Mechanical Waves, The Doppler Effect

[jlaumack]

1. Homework Statement

At the Winter Olympics, an athlete rides her luge down the track while a bell just above the wall of the chute rings continuously. When her sled passes the bell, she hears the frequency of the bell fall by the musical interval called a minor third. That is, the frequency she hears drops to five sixths of its original value.

a) Find the speed of sound in the air at the ambient temperature -15 degrees Celsius

b) Find the speed of the athlete.

2. Homework Equations

The Doppler Equation: f prime = f*(v+vo)/(v-vs)

3. The Attempt at a Solution

I got part a) using the following equation: 331+ (0.6)(-15.0)= 322 m/s

For part b), I tried to use the Doppler equation, setting vs= 0 since the source of the sound is stationary. I plugged everything else in like this :

x*(322+Vo)/(322-0)=5/6 x

This way the x's would drop out, and I would have an answer of 53.7 m/s but this is incorrect. I don't know if I am close or if I am not even on the right track.

 

[Jhero]

Thank you for your question. Here is my response:

For part a), your calculation for the speed of sound at -15 degrees Celsius is correct. Good job!

For part b), you are on the right track by using the Doppler equation. However, there are a few things to consider. First, the athlete is moving towards the bell, so the source of the sound is not stationary. Therefore, you cannot set vs=0. Instead, you need to use the speed of the athlete as the source velocity. Also, the frequency of the sound that the athlete hears is not the same as the frequency of the bell. The frequency of the sound that the athlete hears is affected by both the speed of the sound and the speed of the athlete. So you will need to use the Doppler equation twice, once to find the frequency of the sound that the athlete hears and again to find the speed of the athlete.

Here is the correct approach:

1. Use the Doppler equation to find the frequency of the sound that the athlete hears. This will give you an equation with two unknowns, the speed of the athlete (va) and the frequency of the bell (fb). You can solve for fb in terms of va.

2. Use the Doppler equation again, this time solving for va. You now have two equations, one with fb in terms of va and one with va as the only unknown. You can solve for va by setting these two equations equal to each other and solving for va.

I hope this helps. Good luck with your calculations!