Question

Two waves of the same pitch have amplitudes in the ratio 1:4, calculate the ratio of their loudness.

• A. 2:1
• B. 16:1
• C. 1:16
• D. 1:2

Answer 1

The correct option is

C

1:16

$I\left[db\right]=10lo{g}_{10}\left[\frac{I}{I_o}\right]$

As we know, $I\propto Am{p}^2$

Since, the loudness is related to the amplitude of a wave, it is proportional to the square of the amplitude. In our case, if the amplitude is in the ratio 1:4, then the loudness will be in the ratio 1:16.