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

Question #136228
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
1
Expert's answer
2020-10-01T10:07:53-0400

The Dimension o f Young Modulus E is shown as;

Nm2=kgms2m2=kgs2m\frac{N}{m^2}=\frac{kgm}{s^2m^2}=\frac{kg}{s^2m}


This means that;

(kgs2m)α(kgm3)β(m)γ=ms(\frac{kg}{s^2m})^\alpha (\frac{kg}{m^3})\beta (m)^\gamma=\frac{m}{s}


Hence; α=0.5=βandγ=0\alpha=0.5=-\beta and \gamma=0

Consequently;


v=Eρv=\sqrt\frac{E}{\rho}

i.e ρ\rho is the Density


Answer: v=Eρv=\sqrt\frac{E}{\rho}


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