Astronomy Lab The Doppler Effect Using Sound

OBJECTIVES: Record, listen to, and describe the changes in frequency of a car horn as the car passes you. Explain why the changes in frequency occur. Read graphs of Amplitude versus Frequency. Calculate speeds using the Doppler Effect. Perform simple calculations using the correct number of significant figures. Use dimensional analysis to convert from one set of units to another (e.g., miles per hour to feet per second). Practice good record keeping. BEFORE YOU COME TO LAB: Review previous exercises: "Significant Figures", "Dimensional Analysis". If you have not already done so, work the practice problems from those two exercises in your lab notebook. Review your notes and the text on the Doppler Effect (Go to the lecture calendar and find the powerpoint slideshow if you missed this lecture). Read this write up. At the top of a right hand page, enter the title “Doppler Effect Using Sound” (Table of Contents too). Under that, write one sentence describing what you think the pitch of the car horn will sound like as the car approaches you and as the car recedes from you. Under that, explain why the frequency changes in the above case. Use a diagram. (Good reference: http://www.acs.psu.edu/drussell/Demos/doppler/doppler.html) Under that, write the equation you will use in this exercise (Equation 1) and what each variable means. (or cut and paste from this write-up) Read through the explanation of the formula. Under that, use dimensional analysis to convert 35.8 km/h to ft/s (show your work and have answer in correct significant figures). BRING TO LAB: Calculator that handles scientific notation, your lab notebook with above information, and this write-up. THEORY: The Doppler Effect is the change (or shift) in the observed frequency of a source due to motion of the source and/or the observer. For example, the pitch of a car horn approaching you sounds higher than if the car is standing still. Conversely, the pitch of the car horn is lower as the car recedes from you. This is the same effect that you hear from a race car. The sound from the car noticeably decreases in pitch as the car zooms by you. The Doppler Effect works for any wave so the same thing will happen for light as well as sound. If a star moves toward Earth, astronomers detect slightly higher frequencies coming from this star. They use the shift in frequency to measure the speed of the star. The larger the shift, the greater the speed.

Doppler Effect Using Sound Page 2 of 10 In this exercise we will use sound waves instead of light waves. We will hear, record, and measure the shift in frequency of a car horn as the car passes. We will calculate the speed of the car from the shift. In order to calculate the speed of an object, we must know how the speed relates to the shift in frequency. As long as the speeds do not get too close to the speed of light, then Shift in frequency Speed of object = True frequency Speed of wave

In formula form this becomes: wv

v

f

f

Solving for v yields

wv*f

fv

Equation 1

where v = speed of object relative to observer = (in this case) speed of car relative to you

f = shift in frequency (difference between shifted and true frequency)

(Remember means change in. So f means change in frequency) f = true frequency (frequency of car horn when car is stationary) vw = speed of wave being measured; (in this case) speed of sound in air is about 1100 ft/s or 330 m/s PROCEDURE (RECORD FREQUENCIES): Write down the date and the name(s) of your partner(s). Ideally, we would go outside and record a car horn but we are keeping the class safe by using prerecorded data. Record in your notebook that a car horn was recorded moving toward you (approaching), moving away from you (receding) and at rest. MEASURE FREQUENCIES (Back in the laboratory): The instructor will show you how to measure the frequencies that were recorded. There are 3 sets of 3 graphs. The 3 sets (1, 2, 3) are for 3 cars (car 1, car 2, and car 3). The 3 graphs are for movement (A, B, C): approaching, receding and stationary (toward, away, stationary, but not necessarily in that order).

Doppler Effect Using Sound Page 3 of 10 Car1: Look at the three graphs for car 1 (1A, 1B, 1C) on the next page.

1. Label the frequency (middle of the peak) on each of the 3 graphs in Hz. 2. Which graph shows the car horn at rest? Explain why you chose that graph. 3. Explain why you really cannot use the amplitude to tell which car horn is moving toward or

away. 4. Read and write down the frequency of the horn when:

The car is at rest (true frequency). The car is moving toward you. The car is moving away from you. CALCULATE SPEED OF CAR:

5. For the case in which the car moves toward you, find the shift in the frequency (f). It is the

difference between the true and the shifted frequency. You now know f (the shift in frequency), f (the true frequency), and vw (the speed of the wave). Use these in the Doppler formula (Equation 1) to find v (the speed of the car). Express your answer with the correct units (mi/h and km/h) and the correct number of significant figures (answer should be displayed with the lowest number of significant figures in the problem).

6. Repeat the same calculation for the case in which the car moves away from you. Write down

the car speed including units (mi/h and km/h).

7. Average the absolute values of these two speeds (mi/h and km/h). Now show the instructor your result and they will verify the speedometer reading.

Doppler Effect Using Sound Page 4 of 10

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Astronomy Lab – Doppler

Effect – Car Horn 1 Graphs A

B

C

Doppler Effect Using Sound Page 5 of 10 Car2: Label the graphs for Car 2 with each frequency and which is toward, away, and rest. Repeat procedure (parts 4, 5, & 6 from car 1) for the set of three graphs for car 2 to calculate the speed in km/h and mi/h. Verify with the instructor. Answers should be about 89 km/h and 55 mi/h. Car 3: Use the set of three graphs for car 3 for practice at home. Answers should be about 54 km/h and 33 mi/h. BEFORE YOU LEAVE LAB: Check with your team members that they can satisfy the objectives listed above. Tape or staple the sets of graphs into your notebook. MORE REVIEW? Here are some other websites on the Doppler Effect. http://www.grc.nasa.gov/WWW/k-12/airplane/doppler.html http://imagine.gsfc.nasa.gov/YBA/M31-velocity/Doppler-shift-2.html HOMEWORK: Work the Practice Problems following this in your notebook as needed.

Doppler Effect Using Sound Page 6 of 10 Astronomy Lab - Doppler Effect – Car Horn 2 Graphs

Amplitude

Amplitude

Amplitude

A

B

C

Doppler Effect Using Sound Page 7 of 10 Astronomy Lab – Doppler Effect – Car Horn 3 Graphs

Amplitude

Amplitude

Amplitude

A

B

C

Doppler Effect Using Sound Page 8 of 10 Practice Problems

Use these exercises as practice after you finish the lab exercise. Use the speed of sound as 1100 ft/s or 330 m/s. Pay attention to significant figures. Useful conversion factors: 1 mile = 5280 feet, 1 mile ~ 1.6 kilometers, 1 AU ~ 93 000 000 miles 1) A train’s horn emits a frequency of 100. Hz. When the train approaches a stationary observer, the observer hears a frequency of 110. Hz. Find the speed of the train in ft/s, mi/h, km/h, and m/s. 2) A car horn has a stationary frequency of 401 Hz. An observer at rest detects a frequency of 381 Hz. Is the car approaching or receding from the observer? Find the speed of the car in ft/s, mi/h, km/h, and m/s. 3) A physics student hears the whine of an approaching car engine and measures a frequency of 1350 Hz. As the car recedes from the student, the student measures a frequency of 1290 Hz. Find the speed of the car in ft/s, mi/h, km/h, and m/s. Hint: What do you think the stationary frequency is? 4) A car drives by you with its horn blaring. You analyze the frequency spectrum from the horn of the car. The results for the stationary horn and the horn as it approaches you are shown below. Carefully find the frequency of the stationary and moving horns. Then find the speed of the car. Express your answer in ft/s and in km/h using dimensional analysis to convert from one set of units to the other. | | | | | | | | | | 300 Frequency (Hz) 320 300 Frequency (Hz) 320 Stationary Approaches 5) The same process occurs for light as well as for sound. Use light as the wave in this problem. Suppose you use some very accurate equipment and measure the wavelength of a laser coming from a speeding car. You know the laser has a stationary frequency of 4.6296 X 1016 Hz. The shift in the frequency is 5.396138 X 109 Hz. You also happen to know that the speed of light is 2.99792 X 108 m/s. Find the speed of the car. Remember you are using light not sound as the wave so the wave speed is different than in the previous problems.

Doppler Effect Using Sound Page 9 of 10 6) A pitcher throws a cheap Radio Shack buzzer at a catcher. The buzzer emits a 225.6 Hz signal but the catcher hears 251.2 Hz. How fast did the pitcher throw the buzzer? Express your answer in ft/s, mi/h, m/s, and km/h. 7) How fast would the pitcher have to throw the ball in order for the catcher to hear twice the frequency? 8) In order to demonstrate the Doppler Effect, a student twirls a different buzzer around her head on the end of a 3 m long string in a horizontal circle (like we saw in the video). Some other students, standing outside the circle, hear the sound vary in pitch from a high frequency of 337.9 Hz to a low frequency of 320.7 Hz. Find the speed of the buzzer. (Hint: What would the stationary frequency have to be?) 9) A baseball containing a high frequency emitter is thrown past you and you record and analyze the frequency spectrum from the emitter. The results for the approaching and receding emitter are shown below. Find the speed of the baseball/emiiter. Express your answer in ft/s, mi/h, and km/h using dimensional analysis to convert from one set of units to the other. | | | | | | | | | | | | 13100 13200 15700 15800 Receding Frequency (Hz) Approaching Frequency (Hz) 10) The frequency of a particular color of light coming from a star is measured as 6.51 X 1014 Hz. The frequency of the same spectral line when measured from a source at rest in the lab is 6.48 X 1014 Hz. Is the star approaching or receding from earth? Find the speed of the star in m/s and mi/s. Remember you are using light not sound as the wave so the wave speed is different than in the previous problems. 11) Use the set of three graphs of car 3 handed out in lab to find the speed of that car in mi/h and km/h.

Doppler Effect Using Sound Page 10 of 10 Answers (Your answers may differ slightly from the answers below depending on which conversion factors you use.) 1) 110 ft/s, 75 mi/h, 120 km/h, 33 m/s 2) Lower frequency means car receding at 55 ft/s, 38 mi/h, 60 km/h, 17 m/s 3) 25 ft/s, 17 mi/h, 27 km/h, 7.6 m/s (f_stationary = 1320 Hz) 4) Stationary freq. = 308 Hz, Approaching freq. = 312 Hz, Speed = 14 ft/s or 15km/h 5) 34.943 m/s 6) 120 ft/s, 81 mi/h, 140 km/h, 38 m/s 7) 1100 ft/s or 330 m/s 8) 29 ft/s or 20 mi/h or 8.6 m/s 9) 98 ft/s, 67 mi/h, 108 km/h 10) Approaching at 1.38 X 106 m/s, 875 mi/s 11) Your answers will vary a bit depending on what readings you had for the frequencies but the speed should be around 33 mi/h or 54 km/h and probably only 2 sig figs.