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 .
1
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=\\sqrt{\\frac{E}{\\rho}},\\\\\n\\space\\\\\n\\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\\\\\n=\\text{m s}^{-1}."

The wavelength is not necessary.


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