For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0 * 10-5 Pa. Calculate the (a) intensity

Video transcript

Hey everyone. So in this video we are working with sound pressure and intensity. See what they're asking, they're telling us the sound pressure amplitude at the threshold of hearing is defined as a pressure of two times 10 to the minus five pascal's. And they're asking us to determine the intensity at the threshold appearing. So at first glance we don't really have a ton of information, but I'm going to show you how we actually can solve for this intensity. So first we need to recall that our intensity equation in terms of pressure is the times p max squared over to be and we know that this is in air. So our um bulk modulates the bulk modular of air is a constant 1.42 times 10 to the fifth pascal's. And the sound, the speed of sound in air is 343 m/s. So when we look at this plus the given in the equation or in the problem statement, that p max equals two times 10 to the negative fifth pascal's, we can actually just plug and chug into this intensity equation. So I intensity equals 343 m/s, times two times 10 to the -5 pascal's squared All over two times one. Uh 1.4, 2 times 10 to the 5th Pascal's Plug that into our calculator and we get 4.83 times 10 to the -13. But what are those units? This is a little strange. We know intensity is in watts per meter squared. And we do see that 4.83 is one of the times 10 to the minus 13 is one of the choices given. But when it's not really clear to me how we get from these units. Two watts per meter squared. I always like to just do kind of a gut check and let's see if these units actually do make sense. So to do that, we need to recall that a pascal is a newton per meter squared and a watt is a newton meter per second. So from the units we have a meter per second times to pascal's over pascal. So one of those pascal's does cancel out pretty easily. And then we are left with a meter per second times a newton per meter squared. That gives us a newton per second peter, we can rewrite so we wanted, so we know we're gonna end up with watts and we can rewrite this in terms of newton's, so that becomes a watt second per meter Plug that in over here. And then we get a watch, 2nd per meter times a second meter times one over a second meter, those seconds cancel. And then we are actually left with watts per meter squared. And that is our unit. And we know now that we are all good to go. Our answer is 4.83 times 10 to the 13th watts per meter squared. That's all for this video. We'll see you in the next one