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Q.
The amplitude of the two waves is in ratio $5:2$ . If all other conditions for the two waves are same, then what is the ratio of their energy densities?
NTA AbhyasNTA Abhyas 2022
Solution:
Energy density of wave is given by
$u=2\pi ^{2}n^{2}\rho a^{2}$
Or $u \propto a^{2} \, \left(a s \, n \, a n d \, \rho \, a r e \, c o n s a n t s\right)$
$\therefore \frac{u_{1}}{u_{2}}=\frac{a_{1}^{2}}{a_{2}^{2}}=\frac{5^{2}}{2^{2}}$
So, $u_{1}:u_{2}=25:4$
Hence, the ratio of energy densities will be $=25:4$