Question

Two waves of the same pitch have amplitudes in the ratio 1 : 3. What will be the ratio of their:

1. intensities and
2. frequencies

Two waves of the same pitch have amplitudes in the ratio 1:3. What will be the ratio of 1:3? What will be the ratio of their

1. intensities and 
2. frequencies

Answer 1

Given amplitude ratio:

\[ A_1:A_2=1:3 \]

\[\frac{A_1}{A_1} = \frac{1}{3}\]

(i) Intensity is proportional to the square of amplitude.

\[I\propto A^{2}\]

\[ I_1:I_2=A_1^2:A_2^2 \]

\[ I_1:I_2=1^2:3^2=1:9 \]

\[\therefore\frac{I_1}{I_2} = \frac{1}{9}\]

(ii) The waves have the same pitch, so their frequencies are equal.

\[f_{1}:f_{2}=1:1\]