Suppose a sound of frequency 1200 Hz is emitted from a speaker 15 meters away from you. At YOUR location, the intensity is 1.0E-7 W/m2. Let me assume your eardrum has area 8E-5 m2. If the sound continues for 20 seconds, what total amount of energy is received by your ear?
Find your answer in Joules, but do not enter units.
To find the total amount of energy received by your ear, we can start by calculating the power received by your ear.
Power is defined as the rate at which energy is transferred or converted per unit time. In this case, it represents the rate at which sound energy is reaching your ear.
The formula for power is:
Power = Intensity * Area
Given:
Frequency of the sound = 1200 Hz
Intensity = 1.0E-7 W/m^2
Area of your eardrum = 8E-5 m^2
Substituting these values into the formula, we have:
Power = (1.0E-7 W/m^2) * (8E-5 m^2)
= 8E-12 W
Now, to find the total amount of energy received by your ear, we need to calculate the total energy over a period of time.
The formula for energy is:
Energy = Power * Time
Given:
Time = 20 seconds
Substituting the values into the formula, we have:
Energy = (8E-12 W) * (20 s)
= 1.6E-10 J
Therefore, the total amount of energy received by your ear is 1.6E-10 Joules.