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The question is as stated in the title. I am not sure if the Snell's law for light is derived using any property which is true only for light but not for sound.

So suppose the wavelength of sound wave is short that it can be treated as rays. Can I apply Snell's law in refraction of sound wave?

velut luna
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1 Answers1

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Yes you can and you still use for it the ratio of propagation speeds in the mediums either side of an interface, just as for optics. Snell's law can be derived for any wave phenomenon described by a wave equation that:

  1. Has plane wave solutions in homogeneous mediums, i.e. for which the disturbance's dependence on space $\vec{r}$ and time $t$ is proportional to $e^{i\,(\mathbf{k}\cdot\mathbf{r}-\omega\,t)}=\exp\left(i\,\omega\,\frac{n}{c}\left(\hat{\mathbf{k}}\cdot\mathbf{r}-t\right)\right)$ where $c$ is the wave speed in a reference medium and $n$ the scale factor which the speed in the medium in question is slowed down by relative to the reference medium; and
  2. Has solutions that must be continuous at the interface.

You simply write down the continutiy condition for two inclined plane waves meeting at an interface, and you've got Snell's law. See my answer here for further details. You'll see that the continuity condition can be somewhat relaxed. You only need continuity of one component of a vector field and this is enough to force the relationship between the wave vectors which is Snell's law. In scalar sound, continuity of the scalar pressure readily follows by applying mass flux balance and Newton's second law to a small volume straddling the interface.

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