A concert loudspeaker suspended high above the ground emits 35 W ...

Question

A concert loudspeaker suspended high above the ground emits 35 W of sound power. A small microphone with a 1.0 cm² area is 50 m from the speaker.

a. What is the sound intensity at the position of the microphone?

Accepted Answer

Hey, everyone in this problem, we have a car horn that emits 50 watts of sound power. And we're gonna assume that we're standing 10 m away from the car. And we're asked to determine the intensity of sound. At that point, we're standing, we have four answer choices all in watts per meter squared. Option A is 78.9 times 10 to the exponent negative three. Option B 87.9 times 10 to the exponent negative three. Option C 93.8 times 10 to the exponent negative three and option D 39.8 times 10 to the exponent negative three. Now, what we wanna do is think about the type of sound we have, OK. So we have a car horn that's emitting sound. So we're gonna assume that that's gonna be a uniform spherical way and the sound is gonna radiate uniformly in all directions from that car, which makes sense. OK. This is a car horn. We want that sound to be heard all around the car if you're driving. So now we're looking for the intensity and I called it the intensity of sound, I for a uniform spherical wave is given by the power of the source P source divided by four pi R squared where R is a distance that you are from the source. Now, we know the power of the source. We're given that in the problem, we know the distance that we are from the source. So we have everything we need, just need to substitute our values in and solve the intensity of sound is gonna be equal to that power, which are told is 50 watts divided by four pi multiplied by the distance we are from that source, which we're told is 10 m. What simplify we have that the intensity is equal to 50 watts divided by four high multiplied by 100 m squared. Now we can simplify a little bit. Both the numerator and denominator are divisible by 50. So we can divide both by 50. We have one in the numerator. We get that two in the denominator. So we can write this as one watt divided by eight pi meters squared. And now we want to put this into our calculator and approximate to compare to our answer choices. Hey, if we do that, we get that the intensity of sound I is approximately equal to 0.398 watts per meter squared. And if we look at our answer choices, we can see that all of them have two digits before the decimal place. So we want to rewrite our intensity to have two digits before the decimal place. In order to do that, we need to move our decimal place to the right one, two, three units. So we can write this as 39.8. And because we've moved it three places to the right, that's gonna be times 10 to the exponent negative three watts per meter squared. And that is that sound intensity we were looking for from the car horn at m away. If we compare this to our answer choices, we can see that this corresponds with answer choice. D Thanks everyone for watching. I hope this video helped you in the next one.

A concert loudspeaker suspended high above the ground emits 35 W of sound power. A small microphone with a 1.0 cm² area is 50 m from the speaker. a. What is the sound intensity at the position of the microphone?

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