Example 16.1 (Section 16.1) showed that for sound waves in air with frequency 1000 Hz, a displacement amplitude of 1.2 * 10-8 m produces a pressure amplitude of 3.0 * 10-2 Pa. (a) What is the wavelength of these waves?

Video transcript

Hey, everyone in this problem, we have a basketball fan watching a game on his TV. The speaker generates sound waves of a 1.2 kilohertz. We're given the displacement amplitude of the vibrations as well as the pressure amplitude. And we're gonna come back to that and we're asked to find the wavelength lambda of the waves. We're given four answer choices. Option A lambda is equal to 3.5 times 10 to the exponent negative three m. Option B lambda is equal to 0.286 m. Option C lambda is equal to 3.5 m or option D lambda is equal to 285 m. Now I mentioned we were gonna come back to the amplitude and the pressure amplitude and we could use those values to solve this problem. OK. We could use that our maximum pressure amplitude equation to find the wavelength. However, there's a simpler way to tackle this and we recall that the wavelength lambda is equal to the speed V divided by the frequency of, we're given the frequency F 1.2 kilohertz and we know the speed of sound in air and it's a value that we can look up in our textbook. And so we can calculate the wavelength simply off of this equation. And those two values. So the wavelength lambda is going to be equal to m per second. OK. The speed of sound and air divided by the frequency which is 1.2 kilohertz. Now, in order to use it in this equation, we want to convert it to Hertz. Hey, we have a prefix of kilo. We wanna convert that to just Hertz. And so what we do is multiply by 10 to the exponent three. And that is now in Hertz, when we look at units, we have meters per second divided by Hertz. Recall that a Hertz can also be written as one divided by second. OK? Or per second. So meters per second divided by one divided by second, we're left with just a unit of meters. OK? Those per seconds divide out. And that's exactly what we want for wavelength. When we look at the numbers, we have 343 divided by 1.2 times 10 to the exponent three, which gives us a wavelength of 0. meters. OK. And that's the wavelength we were looking for. We found the wavelength is 0.286 m which corresponds with answer choice B and that's it for this one. Thanks everyone for watching. I hope this video helped