# Pressure equation of sound wave

1. Jan 26, 2010

### abhineetK

Let us consider sound (longitudinal) wave
y=A.sin($$\omega$$t-kx)

See attachment for diagram

Consider air column of length $$\Delta$$x and cross-sectional area S at distance x from source.
I want to derive the pressure equation of the sound wave using
Bulk modulus, B=-$$\Delta$$P/($$\Delta$$V/V)
implying $$\Delta$$P=-B.$$\Delta$$V/V

But the trouble is that I am not able to select the expression for $$\Delta$$V
1) $$\Delta$$V=S.y
2) $$\Delta$$V=S$$\Delta$$y
TELL ME WHICH EXPRESSION OUT OF THE TWO SHOULD I USE with EXPLANATION.

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2. Jan 27, 2010

### abhineetK

I give you a hint about what I was actually thinking.

1)$$\Delta$$V=S.y
It would mean that $$\Delta$$P is the difference between the initial pressure of the volume considered and the final pressure of the same column (now volume is reduced to (V-$$\Delta$$V) but mass(amount) remains same).

2)$$\Delta$$V=S.$$\Delta$$y
It would mean that $$\Delta$$P is the change in pressure for a change $$\Delta$$y
in the length of the column.

Which of the above does the pressure equation of sound wave denotes? Please, tell.

NOTE: If you find any problem in understanding what I want to say, please tell.