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Physics lab experiment on Doppler shift

At-Home Experiment 1
PURPOSE
This experiment was designed to understand and measure Doppler shift.

Equipment Setup
Tuning fork (with a known frequency)
Nylon string
Stopwatch
Meter Stick

Tie the string (1 meter long) to the end of the tuning fork.

Procedure
First, practice swinging the tuning fork in a horizontal circle above your head at a constant angular speed. Use the stopwatch to time how long it takes to complete 5
10 revolutions and then do it again to see if you're consistent.

When you are ready, strike the tuning fork and put it into the horizontal circle. You should be hearing the Doppler effect.

Analyzing the Data
1. With the tuning fork ringing, use the stopwatch to time how long it takes to complete 5 revolutions. From this you should be able to calculate the period of one revolution. Record your work and this value below:

2. With this time period and the known radius of the circle, calculate the constant linear speed of the tuning fork as it moves in the circle. Show work here:

3. As the tuning fork rotates away from you, the actual frequency is Doppler shifted down to a lower frequency; and when it is rotating towards you, the actual frequency is Doppler shifted up to a higher frequency. Using the actual frequency of the tuning fork and speed you calculated above, figure out the two Doppler-shifted frequencies you hear as the tuning fork moves in the circle. Show work and solutions below:

Experiment 2
You are going to need some help with this experiment. Try to go someplace that is open and generally quiet. Going outside on a quiet, non-windy day would be ideal.

Now have someone ring the tuning fork and hold it straight out in his or her outstretched arm. You should keep walking away from him or her until you can just barely hear the tuning fork when it is first struck (this is important since the sound of the tuning fork naturally fades away with time).

This distance that you are away from him or her corresponds to the threshold of hearing (0 decibels).

Procedure
Measure this distance by perhaps using the string and then measuring the string (or a tape measure or using the Meter Stick carefully).

Analyzing the Data
1. Using the definition of sound intensity and knowing you are at the threshold of hearing, calculate the power output of the tuning fork when it is first struck. Assume that the sound is being carried outward on spherical waves. Show work below:

2. For most people, there needs to be a change of 10 decibels for a noise to sound twice as loud. Calculate how close you would have to get for the decibel level to increase to 10 decibels using the same power value you found above:

3. Now test this out. Move to the distance away from the tuning fork you calculated above. How would you describe the loudness of the sound now? Would you say it is twice as loud?

After completing the experimental procedures, make a report for each experiment.

Solution Preview

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Doppler Shift Lab

Experiment I - Procedure

First, practice swinging the tuning fork in a horizontal circle above your head at a constant angular speed. Use the stopwatch to time how long it takes to complete 5
10 revolutions and then do it again to see if you're consistent.

When you are ready, strike the tuning fork and put it into the horizontal circle. You should be hearing the Doppler effect.

Experiment I - Data Analysis

1. With the tuning fork ringing, use the stopwatch to time how long it takes to complete 5 revolutions. From this you should be able to calculate the period of one revolution. Record your work and this value below:

Length of the string = 100 cm = 1.0 m
The tuning fork was swirled in a horizontal circle of radius r using this string.
Hence,
r = 1.0m

Time for 10 revolutions = 5.6 s
Therefore, time for one revolution = Tf = 0.56 s (This is the period of revolution)

2. With this time period and the known radius of the circle, calculate the constant linear speed of the tuning fork as it moves in the circle. Show work here:

Let the linear speed of the tuning fork = Vf
Vf = distance/time = circumference / Tf
Vf = 2 pi r / Tf = 2 pi * 1.0 / 0.56 = 11.2 m/s

Vf = 11.2 m/s

3. As the tuning fork rotates away from you, the actual frequency is Doppler shifted down to a lower frequency; and when it is rotating towards you, the actual frequency is Doppler shifted up to a higher frequency. Using the actual frequency of the tuning fork and speed you calculated above, figure out the two Doppler-shifted frequencies you hear as the tuning fork moves in the circle. Show work and solutions below:

Frequency of the tuning fork, f = 440 Hz
Vs = 340 ...

Solution Summary

Two Physics experiments were performed involving doppler shift. First experiment involved a swinging tuning fork. Doppler effect is the apparent change in pitch/frequency of a sound as it moves towards or away from the listner. I have determined the apparent frequencies of the tuning fork using my experimental data. In the second experiment, I determined the power output of our tuning fork, the distance at which the sound level is zero and the distnace at which the loudness doubled.

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