Sound is passing perpendicularly through an open window whose dimensions are 1.1 m x 0.75 m. The sound intensity level is 71 dB above the threshold of human hearing. How much sound energy comes through the window in one hour?
To calculate the sound energy that comes through the window in one hour, we need to know the intensity of the sound in terms of watts per square meter (W/m²).
The sound intensity level (L) in decibels (dB) is given by the formula:
L = 10 * log10(I/I₀)
Where I is the sound intensity in W/m² and I₀ is the reference intensity, which is the threshold of human hearing at 10^(-12) W/m².
In this case, the sound intensity level is given as 71 dB above the threshold of human hearing. So we can calculate the sound intensity (I) using:
L = 10 * log10(I/I₀)
71 = 10 * log10(I/10^(-12))
Rearranging the formula, we have:
I = 10^((L/10)) * I₀
We need to find the sound energy that comes through the window in one hour. Sound energy (E) is given by the formula:
E = P * t
Where P is the power in watts and t is the time in seconds.
To find the power (P), we can use the formula:
P = I * A
Where I is the sound intensity in W/m² and A is the area of the window in square meters.
Given that the dimensions of the window are 1.1 m x 0.75 m, the area (A) is:
A = 1.1 * 0.75 = 0.825 m²
Now, let's calculate the sound intensity (I):
I = 10^((71/10)) * 10^(-12)
And the power (P):
P = I * A
Finally, we can calculate the sound energy (E):
E = P * t
Since we want the energy in one hour, we need to convert the time to seconds. There are 3600 seconds in an hour. So, t = 3600 s.
Plugging the values into the equation, you can calculate the sound energy that comes through the window in one hour.