Wave equation for sound waves

  • Thread starter pardesi
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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 [tex] s=s_{0} \sin(kx-wt)[/tex] 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 [tex]x[/tex] a any time [tex] t [/tex].
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 [tex]x+\delta x[/tex] be [tex]s+ \delta s[/tex].then we have
change in volume [tex]\delta V=-A\delta s=-Ak \cos(kx-wt) \delta x[/tex]
hence he said excess pressure on the material at x is [tex]\delta P=\frac{-B \delta V}{V}[/tex]
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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He is considering the region between x and ##x+\delta x##.
 

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