Question

The ratio of amplitude of two waves is $3:4$.What is the ratio of their loudness?

Answer 1

Step 1: Given data:

The amplitude of two waves is $3:4$

Step 2: Calculating the ratio of loudness:

We know that,

The loudness of sound is directly proportional to the square of the amplitude.

Therefore,$Loudness\propto {\left(Amplitude\right)}^2$

or $\frac{L_1}{L_2}={\left(\frac{A_1}{A_2}\right)}^2={\left(\frac{3}{4}\right)}^2=\frac{9}{16}$

Where $L_1{L}_2$is the loudness and $A_1{A}_2$is the amplitude.

Hence, the ratio of their loudness is $\frac{9}{16}.$