Question

A woman wearing an in-ear hearing aid listens to a television set at a normal volume of approximately60 dB. To hear it, she requires an amplification of30 dB, so the hearing aid supplies sound at90 dB to the ear canal, which we assume to be circular with a diameter of 6.4 mm .

What is the output power of the hearing aid?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

the output power of the hearing aid in two significant figures is 3.2 × 10⁻⁸ W

Explanation:

Output power of sound is given as;

P = I*A

where;

I is the sound intensity = 90dB = 1 × 10⁻³ W/m²

A is the area through which the transmits;

$A = \frac{\pi D^2}{4}$ since the canal is circular in shape.

Given;

D as diameter = 6.4mm = 0.0064 m

$A = \frac{\pi*0.0064^2 }{4} =3.217X10^{-5} m^2$

Output power of the hearing aid = (1 × 10⁻³ W/m²)*(3.217 × 10⁻⁵ m²)

                                                      = 3.2 × 10⁻⁸ W

Therefore, the output power of the hearing aid in two significant figures is 3.2 × 10⁻⁸ W.