Concept explainers
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 θo and θs are defined in figure P13.7la. 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 P13.71b. 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?
(a)
The frequency heard by the passengers in the car.
Answer to Problem 71P
The frequency heard by the passengers in the car is
Explanation of Solution
The Doppler equation is given by,
Here,
In this case the value of
Conclusion:
Since the train is
Substitute
Therefore, The frequency heard by the passengers in the car is
(b)
The range of frequencies that heard by the passenger.
Answer to Problem 71P
The range of frequencies that heard by the passenger is from
Explanation of Solution
The value of
Conclusion:
Substitute
Substitute
Therefore, The range of frequencies that heard by the passenger is from
(c)
The frequency heard by the passengers in the car when the car is
Answer to Problem 71P
The frequency heard by the passengers in the car when the car is
Explanation of Solution
Since the rain is
Substitute
Conclusion:
Therefore, The frequency heard by the passengers in the car when the car is
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Chapter 13 Solutions
Principles of Physics: A Calculus-Based Text
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