Question

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

A. Double the intensity
B. Halve the intensity
C. Quadruple the intensity
D. Quarter the intensity
E. Increase the intensity by factor

Answer 1

C. Quadruple the intensity

Step-by-step explanation:

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

I ∝ A²

`(I_1)/(A_1^2) = (I_2)/(A_2^2)\\\\I_2 = (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 = (I_1A_2^2)/(A_1^2) \\\\I_2 = (I_1(2A_1)^2)/(A_1^2) \\\\I_2 = (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