Question

A person wears a hearing aid that uniformly increases the intensity level of all audible frequencies of sound by 24.7 dB. The hearing aid picks up sound having a frequency of 250 Hz at an intensity of 2.70 ✕ 10⁻¹¹ W/m². What is the intensity delivered to the eardrum?

Answer in W/m²

Answer 1

Intensity level=10 log(I/I0) , where I is intensity of sound and I0=10-12 W/m2.

When I=2.7*10^-11 W/m2, intensity level= 10 log [(2.7*10^-11)/10^-12]=14.31 dB.

Hearing aid that uniformly increases the intensity level of all audible frequencies of sound by 24.7 dB.

So, final intensity level= 14.31+24.7 = 39.01 dB.

Now,10 log[I/10^-12] = 39.01, where I  is the intensity delivered to the eardrum.

=> log[I/10^-12]=3.901

=>I/10^-12= 10^3.901

=>I=10^-12* 10^3.901=7.96*10^-9 W/m2