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Do pressure waves (phase angle) always lead or lag behind a displacement wave in case of sound waves? Or is it something that does not happen "always" and depends on the initial configuration of the system?

I related this idea to that of inductors and capacitors with resistors, so I was wondering whether such a generalization could be made in this case too?

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In a sound wave, the air is moving forward when pressure is highest and backwards when it is lowest, so the displacement is 90 degrees out of phase with the pressure, and is a maximum when the pressure is dropping.

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  • $\begingroup$ What about a shock wave? $\endgroup$
    – John Darby
    Commented Aug 17, 2021 at 11:58
  • $\begingroup$ In a shock wave everything happens at once. The pressure goes up, the temperature goes up, and the air starts to move. $\endgroup$
    – mike stone
    Commented Aug 17, 2021 at 13:00
  • $\begingroup$ Thanks for the simple answer. I had a doubt, If I have been given a displacement sinusoidal or cosine wave, lets say S = Asinwt, then how do I know whether the pressure wave would be P=-BAkcoswt or P=BAkcoswt ? or visa-versa in case of a cosine displacement wave? Do I just differentiate the displacement wave and change the sign of resultant wave? What is the procedure for the same? $\endgroup$
    – marks_404
    Commented Aug 18, 2021 at 11:50
  • $\begingroup$ You can use the linearized mass conservation equation $\partial_t \rho+\rho_0 \partial _x v=0$. Here $\rho_0$ is the undisurbed density and $\rho(x,t)$ is the density including the sound wave. $\endgroup$
    – mike stone
    Commented Aug 18, 2021 at 11:53

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