Question

By how much should the amplitude of vibration be changed to increase the loudness of sound by 9 times?

Answer 1

As we know that intensity is directly proportional to the square of the amplitude.

I ∝ A²

where,

I = intensity  

A = amplitude

Now initial intensity and amplitude be I and A.

The final intensity and amplitude be 9I and A₂.

Then the ratio,

$\frac{9I}{I}$ = $(\frac{A2}{A} )^{2}$

Hence, A₂=3A