Question

A person wears a hearing aid that uniformly increases the sound level of all audible frequencies of sound by 28.1 dB. The hearing aid picks up sound having a frequency of 250 Hz at an intensity of 3.30 10-11 W/m2. What is the intensity delivered to the eardrum?

Answer 1

Answer:

 I₂ = 2.13 x 10⁻⁸ W/m²

Explanation:

given,

increase in sound level = 28.1 dB

frequency of the sound = 250 Hz

intensity = 3.3 x 10⁻¹¹ W/m²

Intensity delivered = ?

the difference of intensity level is give as

$\beta_2-\beta_1 = 10log(\dfrac{I_2}{I_o}) - 10log(\dfrac{I_1}{I_o})$

$\beta_2-\beta_1 = 10(log(\dfrac{I_2}{I_o}) -log(\dfrac{I_1}{I_o}))$

$\beta_2-\beta_1 = 10(log(\dfrac{I_2}{I_1})$

$28.1= 10(log(\dfrac{I_2}{I_1})$

$log\dfrac{I_2}{I_1}=2.81$

$\dfrac{I_2}{I_1}=10^{2.81}$

 I₂ = 645.65 I₁

 I₂ = 645.65 x 3.3 x 10⁻¹¹

 I₂ = 2.13 x 10⁻⁸ W/m²