Question

A sound wave has an amplitude of $15cm$. If it is increased to $60cm$, what happens to the loudness of the sound?

• A. It increases by four times.
• B. It increases by eight times.
• C. It doubles.
• D. It triples.

Answer 1

The correct option is B It increases by eight times.

The loudness of sound is dependent on the amplitude of sound.
$Loundness\propto (Amplitude{)}^2$
If the amplitude of the sound is doubled, the loudness of the sound increases by 4 times.
Given, the amplitude of sound is increased to $60cm$ from $15cm$, i.e. it increased by $\frac{60}{15}=4$ times.
So, the loudness of the sound increases by $4\times 2=8$ times.