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?

Question

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? (A) 5:2 (B) 5:4 (C) 4:5 (D) 25:4

Tardigrade Admin · Accepted Answer

Energy density of wave is given by u=2π 2n2ρ a2 Or u propto a2 (a s n a n d ρ a r e c o n s a n t s) ∴ (u1/u2)=(a12/a22)=(52/22) So, u1:u2=25:4 Hence, the ratio of energy densities will be =25:4

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?

$5 : 2$

$5 : 4$

$4 : 5$

$25 : 4$

Energy density of wave is given by
$u = 2 π^{2} n^{2} ρ a^{2}$
Or $u \propto a^{2} (a s n an d ρ a re co n s an t s)$
$∴ \frac{u _{1}}{u _{2}} = \frac{a _{1}^{2}}{a _{2}^{2}} = \frac{5 ^{2}}{2 ^{2}}$
So, $u_{1} : u_{2} = 25 : 4$
Hence, the ratio of energy densities will be $= 25 : 4$

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?

5:2

5:4

4:5

25:4