Question

The diagram below shows the peaks produced by a wave source that is moving to the right, approaching observer A and receding from observer R. Again, the first peak produced (at time t is shown in light green, the second is shown in dark green, and the third is just about to be produced at the point shown. The wave again has a wavelengthA and a period T.

1. On the diagram, mark with a star the position of the source of the wave when it produced the first peak. With a square, mark the position of the source of the wave when it produced its second peak.

2. What is the distance between the star you’ve drawn and the square you’ve drawn, in terms of previously-defined quantities? (Hint: How long did it take the source to cover this distance, and how quickly did it move?)

3. The first peak produced by the wave source is just now reaching observer A. What distance must the second peak travel before it reaches observer A? Answer in terms of λ and your answer to question 2.

4. How long will it take before the second peak reaches observer A? (Hint: What distance must the wave travel, and how quickly will it travel this distance?)

5. Your answer to question 4 is the period that observer A would record for this wave, that is, the time interval between successive peaks as they reach observer A. What frequency would observer A record for the wave?

6. Show that your answer to question 5 is consistent with the Doppler shift formula given in the text: $f_{+}=\frac{f_{s}}{1-\frac{v_{s}}{v}}$ . You may provide your work on the back of this sheet

Answer 1

(2) Since, this wave is produced at certain interval of time, called time period T. speed ofsource = v,(given) So, distance between X to square mark = d = v,T successive distance of wave is one wavelength. So, distance traveled by 2 nd waved'-v,T 4 since, speed of wave= v= time taken by 2 wave to reach toA-T'-

5, frequency = f'=T'--yT 6, speed of wave = v then, above expression can be written as since 1- f" ,=- Ans. V.