A 1000 Hz sound wave traveling through 20°C air causes the pressure to oscillate around atmospheric pressure by ±0.050%. What is the maximum speed of an oscillating air molecule? Give your answer in mm/s.

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Welcome back, everyone. We are making observations about a 2.5 kilohertz sound wave that causes a point oh 6% fluctuation in pressure. And what we are tasked with finding is we are tasked with finding the peak speed of vibrating gas molecules in millimeters per second. What we're gonna do here is we are gonna consider gas as a compressible fluid. And as such, we are able to say that the peak speed is just equal to the amplitude times omega. Now, in order to find out our V max, let's use another equation here. Let's use the equation for the max pressure deviation to the bulk modulus of air. What we have is that P max is equal to K times our bulk modules times our amplitude, which is really equal to two pi times our frequency times B A divided by the velocity of air wave, uh sound waves through air, which is really equal to omega B A over R V sound. Now rearranging the equation here, we can see that a omega which is equal to V max is equal to P max times V sound all divided by our bulk modulus. Here and we know all of these values. So let's go ahead and plug them in. We have that our V max is equal to, well, for our max pressure to the bulk modulus at room temperature, this is going to be one oh 1 pascals. But remember we're just looking for the point oh 6% fluctuation in the pressure. So we're going to multiply this by six times 10 to the negative fourth. Now, then this of course is multiplied by our velocity of sound through air which at room temperature is 3 43 m per second, all divided by the bulk modulus of air which is 1.42 times 10 to the fifth pass. Gauss. What this gives us when you plug it into a calculator is 100.147 m per second, which corresponds to 147 millimeters per second, giving us a final answer of answer. Choice B Thank you all so much for watching. I hope this video helped. We will see you all in the next one.

A 1000 Hz sound wave traveling through 20°C air causes the pressure to oscillate around atmospheric pressure by ±0.050%. What is the maximum speed of an oscillating air molecule? Give your answer in mm/s.

Verified Solution

Key Concepts

Sound Wave Properties

Oscillation Amplitude

Molecular Speed in Sound Waves