Question

The ratio of amplitudes of two sound waves is 9:49, their loudness will be in the ratio



(1) 3 : 7
(2) 81 : 2401
(3) 13 : 53
(4) 2401 : 81

Answer 1

Answer:

Option 2

Explanation:

We know, loudness is directly proportional to the square of the amplitude of a sound wave.

So, L ♾ a² and L1 : L2 = (a1)² : (a2)²

In the question,

a1: a2 = 9:49

Therefore, L1: L2 = 81 : 2401.

Note : ♾stands for proportionality sign in this answer.

Answer 2

Answer:

(1) The ratio of amplitudes of two sound waves is 9:49, their loudness will be in the ratio 3:7.

Explanation:

The ear's response to sound is referred to as loudness. The amplitude of the vibration body that produces sound is related to the square of its amplitude. The louder the sound, the greater the amplitude of vibration. The sound is weaker as the vibration amplitude decreases.

The loudness of sound is directly proportional to the square of amplitude i.e., Loudness $(\mathrm{L}) \propto \mathrm{a}^{2}$

Ratio of Loudness=  $\frac{\mathrm{L}_{1}}{\mathrm{~L}_{2}}=\frac{\mathrm{a}_{1^{2}}}{\mathrm{a}_{2^{2}}}=\frac{9}{49} =\frac{(3)^{2}}{(7)^{2}}=3: 7$