A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the highest and lowest frequencies heard by a student in the classroom?

Video transcript

Welcome back, everyone. We are making observations about the frequency of a whistle. We're told that it emits a sound with a frequency of three kilohertz or three times 10 to the third hertz. And we are told that it is fixed to a 1.6 m from the axis of rotation, rotating blade. The R is 1.6 m. Now, we are told that it has a frequency of 360 R PM. But in order to get, you know, revolutions per second, we just divide by 60 which gives us six revolutions per second. And we are tasked with finding as the whistle undergoes the Doppler effect, the greatest and least frequencies detected by an observer, which I will denote with F plus and F minus. Well, since it undergoes the Doppler effect, we can use the formula for the Doppler effect or both of our frequencies here. So F plus is going to be our initial frequency divided by one minus the velocity of the whistle divided by the velocity of sound through the air. And then we have F minus is equal to our initial frequency divided by one plus our velocity of the whistle divided by the velocity of sound through air. Now, we have all of our variables except what is the velocity of the whistle? Well, let me go ahead and change color here real quick. The velocity of the whistle is equal to the radius times two pi times the frequency here. What this is going to give us is 1.6 times two pi times six which gives us 60.3 m per second. For the velocity of the whistle, we know that the velocity of sound through air at room temperature is m per second. So we are ready to go ahead and find our two desired frequencies. We have that our greatest frequency equal to three times 10 to the third divided by one minus 60.3 divided by 343, which gives us 3640 Hertz. And we have that our least frequency is three times 10 to the third divided by one plus 60.3, divided by 343, giving us 2550 Hertz. So now we have found the greatest frequency and the least frequency corresponding to answer choice. A thank you all so much for watching. I hope this video helped. We will see you all in the next one.