A railroad train is traveling at 30.0 m>s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m>s and(b) receding from the first?

Video transcript

Everyone in this problem, we have a truck driving at 16.5 m per second, that's emitting a sound of frequency 420 hertz from its horn in motionless air Were asked to calculate the frequency heard by a driver in a vehicle traveling in the opposite direction and receding from the truck at 25 m/s. Alright, so we have our truck here, we're gonna put an S here to indicate that that's the source of the sound. Okay? The truck is the one emitting the sound. So they're gonna have an S and we're gonna say that they're moving to the right at 16.5 m per second and we're gonna come back and look at whether or not that's going to be a positive or a negative speed when we choose our framework reference. Okay, now we have a vehicle. Okay, so we have a vehicle over here, vehicle and that's gonna be our listener. Okay? We're gonna give them an L. There, the one that's gonna be listening to that sound, and we want to know what frequency they here. Now, we're told that they're traveling in the opposite direction and receding from the truck. So they're going to be traveling to the left, the opposite direction and moving away At 25 m/s. Now, when we're doing these source and listener problems, we always want to take the positive direction to be the direction from the listener to the source. Okay, So from the listener to the sources to the right, and that's gonna be our positive direction. So if we look at our speeds ves the speed of the source is going to be positive because it's moving to the right, just like our positive direction. But the speed of the listener VL is going to be negative because it's moving the opposite direction. Alright? And then the frequency of the source. The frequency that that truck is emitting is 420 years. All right, now we want to calculate the frequency heard by the driver in the vehicle. So we want to calculate the frequency um of the listener and recall that for moving source and a moving listener, we have the frequency of that listener is going to be equal to V. The speed of sound plus V. L. The speed of the listener divided by V. The speed of sound plus V. S. The speed of the source times of frequency at the source. All right, now we're told that we're in motionless air. And what that tells us is that the speed of sound is going to be about 343m/s. Okay, so we can go ahead, substitute in the values. We know we get 343 m per second. Okay? Plus the speed of the listener, which is negative 25 meters per second. We're going to divide that by again, the speed of sound 343 m per second. Okay. Plus the speed of the source which is 16. m per second. And we're going to multiply all of that by the frequency emitted hertz. All right, So we simplify in these brackets, we get 318 m/s Divided by And 59.5 m/s. Okay. All times 420 Hz. Alright. And if you look at this, what we have in the brackets. Okay, we have meters per second divided by meters per second. So those units are going to divide out and we're gonna be left with just units of hertz, which is what we want for frequency. So that works out. All right. And if we do this, we're gonna end up with the frequency that the listener hears. 371.516 hertz approximately. Okay. And the answer choices are rounded to the nearest hurts. So we round this to the nearest hurts. We're going to get 372 hertz. And so that is that frequency That the driver in the vehicle traveling the opposite direction is going to hear. Okay. Alright, so we have answer choice a 372 hertz. Thanks everyone for watching. I hope this video helped see you in the next one