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

In summary, the wavelength in a medium for electromagnetic waves is given by λ = λ0/n, where n is the refractive index. The equivalent formula for sound waves in a medium depends on the type of medium, such as gas, liquid, or solid. For example, in a solid medium, the speed of sound is given by c = √(K/ρ), where K is the coefficient of stiffness and ρ is the mass density. There is no standard material for sound wave speed, but it can be calculated by comparing the changes in sound speed between two different media. The relationship between wavelength and sound speed can be expressed as ν = c1/λ1 = c2/λ2, where c1 and c
  • #1
chowdhury
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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
$$c_{0} = \frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$
 
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  • #2
Formula of speed of sound depends on medium; gas, liquid and solid. For an example for solid
[tex]c=\sqrt{\frac{K}{\rho}}[/tex]
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
 
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  • #3
anuttarasammyak said:
Formula of speed of sound depends on medium; gas, liquid and solid. For an example for solid
[tex]c=\sqrt{\frac{K}{\rho}}[/tex]
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?
 
  • #4
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,
[tex]\nu=\frac{c_1}{\lambda_1}=\frac{c_2}{\lambda_2}[/tex]
 
  • #5
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,
[tex]\nu=\frac{c_1}{\lambda_1}=\frac{c_2}{\lambda_2}[/tex]
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.
 
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  • #6
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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1. What is the equivalent formula for a sound wave in a medium like an EM wave?

The equivalent formula for a sound wave in a medium like an EM wave is the wave equation, which is:
∇²ψ - 1/c² * ∂²ψ/∂t² = 0
where ψ represents the disturbance in the medium, ∇² is the Laplace operator, c is the speed of the wave, and ∂²ψ/∂t² is the second derivative of ψ with respect to time.

2. How is the speed of sound in a medium related to the speed of an EM wave?

The speed of sound in a medium is related to the speed of an EM wave through the medium's physical properties, such as density and elasticity. In general, the speed of sound is much slower than the speed of an EM wave, which travels at the speed of light in a vacuum.

3. Can the wave equation be used to describe both sound waves and EM waves?

Yes, the wave equation can be used to describe both sound waves and EM waves. However, the specific form of the equation may vary depending on the medium and the type of wave being described.

4. How does the amplitude of a sound wave compare to the amplitude of an EM wave?

The amplitude of a sound wave is a measure of the maximum displacement of particles in the medium, while the amplitude of an EM wave is a measure of the strength of the electric and magnetic fields. In general, the amplitude of an EM wave is much larger than that of a sound wave.

5. What is the relationship between wavelength and frequency in a sound wave?

The relationship between wavelength and frequency in a sound wave is described by the equation:
v = λ * ƒ
where v is the speed of sound in the medium, λ is the wavelength, and ƒ is the frequency. This equation shows that as the wavelength decreases, the frequency increases, and vice versa.

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