# Wave equation for sound waves

#### pardesi

i saw the 'proof' of the wave equation for a sound wave in a medium assuming the wave equation for a dissplacement wave.
that is the equtaion $$s=s_{0} \sin(kx-wt)$$ is supposed to hold for all points for a wave propagating in the x direction.
then using this he found out the excess pressure at any point $$x$$ a any time $$t$$.
well what he did was let at time t=0 wave started and at time t say the dislpacement of any point x be s and that of $$x+\delta x$$ be $$s+ \delta s$$.then we have
change in volume $$\delta V=-A\delta s=-Ak \cos(kx-wt) \delta x$$
hence he said excess pressure on the material at x is $$\delta P=\frac{-B \delta V}{V}$$
but my question is the fluid at x is no more at x but rather at x+s so how come the pressure calculated from the bulk modulus equtaion is that at x

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#### Chestermiller

Mentor
He is considering the region between x and $x+\delta x$.

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