- #1
pardesi
- 337
- 0
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
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
