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

AI Thread Summary
In electromagnetics, the wavelength in a medium is given by the formula λ = λ₀/n, where n is the refractive index. For sound waves, the speed of sound varies with the medium, and while there is no universal reference speed like the speed of light in a vacuum, the speed can be calculated using c = √(K/ρ) for solids, where K is the stiffness coefficient and ρ is the mass density. The relationship between wavelengths in different media can be established through the shared frequency, expressed as ν = c₁/λ₁ = c₂/λ₂ when transitioning between media. There is no standard material for sound speed, but data for common materials can often be found online. Understanding these principles aids in calculating changes in wavelength and speed across various acoustic media.
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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
$$c_{0} = \frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$
 
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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
 
anuttarasammyak said:
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?
 
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}
 
anuttarasammyak said:
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.
 
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.
 
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