Homework answers / question archive / PHY232 Lab 10 - Doppler Effect: Sound Waves Have you ever noticed that if a car with a horn blowing is moving past you rapidly that the sound waves emitted by the horn seems to change frequency? In 1842 an Austrian physicist, Hans Christian Doppler, observed and analyzed the same phenomenon for sound emitted by a passing train

PHY232 Lab 10 - Doppler Effect: Sound Waves Have you ever noticed that if a car with a horn blowing is moving past you rapidly that the sound waves emitted by the horn seems to change frequency? In 1842 an Austrian physicist, Hans Christian Doppler, observed and analyzed the same phenomenon for sound emitted by a passing train

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PHY232

Lab 10 - Doppler Effect: Sound Waves

Have you ever noticed that if a car with a horn blowing is moving past you rapidly that the sound waves emitted by the horn seems to change frequency? In 1842 an Austrian physicist, Hans Christian Doppler, observed and analyzed the same phenomenon for sound emitted by a passing train. Hence the phenomenon is known as the Doppler Effect.

A similar effect is found for the propagation of light and other electromagnetic waves from moving sources. In fact highway patrol officers use radar to measure Doppler shifts in radio waves so they can determine how fast vehicles are moving.

 

 

LabPro Sound Sensor

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Fig. 1: A car is shown moving at a speed v_s past a sound sensor located at the side of a long straight road.

Suppose a driver is blowing her car horn and hears a predominant frequency denoted by f₀. What frequency, f_F will be detected by a microphone placed in front of the source of sound (consisting of the moving car horn)? Doppler proposed that the frequency, f_F detected in front of the source is given by

                        (Eq. 1: frequency detected the source is moving toward the observer)

where v_w is the speed of the sound wave propagation in air and v_s is the speed of the moving source from which the sound wave emanates.

Similarly, Doppler predicted that the frequency of waves propagating behind a source of sound that moves away from an observer at speed v_s can be determined using the equation

 

                         (Eq. 2: frequency detected the source is moving away from the observer)

We have created movies of a honking car moving fairly rapidly on a straight level road past a stationary microphone. We have recorded the sound waves emanating from the car’s horn separately using a sound sensor attached to the Logger Pro interface, operated by the roadside observer. You will be working with these files in this exercise.

Your goal in this assignment is to verify that the Doppler Equations, shown above, can be used to predict the ratio (f_F / f_B) of the apparent car horn frequencies before and after the car passes the microphone. To complete this assignment you will need to (1) use Equations 1 and 2 to derive an equation for this ratio as a function of the speed of sound waves in air (v_w) and the speed of the moving car horn (v_s), and then (2) use the Logger Pro video analysis tools to determine the value of v_s–the passing car’s velocity.

 

(a)  What happens to the sound of the car’s horn as is passes the sound sensor? Open the movie entitled <CarHornDoppler.mov> and play it. This video clip was recorded by a digital video camera that was placed perpendicular to the road and 10.0 meters away from the center of the car just as it passes the sound sensor in the center of the frame as shown in Figure 2. The sound dubbed into the Car Horn Doppler movie was recorded at the roadside by this sound sensor. What happens to the sound of the car’s horn as the car moves from an initial position to the left of the camera to a final position to the right of the camera? Replay the movie and listen several times, does the frequency of sound change? Is the loudness changing? Describe what you hear.  10 pts

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 m

20 m between markers

Camera

Car’s Path

LabPro sound sensor

Figure 2: Overhead view of the recording apparatus

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a)  Use the Doppler Equations 1 and 2 to derive an equation for the ratio f_F/f_B as a function of the speed of sound waves in air (v_w) and the speed of the moving car horn (v_s). Show your work.  10 pts

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)  Open the Logger Pro file entitled <CarSpeed.cmbl>, which has a shortened version of the movie inserted in it.  Use the video analysis tools to find the speed of the car with its blowing horn “sound source,” (v_s). Explain what you did to find (v_s). Record your value for (v_s) in the box below to three significant figures. Hints: Don’t forget to scale the movie and figure out how to find the car’s velocity using x vs. t data.  10 pts

 

 

 

 

vs =                              m/s

 

 

 

 

 

 

(c)  Calculate the speed on sound on the day the movie was made: It turns out that the speed of sound in air (v_w) depends on the air temperature (T_c) and can be calculated using the equation[1] 

 

      When the movie was made, the air temperature (T_c) was recorded as 27.2°C. Calculate the speed of sound in air (v_w) on that day. Show your calculations!  10 pts

 

 

 

 

(d)  Find the expected value of the ratio f_F/f_B in terms in terms of your calculated value of the speed of sound in air (v_w) and your measured value of the speed of the sound source (v_s). Hint: Use the equation you derived in Part 2(a). Show your calculations and round your answer to three significant figures.  10 pts

 

 

 

 

 

 

(e)        Compare your calculated Ratio with Logger Pro frequency measurements: This comparison serves as a direct test of the validity of the Doppler Equations. We have recorded the sound pressure using a LabPro Sound Sensor placed at the side of the road for about one second before the car passes the sound sensor and for about one second after it passes the sensor. In each case the Logger Pro a Fast Fourier Transform analysis (FFT) of the sound pressure waves can be used to find the predominant frequency just before (f_F) and just after (f_B) the car passes the roadside sound sensor.

      Start by opening the Logger Pro file entitled <FrequencyShift.cmbl>. Look for the largest peak on the FFT graph describing the frequencies between 0 s and 1 s to find the predominant frequency just before (f_F) the car passes the sensor. Change the scale on the horizontal axis so that you see this region in more detail. You can accomplish this by selecting the Additonal Graph Options ® FFT Graph Options from the Options menu or by double clicking on the FFT graph to reset the frequencies displayed so that you focus only on the highest amplitude frequencies.  Next, use the Examine tool to find the predominant frequency just before (f_F) the car passes the sensor.  Repeat the procedure between 2 s and 3 s to find the predominant frequency just after (f_B) the car passes the sensor. Summarize your results in the appropriate spaces below and calculate the ratio f_F/f_B.  10 pts

FFT Max 0s to 1s:  f_F =                    Hz

FFT Max 2s to 3s:  f_B =                     Hz                    f_F/f_B =                  

a)  How did the ratio f_F/f_B that was determined from the Doppler Equations (in Part 2 (d)) compare to the ratio determined from direct measurements (in Part 2(e))?  Find the percent difference between the two results.  10 pts

 

 

 

 

 

b)  Suppose you are assisting a policeman, who is sitting in stationary cruiser and is pointing his radar “gun” at the approaching car. His detector shows the car’s speed. Describe how you could use your sound data for the car’s resting frequency f₀ and measured frequency f_F while moving toward the policeman to calculate the speed of an approching car (v_s) in order to check the reliability of the radar gun.        10 pts

 

 

 

 

 

c)  The equation for the Doppler affect when the source is stationary and the observer is moving is given by

Where the plus sign, +, is used when the observer is moving toward the source and the negative sign, -, when the observer is moving away from the source.  If both the source and the observer are moving then the equation becomes

 

 

where the choice of sign depends on the relative motion of the source and observer.

If a horn is blowing at 480 Hz and the observer is moving toward the horn at 10 m/s and the source is moving toward the observe at 20 m/s, what is the frequency heard by the observer?  Show your calculations.  10 pts