Question

If the amplitude of a sound is tripled, what will be the effect on its loudness?

Answer 1

The loudness of sound depends on its amplitude. Loudness is proportional to the square of its amplitude.
So, loudness $\propto$ (amplitude)${}^2$

Here amplitude of sound is tripled.

Let,
Initial Loudness = $L$
Initial Amplitude = $A$
Final Loudness = $L_1$
Final Amplitude = $A_1$ = $3A^{}$
Since, loudness $\propto$ (amplitude)${}^2$,
$\frac{L_1}{L}={\left(\frac{A_1}{A}\right\}}^2$
or, $\frac{L_1}{L}={\left(\frac{3A^{}}{A}\right\}}^2$
or, $\frac{L_1}{L}=9{\left(\frac{A^{}}{A}\right\}}^2$
or, $L_1=9L$
Hence, if the amplitude of a sound is tripled, loudness increases nine times.