment
demonstrating directivity - and you draw the conclusion that it isn't
so, and efficiency has been increased.

I'm stunned.


OK, in my terminology, 40Hz is a HIGH frequency if the drivers are
placed 16 feet (~4.8 m) apart. The wavelength at 40 Hz is 8.6 m which
in the same order of magnitude as the driver distance. In this case
there will be directivity, and the efficiency, averaged over
directions would not increase as much or at all. If the speakers would
have been close together (and f=40Hz still (which is now LOW
frequency)) the directivity would be almost zero, but the level
straight in front of the speakers would still be +6dB. ...and in all
other directions, since there is no directivity. So the efficiency has
increased, since input power is only +3dB.

I agree that the experiment does not demonstrate increased efficiency,
but it demonstrates increased sensitivity, straight in front of the
speaker. If the speakers would have been moved close together, it
would have demonstrated an increased efficiency as well.


  #71   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

Don Pearce wrote in message . ..
On Mon, 01 Dec 2003 02:41:17 GMT, (gregs)
wrote:

In article ,
(Svante) wrote:
Don Pearce wrote in message
. ..
On 30 Nov 2003 02:06:41 -0800,
(Svante)
wrote:



I understand what you mean, and it is all based on that there is
directivity. At low frequencies there is no directivity. The increased
level will occur at all directions. I will also repeat for clarity:
"EFFICIENCY IS INCREASED BY ADDING DRIVERS".


Forget directivity. At low frequencies there is plenty phase shifting.
It doesn't take much to vary the phases. Many repeat having the need to closly space drivers.
Well this help control the phasing, especially if multiple drivers are directed
into a channel or common waveguide. I was trying to remember the term, but EV used a common
chamber for some of their LF PA boxes. I tried an experiment in the backyard afew years ago.
To speakers about 16 feet apart. At the exact center, the sound was 6 dBhigher over one speaker.
Even at my low test frequency of perhaps 40 Hz, it only took inches either direction with the SLM
toget significant change in SPL. So its basically true, if the wavefronts are combined at the
source, it helps maintain high constant SPL when you move around.

Yes, efficiency is increased by adding drivers.

greg


You've just given us a perfect description of an experiment
demonstrating directivity - and you draw the conclusion that it isn't
so, and efficiency has been increased.

I'm stunned.


OK, in my terminology, 40Hz is a HIGH frequency if the drivers are
placed 16 feet (~4.8 m) apart. The wavelength at 40 Hz is 8.6 m which
in the same order of magnitude as the driver distance. In this case
there will be directivity, and the efficiency, averaged over
directions would not increase as much or at all. If the speakers would
have been close together (and f=40Hz still (which is now LOW
frequency)) the directivity would be almost zero, but the level
straight in front of the speakers would still be +6dB. ...and in all
other directions, since there is no directivity. So the efficiency has
increased, since input power is only +3dB.

I agree that the experiment does not demonstrate increased efficiency,
but it demonstrates increased sensitivity, straight in front of the
speaker. If the speakers would have been moved close together, it
would have demonstrated an increased efficiency as well.
  #72   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On Sun, 30 Nov 2003 09:47:42 +0000, Don Pearce
wrote:

No, you haven't understood.


I think I see the problem now. With your background you probably have
in the back of your mind a radio antenna where you can not have gain
in all directions and it is a matter of "squeezing the balloon" to
get gain. Now here is the crunch: A properly matched antenna is 100%
efficient but what if the antenna is a bit of wet string and 99% of
the power is reflected. Can this "bit of wet string" be improved upon?
There is no need to read what Svante and I have written if it must
violate your antenna law, right?
  #73   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

On Sun, 30 Nov 2003 09:47:42 +0000, Don Pearce
wrote:

No, you haven't understood.


I think I see the problem now. With your background you probably have
in the back of your mind a radio antenna where you can not have gain
in all directions and it is a matter of "squeezing the balloon" to
get gain. Now here is the crunch: A properly matched antenna is 100%
efficient but what if the antenna is a bit of wet string and 99% of
the power is reflected. Can this "bit of wet string" be improved upon?
There is no need to read what Svante and I have written if it must
violate your antenna law, right?
  #74   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Dick Pierce) wrote in message . com...
(Svante) wrote in message ...
"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is
actually


Sorry, Mr. Svante, you can't read what I wrote and you chose
to omit the crucial piece of text that I EXPLICITLY wrote.

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers.


You apparently did not read or chose to ignore what I wrote
in my original replay. I said the following, QUITE clearly:

"Ignoring acoustic effects, and just concentrating on the
electrical properties, you essentially examine what the
total impedance of the array is, and then examine how it
is divided amongst the drivers."

Do you see how I EXPLICITLY chose to NOT talk about the acoustical
effects? The reason being is precisely BECAUSE of the complex
depednecny on frequency.
Now, within the context that I had writtenm as I have just reiterated,
would you care to show where my error was?


I think your error is to assume that ignoring acoustic effects, you
can still calculate sensitivity. For some reason you to not include
the next paragraph where you wrote:

----quote

So, in general, you can say that n drivers in parallel will have
n times the sensitivity of one, while n in series will have 1/n
the sensivitity.

----End quote

Given that you ignore acoustical effects, this is correct, but
misleading since acoustical effects are so important.

Could you please enlighten us regarding your view on the sensitivity
for low frequencies for the 2x2 array, and for higher frequencies
straight in front of the same 2x2 array? Including acoustic effects
and assuming free field conditions.

From what I have seen in this group you have provided many good
insights, and I beleive that you would say the same thing as I do,
regarding this. I think your input could help this thread to "settle".

The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)

  #75   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Dick Pierce) wrote in message . com...
(Svante) wrote in message ...
"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is
actually


Sorry, Mr. Svante, you can't read what I wrote and you chose
to omit the crucial piece of text that I EXPLICITLY wrote.

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers.


You apparently did not read or chose to ignore what I wrote
in my original replay. I said the following, QUITE clearly:

"Ignoring acoustic effects, and just concentrating on the
electrical properties, you essentially examine what the
total impedance of the array is, and then examine how it
is divided amongst the drivers."

Do you see how I EXPLICITLY chose to NOT talk about the acoustical
effects? The reason being is precisely BECAUSE of the complex
depednecny on frequency.
Now, within the context that I had writtenm as I have just reiterated,
would you care to show where my error was?


I think your error is to assume that ignoring acoustic effects, you
can still calculate sensitivity. For some reason you to not include
the next paragraph where you wrote:

----quote

So, in general, you can say that n drivers in parallel will have
n times the sensitivity of one, while n in series will have 1/n
the sensivitity.

----End quote

Given that you ignore acoustical effects, this is correct, but
misleading since acoustical effects are so important.

Could you please enlighten us regarding your view on the sensitivity
for low frequencies for the 2x2 array, and for higher frequencies
straight in front of the same 2x2 array? Including acoustic effects
and assuming free field conditions.

From what I have seen in this group you have provided many good
insights, and I beleive that you would say the same thing as I do,
regarding this. I think your input could help this thread to "settle".

The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)



  #76   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Dick Pierce) wrote in message . com...
(Svante) wrote in message ...
"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is
actually


Sorry, Mr. Svante, you can't read what I wrote and you chose
to omit the crucial piece of text that I EXPLICITLY wrote.

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers.


You apparently did not read or chose to ignore what I wrote
in my original replay. I said the following, QUITE clearly:

"Ignoring acoustic effects, and just concentrating on the
electrical properties, you essentially examine what the
total impedance of the array is, and then examine how it
is divided amongst the drivers."

Do you see how I EXPLICITLY chose to NOT talk about the acoustical
effects? The reason being is precisely BECAUSE of the complex
depednecny on frequency.
Now, within the context that I had writtenm as I have just reiterated,
would you care to show where my error was?


I think your error is to assume that ignoring acoustic effects, you
can still calculate sensitivity. For some reason you to not include
the next paragraph where you wrote:

----quote

So, in general, you can say that n drivers in parallel will have
n times the sensitivity of one, while n in series will have 1/n
the sensivitity.

----End quote

Given that you ignore acoustical effects, this is correct, but
misleading since acoustical effects are so important.

Could you please enlighten us regarding your view on the sensitivity
for low frequencies for the 2x2 array, and for higher frequencies
straight in front of the same 2x2 array? Including acoustic effects
and assuming free field conditions.

From what I have seen in this group you have provided many good
insights, and I beleive that you would say the same thing as I do,
regarding this. I think your input could help this thread to "settle".

The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)

  #77   Report Post  
Svante
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Dick Pierce) wrote in message . com...
(Svante) wrote in message ...
"Rusty Boudreaux" wrote in message ...
"Svante" wrote in message
om...
(Dick Pierce) wrote in message
. com...
Stager wrote in message

...
How does using speakers in arrays affect their sensitivity

and
total resonant frequency?

For example, say I have four 8 ohm mids, each individually
rated at 90 dB sensitivity (at 1 meter, 1 watt).

If I do a series-parallel array, I know I'll still be at 8

ohms,
but how will the sensitivity change from the original

individual
90 dB.

In a series parallel array of the kind you're talking about,
for a given voltqge across the array, the total power in the
array is the same, since the impedance is the same, but each
driver dissipates 1/4 of the total power, leading to the same
sensitivity as a single driver.

Sorry, Dick, I think you are wrong here. The efficiency is
actually


Sorry, Mr. Svante, you can't read what I wrote and you chose
to omit the crucial piece of text that I EXPLICITLY wrote.

Nope, Mr. Pierce is quite correct and you are wrong.


Nopenope... :-)

Since the impedance is the same and the drive level is the same
the total output is the same.


Nope

Please explain how four drivers at one quater 'X' watts can be
anything other than the same as a single driver driven at 'X'
watts.


There is an efficiency gain on the acoustic side, due to the
interaction between the drivers.


You apparently did not read or chose to ignore what I wrote
in my original replay. I said the following, QUITE clearly:

"Ignoring acoustic effects, and just concentrating on the
electrical properties, you essentially examine what the
total impedance of the array is, and then examine how it
is divided amongst the drivers."

Do you see how I EXPLICITLY chose to NOT talk about the acoustical
effects? The reason being is precisely BECAUSE of the complex
depednecny on frequency.
Now, within the context that I had writtenm as I have just reiterated,
would you care to show where my error was?


I think your error is to assume that ignoring acoustic effects, you
can still calculate sensitivity. For some reason you to not include
the next paragraph where you wrote:

----quote

So, in general, you can say that n drivers in parallel will have
n times the sensitivity of one, while n in series will have 1/n
the sensivitity.

----End quote

Given that you ignore acoustical effects, this is correct, but
misleading since acoustical effects are so important.

Could you please enlighten us regarding your view on the sensitivity
for low frequencies for the 2x2 array, and for higher frequencies
straight in front of the same 2x2 array? Including acoustic effects
and assuming free field conditions.

From what I have seen in this group you have provided many good
insights, and I beleive that you would say the same thing as I do,
regarding this. I think your input could help this thread to "settle".

The total electric input power to the
speakers will be the same in the 2x2 series/parallel connection, but
the acoustic output power will be quadrupled, due to this acoustic
coupling, see my other posts in this thread. I know, it seems terribly
wrong, but is not. It is acoustics... :-)

  #78   Report Post  
Bob-Stanton
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Svante) wrote in message


You cannot sum the powers. You have to sum the sound pressures. The
sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
dB) for the same input power.
...

No, again you cannot sum the individual powers.


To say: "You cannot sum individual powers", is a violation of the law
of conservation of energy.

Another fundamental law a physics is Energy = Force * Distance. If
each of four drivers in an array is pushing the air with half the
force, for half the distance, each puts out 1/4 the energy. The total
power output of four will be only the same as a single driver.


For the system, total
displacement will be x*2. This is acheived with the the same input
power. This corresponds to an increased efficiency of +6.02 dB.


Thats right. BUT
the force exerted by the drivers in the array is only 1/2 that of a
single driver, that corresponds to a decreased efficiency: -6.02 dB.

6.02 dB -6.02 dB = 0 dB change.

P = F/2 * x*2 is the same pressure as: F * x. That means NO increase
in pressure, No incease in effiency and no increase in power.


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)



No. Given an ideal piston driven to an acceleration corresponding to
the signal, the level EXACTLY straight in front of and far away from
the piston does NOT vary with frequency. To the sides it does. To the
sides the level will vary towards higher frequencies due to
interference from the different parts of the piston. This will cause
on-axis level to be constant (vs frequency), but efficiency to drop
towards higher frequencies. Thus, the efficiency gain I have described
in this thread is only acheived in the low-frequency region.


At higher frequencies, as the polar pattern narrows, the energy will
be concentrated toward the front. The sound pressure level will
increase.

Bob Stanton
  #79   Report Post  
Bob-Stanton
 
Posts: n/a
Default Speaker sensitivity and fs in multiples.

(Svante) wrote in message


You cannot sum the powers. You have to sum the sound pressures. The
sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
dB) for the same input power.
...

No, again you cannot sum the individual powers.


To say: "You cannot sum individual powers", is a violation of the law
of conservation of energy.

Another fundamental law a physics is Energy = Force * Distance. If
each of four drivers in an array is pushing the air with half the
force, for half the distance, each puts out 1/4 the energy. The total
power output of four will be only the same as a single driver.


For the system, total
displacement will be x*2. This is acheived with the the same input
power. This corresponds to an increased efficiency of +6.02 dB.


Thats right. BUT
the force exerted by the drivers in the array is only 1/2 that of a
single driver, that corresponds to a decreased efficiency: -6.02 dB.

6.02 dB -6.02 dB = 0 dB change.

P = F/2 * x*2 is the same pressure as: F * x. That means NO increase
in pressure, No incease in effiency and no increase in power.


This reasoning holds for low frequencies, ie when the drivers are
mounted close to each other compared to the wavelength. For higher
frequencies it holds straight in front of the speaker (anechoic
conditions) but to the sides, interference will decrease the sound
pressure. So for higher frequencies, on average (over frequencies and
directions) your statement ends up correct (ie the
efficiency/sensitivity is the same)



No. Given an ideal piston driven to an acceleration corresponding to
the signal, the level EXACTLY straight in front of and far away from
the piston does NOT vary with frequency. To the sides it does. To the
sides the level will vary towards higher frequencies due to
interference from the different parts of the piston. This will cause
on-axis level to be constant (vs frequency), but efficiency to drop
towards higher frequencies. Thus, the efficiency gain I have described
in this thread is only acheived in the low-frequency region.


At higher frequencies, as the polar pattern narrows, the energy will
be concentrated toward the front. The sound pressure level will
increase.

Bob Stanton
Reply
Thread Tools
Display Modes

Posting Rules

Smilies are On
[IMG] code is On
HTML code is Off


Similar Threads
Thread Thread Starter Forum Replies Last Post
rec.audio.car FAQ (Part 4/5) Ian D. Bjorhovde Car Audio 0 March 6th 04 06:54 AM
rec.audio.car FAQ (Part 3/5) Ian D. Bjorhovde Car Audio 0 March 6th 04 06:54 AM
rec.audio.car FAQ (Part 2/5) Ian D. Bjorhovde Car Audio 0 March 6th 04 06:54 AM
rec.audio.car FAQ (Part 1/5) Ian D. Bjorhovde Car Audio 0 March 6th 04 06:54 AM
Question re. Speaker Sensitvity Bruce J. Richman High End Audio 0 August 6th 03 07:29 AM


All times are GMT +1. The time now is 04:59 PM.

Powered by: vBulletin
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
Copyright ©2004-2024 AudioBanter.com.
The comments are property of their posters.
 

About Us

"It's about Audio and hi-fi"