Question

If the loudness of two sounds are in the ratio 9:4, what is the ratio of their amplitudes?

• A.
  3:2
• B.
  2:3
• C.
  81:16
• D.
  16:81

Answer 1

The correct option is A

3:2
Let:
$L_1$ = Loudness of first sound
$L_2$ = Loudness of second sound
$A_1$ = Amplitude of first sound
$A_2$ = Amplitude of second sound
Given:
Ratio of loudness of sounds = $L_1$/$L_2$ = 9/4
Since, loudness is proportional to square of the amplitude of sound, i.e.
Loudness ∝ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $Amplitud{e}^2$
=> $L_1$/$L_2$ = $A_1$${}^2$ / $A_2$${}^2$
=> $A_1$ / $A_2$ = √$L_1$/$L_2$ = √9/4 = 3/2

Therefore, the ratio of their amplitudes is 3:2