An 8 hour exposure to a sound level of 95.0 dB may cause hearing damage. What energy in joules falls on a 0.850 cm diameter eardrum so exposed?
To calculate the energy falling on the eardrum, we need to use the formula for sound intensity:
Sound Intensity (I) = Power (P) / Area (A)
where:
I = Sound intensity in watts per square meter (W/m²)
P = Power in watts (W)
A = Area in square meters (m²)
We know the diameter of the eardrum, so we can calculate the area:
Area (A) = π * (radius)²
The radius is half of the diameter:
Radius = 0.850 cm / 2
Convert the radius to meters:
Radius = 0.850 cm / 2 * 100 cm/m
Now, we need to find the power using the given sound level. The sound level is given in decibels (dB), but we need to convert it to power:
Power (P) = 10^(dB/10) * reference power
The reference power is the threshold of hearing, which is 1.0 × 10^(-12) watts (W).
Now we can calculate the energy (E) using the formula:
Energy (E) = Power (P) * time (t)
The time is given as 8 hours, but we need to convert it to seconds:
Time (t) = 8 hours * 60 minutes/hour * 60 seconds/minute
Finally, we can substitute all the values into the equations to calculate the energy in joules.
Please note that we need to know the power corresponding to a sound level of 95 dB to provide an accurate answer.