A sound with ten times the amplitude of another sound is judged to be
A)twice as loud.
B)ten times as loud.
C)10 dB higher in sound level.
D)20 dB higher in sound level.

Question

Quizplus · Accepted Answer

The sound level in decibels (dB) is calculated using the equation: L = 10*log10(I/I_0), where L is the sound level, I is the sound intensity, and I_0 is the reference sound intensity (typically considered to be 10^-12 W/m^2). If the amplitude of a sound wave is increased by a factor of 10, the intensity of the sound wave is increased by a factor of 10^2 = 100, since power is proportional to the square of the amplitude. Therefore, the sound level is increased by 10*log10(100) = 20 dB. So, a sound with ten times the amplitude of another sound is 20 dB higher in sound level, which is answer choice D.

A Sound with Ten Times the Amplitude of Another Sound