# Equivalent formula for a Sound wave in a medium like an EM wave

• I
chowdhury
TL;DR Summary
Is there a equivalent reference of acoustic speed like sound wave, and in this case, wavelength in a acoustic medium just like electromagnetic medium
1.) In electromagnetics, wavelength in a medium is
$$\lambda = \frac{\lambda_{0}}{n}$$, where $$n$$ is the refractive index.
What is the equivalent formula for sound wave in a medium?

2.) Is there a reference sound velocity, like electromagetic wave speed in vacuum is
$$c_{0} = \frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$

Gold Member
Formula of speed of sound depends on medium; gas, liquid and solid. For an example for solid
$$c=\sqrt{\frac{K}{\rho}}$$
where K is coefficient of stiffness and ##\rho## is mass density. I don't think people set standard material for sound speed but you can calculate change of sound speed between the two media to know the change of wave length.

ref. https://en.wikipedia.org/wiki/Speed_of_sound

PeroK
chowdhury
Formula of speed of sound depends on medium; gas, liquid and solid. For an example for solid
$$c=\sqrt{\frac{K}{\rho}}$$
where K is coefficient of stiffness and ##\rho## is mass density.

ref. https://en.wikipedia.org/wiki/Speed_of_sound
I understand this, what I wanted to know is for example, in optics, wavelength in a medium of refractive index is $$\lambda_{\mathrm{medium}} = \frac{\lambda}{n}$$. Hence I want to traverse equivalent length in that medium, I just need to divide the vacuum wavelength by $$n$$. Is there such a relationship for acoustic waves, meaning, by what equivalent constant of refractive index I have to divide by to have the same length in an acoustic medium?

Gold Member
Say sound in medium 1 of speed ##c_1## goes beyond the boundary into medium 2 where sound speed is ##c_2##. The frequency is shared so we can get the relation between ##\lambda## s,
$$\nu=\frac{c_1}{\lambda_1}=\frac{c_2}{\lambda_2}$$

chowdhury
Say sound in medium 1 of speed ##c_1## goes beyond the boundary into medium 2 where sound speed is ##c_2##. The frequency is shared so we can get the relation between ##\lambda## s,
$$\nu=\frac{c_1}{\lambda_1}=\frac{c_2}{\lambda_2}$$
Thanks. this is what I also found, but is there a reference value of sound, in analogy of electromagnetic wave in vacuum? I do not find it.

tech99
Gold Member
I repeat I don't think there is a standard material for sound wave speed (#2). In the wikipedia webpage I referred you will see some formula and external links. I hope this will lead you to get proper estimates or values for your special settings. If your materials are popular ones sound speed data are frequently included in webpages for the materials.

Dale