Sound is passing perpendicularly through an open window whose
dimensions are 1.1 m � 0.75 m. The sound intensity level is 95 dB above
the threshold of hearing. How much sound energy comes through the
window in one hour?
To calculate the sound energy that passes through the window in one hour, we need to use the sound intensity level and the dimensions of the window.
Step 1: Convert the sound intensity level to the sound intensity.
The sound intensity level (L) is given as 95 dB above the threshold of hearing. The threshold of hearing is typically taken as 10^(-12) W/m^2.
Using the formula for sound intensity level:
L = 10 * log10(I/I0),
where I is the sound intensity and I0 is the threshold of hearing.
Rearranging the formula:
I = I0 * 10^(L/10).
Substituting the given values:
I = (10^(-12)) * 10^(95/10)
I = 10^(-12 + 9.5)
I = 10^(-2.5)
I = 10^(-2.5) W/m^2
Step 2: Calculate the area of the window.
The area of the window (A) is given as 1.1 m * 0.75 m.
Calculating the area:
A = 1.1 m * 0.75 m
A = 0.825 m^2
Step 3: Calculate the sound energy passing through the window in one second.
The sound energy passing through the window in one second is given by:
Energy = Intensity * Area
Substituting the calculated values:
Energy = (10^(-2.5) W/m^2) * 0.825 m^2
Energy = 8.25 * 10^(-3.5) W
Step 4: Convert the sound energy to energy per hour.
Since we have the sound energy per second, we need to convert it to energy per hour.
There are 60 seconds in a minute and 60 minutes in an hour, so there are 60 * 60 = 3600 seconds in an hour.
To convert the sound energy per second to energy per hour, we multiply it by the number of seconds in an hour:
Energy per hour = Energy per second * 3600
Substituting the calculated value:
Energy per hour = (8.25 * 10^(-3.5) W) * 3600
Energy per hour = 29.7 W
Therefore, the amount of sound energy that comes through the window in one hour is 29.7 watts (W).
To calculate the amount of sound energy that comes through the window in one hour, we need to determine the power of the sound wave passing through the window and then multiply it by the duration.
First, let's calculate the power of the sound wave passing through the window. The power of sound is given by the formula:
Power = Intensity × Area
Given:
Sound intensity level = 95 dB above the threshold of hearing
Threshold of hearing = approximately 10^(-12) W/m^2 (reference intensity)
To convert the sound intensity level from dB to W/m^2, we can use the formula:
Intensity = 10^((Sound Intensity Level - Threshold of Hearing Level) / 10)
Let's calculate the intensity:
Intensity = 10^((95 dB - 0 dB) / 10)
Intensity = 10^(9.5)
Intensity ≈ 3.16 × 10^9 W/m^2
Next, we need to calculate the area of the window:
Area = Length × Width
Area = 1.1 m × 0.75 m
Area = 0.825 m^2
Now, let's calculate the power passing through the window:
Power = Intensity × Area
Power = (3.16 × 10^9 W/m^2) × (0.825 m^2)
Power ≈ 2.61 × 10^9 W
Since power is given in watts, we can now calculate the energy by multiplying the power by time:
Energy = Power × Time
Time = 1 hour = 3600 seconds
Energy = 2.61 × 10^9 W × 3600 s
Energy ≈ 9.40 × 10^12 J
Therefore, approximately 9.40 × 10^12 joules (J) of sound energy come through the window in one hour.