The Doppler equation presented in the text is valid when the motion between the
ID: 1522015 • Letter: T
Question
The Doppler equation presented in the text is valid when the motion between the observer and the source occurs on a straight line so that the source and observer are moving either directly toward or directly away from each other. If this restriction is relaxed, one must use the more general Doppler equation where theta_0 and theta_s are defined in Figure P13.71a. Use the preceding equation to solve the following problem. A train moves at a constant speed of v = 25.0 m/s toward the intersection shown in Figure A car is stopped near the crossing, 30.0 m from the tracks. The train's horn emits a frequency of 500 Hz when the train is 40.0 m from the intersection, (a) What is the frequency heard by the passengers in the car? (b) If the train emits this sound continuously and the car is stationary at this position long before the train arrives until long after it leaves, what range of frequencies do passengers in the car hear? (c) Suppose the car is foolishly trying to beat the train to the intersection and is traveling at 40.0 m/s toward the tracks. When the car is 30.0 m from the tracks and the train is 40.0 m from the intersection, what is the frequency heard by the passengers in the car now?Explanation / Answer
a) frequency heard by passenger = [(343)/(343 - 25 * 40/50) ] * 500
= 530.96 Hz
b) Lowest frequency heard = [(343)/(343 + 25 ) ] * 500
= 466.03 Hz
Highest frequency heard = [(343)/(343 -25 ) ] * 500
= 539.308 Hz
=> Range of frequency = 466.03 Hz to 539.308 Hz
c) frequency heard by passenger = [(343 + 40 * 30/50)/(343 - 25 * 40/50) ] * 500
= 568.11 Hz
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