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

Respuesta :

Answer:

C. Quadruple the intensity

Explanation:

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

I ∝ A²

[tex]\frac{I_1}{A_1^2} = \frac{I_2}{A_2^2}\\\\I_2 = \frac{I_1A_2^2}{A_1^2}[/tex]

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

A₂ = 2A₁

[tex]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[/tex]

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