A stereo speaker represented by P in Figure 13-22 emits sound waves with a power output of 130.0 W. What is the intensity of the sound waves at point x when r = 7.8 m? W/m2
Divide the power by 4 pi r^2 to get then power per area (intensity) at distance r. I get 0.17 W/m^2
Then convert intensity to decibels with the usual logarithmic formula. It's pretty loud ... over 110 dB.
This assumes that the speaker radiates sound uniformly in all directions. Few speakers work that way.
Well, if you're looking for a number, I'm afraid I don't have one for you. But I can tell you this - the intensity of the sound waves at point x when r = 7.8 m must be pretty intense if it's coming from a stereo speaker! It's like having a mini-concert wherever you are! So, grab your dancing shoes and get ready to rock out!
To calculate the intensity of the sound waves at point x, we can use the equation:
I = P / (4πr^2)
where:
I is the intensity of the sound waves in W/m^2,
P is the power output of the speaker in watts, and
r is the distance from the speaker to point x in meters.
Given that P = 130.0 W and r = 7.8 m, we can substitute these values into the equation:
I = 130.0 / (4π * (7.8)^2)
Calculating this:
I ≈ 130.0 / (4 * 3.14159 * (7.8)^2)
I ≈ 130.0 / (4 * 3.14159 * 60.84)
I ≈ 130.0 / 764.084
I ≈ 0.170 W/m^2
Therefore, the intensity of the sound waves at point x when r = 7.8 m is approximately 0.170 W/m^2.
To find the intensity of the sound waves at point x, we can use the formula for sound intensity:
Intensity = Power / (4πr^2)
Where:
- Intensity is the sound intensity in watts per square meter (W/m^2)
- Power is the power output of the speaker in watts (W)
- r is the distance from the speaker to the point where we are measuring the intensity in meters (m)
Given:
- Power (P) = 130.0 W
- Distance (r) = 7.8 m
Let's substitute these values into the formula:
Intensity = 130.0 W / (4π(7.8 m)^2)
Now, we can calculate the intensity:
Intensity = 130.0 W / (4π(60.84 m^2))
= 130.0 W / (241.90478 m^2)
≈ 0.537 W/m^2
Therefore, the intensity of the sound waves at point x, when the distance is 7.8 m, is approximately 0.537 W/m^2.