There is a point source of sound radiating a power of 10 103...

There is a point-source of sound radiating a power of 1.0 × 10−3 W at 240. Hz. At a distance 4.00 m away from the source. Take the density of air to be 1.225 kg/m3. What is the displacement amplitude?

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Transcript

00:01 Hi there.

00:02 So for this problem, the information that we are given is the power that is equal to 1 times 10 to the minus 3 whaps.

00:13 We are also given the frequency for this that is equal to 240 hertz.

00:23 And at a distance, so let's call this distance art that is equal to 4 meters.

00:29 And so the density that we are given for this, also the density of earth, is 1 .25 kilograms per cubic meter.

00:48 And the question is, what is the displacement amplitude? so we need to calculate that.

00:53 And we're going to call a s -s -subs -0.

00:56 So, f -sup 0 is in fact related to the intensity, because s -sup 0 is equal to the square root of the intensity, this divided by 2 times pi to the square times the frequency to the square times the density times the speed.

01:19 Now remember that in this case we're going to use that the speed corresponds to the speed of sound, that is equal to approximately 340, per second.

01:29 Now that we have all of these values, we need first to calculate the intensity.

01:34 Now, the intensity is the power divided by four times pi times the distance square.

01:41 So we substitute the values in here that we are given.

01:44 So the power is 1 times 10 to the minus 3.

01:51 This divided by 4 times pi times the separation distance, which is 4, and that to 3, the square...

Question

There is a point-source of sound radiating a power of 1.0 × 10−3 W at 240. Hz. At a distance 4.00 m away from the source. Take the density of air to be 1.225 kg/m3. What is the displacement amplitude?

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