Question

To make a given sound seem twice as loud, how should a musician change the intensity of the sound?

Answer 1

Answer:

C. Quadruple the intensity

Explanation:

The intensity of the sound is proportional to square of amplitude of the sound.

I ∝ A²

$\frac{I_1}{A_1^2} = \frac{I_2}{A_2^2}\\\\I_2 = \frac{I_1A_2^2}{A_1^2}$

When the given sound is twice loud as the initial value, then the new amplitude is twice the former.

A₂ = 2A₁

$I_2 = \frac{I_1A_2^2}{A_1^2} \\\\I_2 = \frac{I_1(2A_1)^2}{A_1^2} \\\\I_2 = \frac{4I_1A_1^2}{A_1^2}\\\\ I_2 = 4I_1$

Thus, to make a given sound seem twice as loud, the musician should Quadruple the intensity