The siren of a fire engine that is driving northward at 30.0 m>s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m>s. (a) What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck?

Video transcript

Hey everyone in this problem, we have a police car chasing a large vehicle at a speed of 33 m per second. The siren on the police car is emitting sound at a frequency of 1400 hertz. The vehicle is running away at a speed of 22 m per second and were asked to determine the frequency of sound reflected by the large vehicle as heard by police in the police car. Now we're gonna have to do this problem in two parts. So let's start with this initial situation. What do we have going on? We have the police car And this is going to be our source because the police car, the siren on the police car is emitting sound and the frequency of that sound will right here. The frequency being emitted by that source is 1400 Hz. Now we also have a large vehicle. Okay, so we have a vehicle and this is gonna be our listener because initially that vehicle is going to be the one listening to that noise and that's where the frequency is going to be reflected from. Alright, so we have our police car, we have our vehicle. Now, when we have a situation like this where we have a source and the listener, we want to take the positive direction to be the direction that goes from the listener to the source. Okay, so from the listener to the source, that's going to be to the left. Now, our police car is chasing the vehicle. So the police car is going to be moving to the right now, that is the opposite direction Of our positive direction. And so the speed of the source. The speed of the police car is going to be negative. We're told it's 33m/s. Now, similarly for the vehicle, the vehicle is running away from the police car, so they're also going to be traveling to the right. And the speed here of the listener we're told is 22 m per second. It's traveling to the right, which is the negative direction. So it's going to be negative 22 m per second. So this is what we have initially. Now, what are we trying to figure out? We're trying to figure out what sound the police hears or what frequency of sound. The police here's when it's reflected by the large vehicle. So we need to figure out first is what frequency the vehicle here's that'll be the frequency that's reflected by the vehicle. And then we can figure out what frequency the police hears from that reflection. So starting with what frequency is reflected. What frequency does that vehicle here? And recall that when we have a source and a listener that are both moving the frequency that the listener hears is given by V. The speed of sound plus V. L. The speed of the listener over V. The speed of sound again plus V. S. The speed of the source all times F. S. The frequency of the source substituting in the values that we have. The frequency that the listener hears is going to be the speed of sound which is 343 m per second Plus the speed of the listener which is -22 m/s, Divided by the speed of sound, 343 m/s. That standard value, you can look up in your textbook Plus the speed of the source which is the speed of the police car, negative 33 m/s. And all of this is going to be multiplied by the frequency of that source, which is the frequency of the siren. 1400 Hz. Alright, so if we work this out we're gonna have 321 m per second divided by 310 meters per second Times 1400 Hz. And this is going to give us a frequency of 1,449. Hz. Alright, so that is the frequency that the vehicle here's which is the frequency that the vehicle reflects. The frequency that is reflected by that vehicle. So now we need to switch this and reverse the rules. Now the vehicle is reflecting a sound. Okay, so that vehicle is emitting a frequency and we want to know what frequency the police hears. So now we're gonna switch roles. So we have the police still on the left hand side here but they're now going to be the listener and then on the right we have our vehicle And they're going to be the source. And the frequency of that source is going to be the frequency that's being reflected, which we just found. aN:aN:000NaN 1,449. Hz. Again, we have a moving source and a moving listener. So we want to take the direction from the listener to the source as a positive direction. So from the listener to the source, that's to the right. So now when we look at our speeds, the speed of the listener is the speed of the police officer. They're moving to the right. And so this is going to be positive 33 m/s now and similarly the speed of the source, which is the speed of the vehicle. They're moving to the right as well, that's the positive direction. And so this is positive 22 m/s. And we're going to do the same thing. We're going to calculate the frequency that the listener hears. This time, the listeners, the police. So the frequency that the listener hears is given by the speed of sound plus the speed of the listener divided by the speed of sound plus the speed of the source, all times the frequency of the source. Using the values in our problem we have m per second plus 33 m per second divided by m per second plus m per second. All times are frequency 1449. hertz. And if we work this out again, we're going to have meters per second divided by meters per second. That unit is going to divide out. We're going to be left with just the unit of hertz and we're going to get a value of 1493. hertz. And that is going to be the frequency that the police car hears from that reflected sound. Now, if we go back up to our answer choices, okay? We round to the nearest hurts. We see that we have answer choice B The frequency of the sound reflected by the large vehicle as heard by the police is going to be 1493 hertz. Answer be Thanks everyone for watching. I hope this video helped see you in the next one.