A sound wave in air at 20°C has a frequency of 320 Hz and a displacement amplitude of 5.00 * 10-3 mm. For this sound wave calculate the (a) pressure amplitude (in Pa)

Video transcript

Hey everyone. So in this problem we are working with sound and pressure amplitude. Let's take a look and see what we're given. We know an alarm amidst sound waves at a frequency of hertz. The air has a temperature of 17.8 degrees Celsius and the wave has an amplitude of six times 10 to the minus third millimeters. They're asking us what the pressure amplitude of this wave is. So the first thing we need to recall is the pressure amplitude equation is P max equals B. A. A. Where B is the bulk module asse. And in air that is a given of 1. times 10 to the fifth pascal's A. Is our amplitude which was given in the problem as six times 10 to the third millimeters. I'm actually going to rewrite that right now as six times 10 to the six m. Just because we normally work in meters with these sound problems. So what's K. K. We need to recall it. K. Is the wave number, and the equation for K. Is two pi F over V. So we are given the frequency in the equation, The frequency is 520 Hz. And recall that the speed of sound in air is 343 m per second. Now that is dependent on the temperature of the air, um 17.8 degrees C. Is close enough to 20 degrees C. That using the speed of sound and air at 20 degrees C. This 343 m per second is a close enough approximation. So we do have everything we need to solve for K. 1st and then we will be able to solve for the pressure amplitude. It's okay, equals two pi times Hz Over 343 meters per second. And that gives us 9.53 And that unit is one per meter. We are going to plug that in to our pressure amplitude equation P max equals 1.42 times 10 to the fifth, pascal's Times 9. one over meters times six times 10 to the negative six m. Let's see now the meters cancel. We are left with an answer in pascal's plug that into our calculators and we get 8.1 to pascal's. You look at our answer choices and that is Answer me. That's all for this problem. We'll see you in the next video.