Question

Two waves of the same pitch have their amplitude in the ratio $2:3$. What will be the ratio of their loudness? What will be the ratio of their frequency?

Answer 1

Step 1: Given data:

Amplitude ratio $=2:3$

Step 2: Calculating the ratio of their frequency:

We know that,

Loudness is directly proportional to amplitude square.

$Loudness\propto {\left(Amplitude\right)}^2$
So, the ratio of loudness will be equal to${\left(\frac{2}{3}\right)}^2=\frac{4}{9}.$

Therefore, the ratio of their loudness is $\frac{4}{9}.$

Since they have the same pitch,

Hence, the ratio of frequencies will be $1:1$