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ICSE Class 10 Physics Question 16 of 16

Sound — Question 3

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Question 3

Two waves of the same pitch have amplitudes in the ratio 1 : 3. What will be the ratio of their (i) loudness and (ii) frequencies?

Answer

Given,

a1 : a2 = 1 : 3

(i) As we know, that loudness is proportional to the square of the amplitude

Loudness ∝ (amplitude) 2

Therefore,

L1L2=(a1a2)2\dfrac{L_1}{L_2} = \Big(\dfrac{a_1}{a_2}\Big)^2 \\[0.5em]

Substituting the values, we get

L1L2=(13)2L1L2=19\dfrac{L_1}{L_2} = \Big(\dfrac{1}{3}\Big)^2 \\[0.5em] \dfrac{L_1}{L_2} = \dfrac{1}{9}

Hence, ratio of loudness between the two waves = 1 : 9

(ii) Pitch of a wave depends on its frequency and if two waves have same frequencies then their pitch will be same.

Hence, ratio of pitch between the two waves = 1 : 1.