The amplitude of two waves are in ratio 5 : 2. If all other conditions for the two waves are same, then what is the ratio of their energy densities

Options

A. `5:2`
B. `5:4`
C. `4:5`
D. `24:5`

Answer

D

Explanation

Energy density of wave is given by
`u=2pi^(2)n^(2)rhoa^(2)`
or `uprop a^(2)` (as n and `rho` are cosntants)
`:.(u_(1))/(u_(2))=(a_(1)^(2))/(a_(2)^(2))=(5^(2))/(2^(2))`
So `u_(1):u_(2)=25:4`
Hence the ratio of energy densities will be
`=25:4`