# Mechanical Waves, The Doppler Effect

• jlaumack
In summary, the athlete is moving towards the bell, so the source of the sound is not stationary. The frequency of the sound that the athlete hears is affected by both the speed of the sound and the speed of the athlete. To find the speed of the athlete, 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.
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.

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!

## 1. What is the difference between mechanical waves and electromagnetic waves?

Mechanical waves require a medium, such as air or water, to travel through whereas electromagnetic waves can travel through a vacuum. Mechanical waves also cause particles in the medium to vibrate in the direction of the wave, while electromagnetic waves consist of oscillating electric and magnetic fields.

## 2. How does the Doppler effect work?

The Doppler effect is the change in frequency and wavelength of a wave when the source of the wave is moving relative to the observer. This results in a perceived change in pitch or color depending on the type of wave. When the source is moving towards the observer, the frequency appears higher and the wavelength appears shorter. When the source is moving away, the frequency appears lower and the wavelength appears longer.

## 3. What is the difference between the Doppler effect in sound waves and light waves?

The main difference is that the Doppler effect in sound waves is perceived as a change in pitch, while the Doppler effect in light waves is perceived as a change in color. This is because sound waves have a lower frequency range and longer wavelengths compared to light waves.

## 4. How is the Doppler effect used in real-life applications?

The Doppler effect has many practical applications, such as in weather forecasting to track the movement of storms, in medicine to measure blood flow, in astronomy to determine the speed and direction of celestial objects, and in traffic monitoring to catch speeding vehicles.

## 5. Can the Doppler effect be observed with all types of waves?

Yes, the Doppler effect can be observed with all types of waves that have a frequency and wavelength, including sound waves, light waves, water waves, and seismic waves. However, the effect may be more noticeable in some waves, such as sound waves, due to their slower speed compared to light waves.

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