Answer to Question #104073 in Mechanics | Relativity for Eryq

Question #104073
The speed of sound V in a medium depends on it's wavelength , the young modulus E, and the density p, of the medium. Use the method of dimensional analysis to derive a formulas for the speed of sound in a medium .
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Expert's answer
2020-03-02T09:09:50-0500

Young's modulus E is measured in kg m−1 s−2

Density ρ has units of kg m-3

Wavelength λ has units of m.

Since the speed of sound is measured in m s-1, we can try to combine the quantities to get m/s:



v=Eρ, m s1=kg m1 s2kg m3= m2 s2= =m s1.v=\sqrt{\frac{E}{\rho}},\\ \space\\ \text{m s}^{-1}=\sqrt{\frac{\text{kg}\text{ m}^{-1}\text{ s}^{-2}}{\text{kg}\text{ m}^{-3}}}=\sqrt{\text{ m}^{2}\text{ s}^{-2}}=\space\\ =\text{m s}^{-1}.

The wavelength is not necessary.


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