Doppler Effect I: Surface Water Waves

LivePhoto Physics Activity 22 Name: ______Page 1 of 4 Doppler Effect I: Surface Water Waves

Have you ever noticed that when a train or car moves past you rapidly its whistle or horn seems to change to a lower note? In 1842 an Austrian Physicist, Hans Christian Doppler, asserted that sound waves emitted by a moving train would have a higher frequency when moving toward a listener and a lower frequency when moving away. For surface waves in water, Doppler predicted the same type of frequency shift. In particular, a decrease in the frequency of waves propagating behind a source that moves away at a speed vs can be predicted using the Doppler equation

v w f B  f 0 (Eq. 1: frequency behind a moving source) v w  v s where vw is the speed of wave propagation in water and f0 is the frequency of the waves created by a stationary source. Doppler also predicted that the frequency increase in front of a source is given by  v w f F  f 0 (Eq. 2: frequency in front of a moving source) v w  v s Modified Doppler effect equations are used to measure blood flow rates in arteries and the rates at which objects in outer space that emit electromagnetic wave are receding from us as the Universe expands. Your goal in this assignment is to verify the Doppler Equations for surface waves in water by using Logger Pro to analyze two high speed (120 fps) QuickTime movies. One movie shows the propagation of surface waves created by a stationary source disturbing the water surface at a steady rate. The other movie shows the same source moving to the right at a constant speed, vs. Before starting you should view these movies: and .

E W W E

Figure 1: A single frame showing the top view of water Figure 2: A single frame showing the top view of water waves when the wave source is stationary and oscillating at waves when the same 20 Hz wave source moves from a set frequency of 20 Hz. West to East.

Physics with Video Analysis 22 - 1 Name: ______Page 2 of 4 1. Preliminary Questions

Note: You will receive full credit for each prediction made in this preliminary section whether or not it matches conclusions you reach in the next section. As part of the learning process it is important to compare your predictions with your results. Do not change your predictions! (a) Examine the photograph in Figure 1. Also open the movie in QuickTime Player and advance the movie frame-by-frame using the computer forward arrow key . Does the frequency along the surface of the water appear to change in any direction from the source (i.e., N, S, E or W)? Are there any directions in which the frequency seems to be larger or smaller? Are there any directions in which the frequency seems to be the same as that for the stationary source? Explain the reasons for your answer.

(b) Examine the photograph in Figure 2. Also open the movie in QuickTime Player and examine it by advancing the movie frame-by-frame. Note that the source is moving from W to E. Does the frequency along the surface of the water appear to change in any direction from the source? Are there any directions in which the frequency seems to be larger or smaller? Are there any directions in which the frequency seems to be the same as that for the stationary source? Explain the reasons for your answer.

2. Activity-Based Questions

(a) Calculate the propagation speed of the stationary source water waves. Open the Logger Pro file entitled and use video analysis to determine the speed of propagation of the waves created by the stationary source in cm/s. Describe your procedure and record your results. Hint: You only need to track one point on a single wave crest as it moves along a straight line toward the edge of the ripple tank. It’s easiest to pick a basic direction such as north or west.

v = m/s w

(b) Measure the wave frequency, f0, caused by wave generator: How many wave crests pass by a point during each second in the movie ? This is how wave frequency in Hertz is defined. Open the file that has the movie inserted in it. If you pick a point in front of the wave source, and then count crests for a known duration, you can measure the frequency, f0, in Hertz for the waves created by the stationary source. Explain your procedure and record your value. Comment on how well your measured result compares with the 20 Hz setting used to generate the waves. Is the setting accurate? 22 - 2 Physics with Video Analysis Note: When advancing a movie that has been inserted into Logger Pro frame by frame, the frame number, time, and the (x,y) location of your mouse time appear at the top right of each frame. You can click on the right arrow key on the Logger Pro screen to advance the frames.

f = 0 Hz

(c) Moving Source–Measure the speed of the source and the frequencies in front and behind it: Open the Logger Pro file entitled with the movie of the moving wave source inserted and do three measurements–

(1) Measure the speed of the source, vs ;

(2) Determine the frequency of the waves in front of the source, fF; and

(3) Determine the frequency of the waves in behind the source, fB. Explain your procedures and record your results in the boxes below. Hints: To measure the frequency in front of the source, pick a point on a wave crest that is due east of the source and use the same procedures your developed in 1(b). To measure the frequency behind the source, we use a similar method starting with a wave crest due west of the moving source

Measured Source Speed Measured Frequency in Front Measured Frequency in Back #Cycles #Cycles vs = m/s Total time s Total time s

fF Hz fB Hz

(d) Use the Doppler Equations to predict frequencies theoretically: You have measured the frequency of the source, f0, which creates the water waves in the tank. You’ve also measured the speed of the water waves, vw, when the source was stationary. Plug your measured values into the Doppler Equations (Eq. 1 and Eq. 2) to compute theoretical values for the shifted frequencies, fB and fF, based on your measurements. Show your work and report your results to three significant figures.

Physics with Video Analysis 22 - 3 Name: ______Page 4 of 4 3. Reflections on Your Findings

(a) Comparing Theory with Experiment. How do your measured values for the frequencies fB and fF you reported in 2(c) compare with the theoretical values obtained from the Doppler Equations in 2(d)? Are they the same or different? Are they within 5% of each other?

(b) Application to Biology: Suppose the source of surface water waves is stationary (as in ) so that vs = 0.00 m/s. Consider a water strider moving along the surface away from the wave source at what it thinks is a very slow speed of vws = 0.10 m/s. Will the apparent wave frequency the strider measures increase, decrease, or stay the same? Explain.

Figure 2: Water striders can skim along the surface of water at an amazing speed of up to 150 cm/s.

22 - 4 Physics with Video Analysis