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I am having trouble understanding the general formulation of specific acoustic impedance:

$$ Z = \frac{P}{s} $$

This equation is telling me that if I, through some means, increase the pressure of an acoustic wave that I can increase the speed of wave propagation indefinitely. However, we know that there is a finite speed of sound in a given homogeneous media.

In attempting to solve my confusion, I stumbled upon the following discussion. I am understanding that if we input additional energy into a driving force (say by increasing the acceleration of a hand clap) that we are capturing more particles per clap, thereby increasing sound intensity rather than increasing particle velocity. However, I am still confused - as the general definition of acoustic impedance is telling me that a simple increase in pressure should consequentially increase sound propagation velocity.

What am I missing here? Any insights into my confusion would be greatly appreciated.

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The acoustic impedance relationship as you have written it should be defined carefully. The acoustic impedance is $Z$, the acoustic pressure is $P$, but $s$ is not the wave speed, but the particle velocity. Under some common assumptions, the particle velocity is actually independent of the wave speed. Thus, the impedance relationship is really saying that if you increase the pressure, the particle velocity will also increase, which is true.

As a side note, I wanted to remind you that this impedance relationship is only valid for propagating plane waves (all of the sound energy moving in one direction), and is inappropriate for standing waves or non-planar waves (although it is approximately valid for propagating spherical waves far from the source).

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  • $\begingroup$ Thank you for the clarification Michael. $\endgroup$
    – Matt
    Feb 16, 2022 at 15:11

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