Answer to Question #104073 in Mechanics | Relativity for Eryq

Question

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 .

Answer 1

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:

$$v=\sqrt{\frac{E}{\rho}},\\ \space\\ \text{m s}^{-1}=\sqrt{\frac{\text{kg}\text{ m}^{-1}\text{ s}^{-2}}{\text{kg}\text{ m}^{-3}}}=\sqrt{\text{ m}^{2}\text{ s}^{-2}}=\space\\ =\text{m s}^{-1}.$$

The wavelength is not necessary.