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(Houghton College)
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Date Posted: 11/30/2007 4:55:59 PM  Status: Live
Please Help!
Course Textbook Chapter Problem
Calculus Based Physics N/A 17 33
Question Details:
A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren producing sount at a frequency of 2500 Hz. (a) What frequency does the driver observe as the police car approaches? (b) What frequency does the driver detect after the police car passes him? (c) Repeat parts a and b for the case when the police car is traveling northbound.
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Date Posted: 11/30/2007 8:54:35 PM  Status: Live
Asker's Rating: Helpful   
Response:
The apparent frequency or the frequency whic you hear is  f1 = ()f

where f is the actual frequency, v is the velocity of sound and vs is the velocity of source. - sign is used when car is approaching you and + sign is used when car is moving away from you. This is called Doppler effect. When approaching, the frequency increases and while moving away, frequency decreases. Since you have not specified velocity of sound, i will consider it 340m/s
 
a) here relative to the dirver the velocity of police car is 25 + 40 (since they are approaching each other) = 65m/s = vs
so freq heard = [340 / (340 - 65) ]*2500 =  3090 Hz
 
b) here the relative to the driver, the velocity of police car is 40 - 25 =15m/s (as police car is moving away) = Vs
 
so freq heard = [340/(340+15)]*2500 = 2394 Hz
 
I think now you can go ahead with (c). If you are having difficulty ask me.
 
TIP: To check whether your answer is correct or not, remember when approaching, higher freq is heard and while moving away lower freq is heard compared to the actual freq
 
ktqu's Comment:
How does it change if they are both going northbound?




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