A 50 dB sound wave strikes an eardrum whose area is 5.0 x 10^-5 m^2.
A.)How much energy is absorbed by the eardrum per second?
B.) At this rate, how long would it take your eardrum to receive a total energy of 1.0 Joule?
To find the answers to these questions, we need to use the formulas related to sound energy and power:
A.) The formula for sound power is:
Power = Intensity x Area
where Power is measured in Watts (W), Intensity is measured in Watts per square meter (W/m^2), and Area is measured in square meters (m^2).
The intensity of a sound wave can be calculated using this formula:
Intensity = (Sound Pressure Level)^2 x (Reference Intensity)
where Sound Pressure Level is measured in decibels (dB) and Reference Intensity is a constant value of 1 x 10^-12 W/m^2.
First, let's convert the Sound Pressure Level from decibels to the intensity:
Intensity = (10^(Sound Pressure Level/10)) x Reference Intensity
In this case, the Sound Pressure Level is 50 dB, so the formula becomes:
Intensity = (10^(50/10)) x 1 x 10^-12 W/m^2
Calculating this gives:
Intensity = 1 x 10^-5 W/m^2
Now, we can substitute the values into the power formula:
Power = Intensity x Area
Power = (1 x 10^-5 W/m^2) x (5.0 x 10^-5 m^2)
Calculating this gives:
Power = 5.0 x 10^-10 W
Therefore, the energy absorbed by the eardrum per second is 5.0 x 10^-10 Joules.
B.) To determine how long it would take the eardrum to receive a total energy of 1.0 Joule, we can use the equation:
Energy = Power x Time
Rearranging the formula, we have:
Time = Energy / Power
Substituting the values, we get:
Time = 1.0 Joule / (5.0 x 10^-10 W)
Calculating this gives:
Time = 2.0 x 10^9 seconds
Therefore, it would take approximately 2.0 x 10^9 seconds for your eardrum to receive a total energy of 1.0 Joule.