Question

An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?

a) (1.78 X 10⁻3) J
b) (1.78 X 10⁻4) J
c) (1.78 X 10⁻5) J
d) (1.78 X 10⁻6) J

Answer 1

To calculate the energy falling on the eardrum, we need to convert the sound intensity level from decibels to watts per square meter and calculate the area of the eardrum. Using the formula Energy = Intensity x Area x Time, we can calculate the energy in joules falling on the eardrum, which is approximately 1.78 x 10⁻³ J.

Step-by-step explanation:

To calculate the energy falling on the eardrum, we need to use the formula:

Energy = Intensity x Area x Time

First, we need to convert the sound intensity level from decibels (dB) to watts per square meter (W/m²) using the formula:

Intensity = 10^((dB - 12)/10)

Given that the sound intensity level is 90.0 dB, the intensity is:

Intensity = 10^((90.0 - 12)/10)

Intensity = 5.01187 W/m²

Next, we need to calculate the area of the eardrum:

Area = πr²

Area = π(0.004)^2

Area = 0.00005027 m²

Finally, we can calculate the energy:

Energy = 5.01187 x 0.00005027 x 8 x 60 x 60

Energy ≈ 1.787912 J

Therefore, the energy in joules falling on the 0.800-cm-diameter eardrum is approximately 1.78 x 10⁻³ J. Answer choice (a) is correct.