A car has a horn which sounds at 490 Hz. The car moves at a constant 13 m/s whil
ID: 1896506 • Letter: A
Question
A car has a horn which sounds at 490 Hz. The car moves at a constant 13 m/s while the horn sounds (Assume that vsound = 343 m/s)(a) What frequency of sound will a stationary observer hear as the car approaches?
Hz
(b) What frequency of sound will a stationary observer hear as the car moves away from them?
Hz
(c) As the car approaches a solid wall the driver hears a beat frequency. What is it?
Hz
(d) If the car horn is the fundamental frequency of a tube closed on one end what is the length of the tube?
m
Explanation / Answer
(a) for a stationary observer in case of car approaching, frequency is :
( u= u_0 rac{c}{c+v_s})
where c is speed of sound and vs is the speed of the car if it moves away, thus vs = -13 m/s
also given, c=343 m/s
thus, ( u=490*343/(343-13)=509.3 Hz)
(b) in this case vs = 13 m/s
thus ( u=490*343/(343+13)=472.1 Hz)
(c) When car approaches the wall the frequency of sound in air which approaches wall given by the the part (a). This then reflects off the wall and then approaches the driver. the frequency of this reflected then is doppler shifted in the frame of driver and combines with the original frequency produced by the horn in the frame of driver.
Thus, we need to find out the frequency of the wave reflected off the wall in the frame of driver, in this case the driver acts as an observer and wall as a source thus,
( u'= u (from part a)*(c+v_o)/c)
here v0 is positive when the observer approaches the source. here car is driving towards the wall, thus vo = 13m/s.
thus, ( u'=509.3*(343+13)/343=528.6 Hz)
thus beat frequency is ( u_{beat}= u'- u_0=528.6-490=38.6 Hz)
(d) For a tube closed at one end, the fundamental wavelength is
(lambda_0=L/4)
Thus fundamental frequency is ( u_0=c/lambda=4c/L)
thus, (L=4c/ u_0=4*343/490=2.8 m)
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