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 approaching the first?

Question

Accepted Answer

Hey everyone welcome back in this problem. A car driving 15 m per second, who'd set a frequency of 410 hertz in the motionless air Were asked to determine the frequency heard by a driver in another car that's moving 25 m/s in the opposite direction and approaching the hooting car. Okay, so let's just draw what we have. So we have the first car and we're gonna call this s to be the source car. That's the source of the sound. Okay? They're honking their horn at a frequency of 410 Hz and then we have the second car. Okay, We're gonna call them l the listener and we want to know what frequency they're going to hear. Now these two cars are moving in opposite directions. K but the listener is approaching the car that is honking. So we're going to have the car honking going to the right and the listening car moving to the left. Now, when we talk about our frame of reference and we're taking our positive direction. When we have problems with source and listeners, 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 source, our arrow is going to go to the left. And so this is going to be our positive direction. Okay, so the speed of the listener is going to be positive then. Okay, they're moving At a speed of m/s In the speed of the source car. Okay? He's moving to the right or positive directions to the left, so this is going to be negative and a negative m/s and 15. We were given in the problem. Alright, so that's our diagram. Now we want to figure out the frequency that the listener hears. Now let's recall in a problem where we have a source and a listener who are both moving the frequency of the listener is going to be given by the speed of sound plus VL and speed of the listener divided by the speed of sound again plus V. S. The speed of the source of all times the frequency of the source. Alright, so we're told that we are in motionless air and what this tells us is that the speed of sound is gonna be about 343 m per second. Okay, so we can use that value for V. We know V. L. V. S and F. S. So we can go ahead, substitute in our values and solve for F. L. So we got 443 m/s Plus 25 m/s Divided by 343 meters per second Plus negative 15 m/s. Okay, so when you're using this equation, you'll notice that the signs really matter. Okay, they change, they will change the answer significantly. So you want to be careful when you're drawing your diagram out and that's why it's a great idea to draw the diagram. Okay, pick your positive direction from the listener to the source and then figure out if your velocity is positive or negative. Alright. And then we're gonna multiply by the frequency which is Hz. Alright, so if we simplify what's in the brackets here, we get 368 m/s divided by m/s. All of that is Times 410 Hz. And you'll notice in this first bracket we have meters per second divided by meters per second. So the unit of meters per second will divide out and we're gonna be left with just the unit of hertz which is what we want for a frequency guys are units check out. It's always a good thing to check to make sure that your units work out And this is going to be equal to 460 Hurts. Okay, so the frequency that the listener hears in that other car is gonna be 460 Hz. If we go back up to our answer choices, we see the frequency heard by the driver in the other car is going to be C 460 hertz. Thanks everyone for watching. I hope this video helped see you in the next one

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 approaching the first?

Verified video answer for a similar problem:

Key Concepts

Doppler Effect

Relative Velocity

Wave Frequency