Karl Uppiano wrote:

"Bob Cain" wrote in message
...


Karl Uppiano wrote:



I understand what "linear" and "sum" mean. When modulated by two
sinusoids, the x position of the diaphragm as a function of time is
defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

It is the piston velocity v(t) that follows this for equal sound pressure
at all frequencies.


Hmmm... what is the equation for x( t ) then?

x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t )

Isn't velocity the first derivative of position? Isn't acceleration the
first derivative of velocity? It seems that acceleration (if we cared about
it) would be

a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) )

Try

a( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )


However, all three equations only differ by a constant. So I believe you
could get the same physical consequences by simply adjusting A and B
accordingly.

And phase. The adjustment to A and B is a constant if W is.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein