Answer to Question #136228 in Atomic and Nuclear Physics for Khairat

Question

The speed of sound v in a medium depend on it's wave length,the Young modulus ,density of the medium use the method of dimensional analysis to derive a formula for speed of sound in a medium.
E=kgm-1s-2

Answer 1

The Dimension o f Young Modulus E is shown as;

$\frac{N}{m^2}=\frac{kgm}{s^2m^2}=\frac{kg}{s^2m}$

This means that;

$(\frac{kg}{s^2m})^\alpha (\frac{kg}{m^3})\beta (m)^\gamma=\frac{m}{s}$

Hence; $\alpha=0.5=-\beta and \gamma=0$

Consequently;

$v=\sqrt\frac{E}{\rho}$

i.e $\rho$ is the Density

Answer: $v=\sqrt\frac{E}{\rho}$