a) Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an

Question

a) Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching police car. After the police car passes, the observed frequency of the siren is 480 Hz. Determine the car’s speed from these observations.

b)
A train is moving parallel to a highway with a constant speed of 20.0 m/s. A car is traveling in the same direction as the train with a speed of 40.0 m/s. The car horn sounds at a frequency of 510 Hz, and the train whistle sounds at a frequency of 320 Hz.
(1) When the car is behind the train, what frequency does an occupant of the car observe for the train whistle?
(2) When the car is in front of the train, what frequency does a train passenger observe for the car horn just after the car passes?

Explanation / Answer

Given data : f01 = 560 hz

                   f02 = 480 hz

                   vs = 340 m/s ( velocity of sound )

                   vx = velocity of source ( police car )

Condition 1 when source approach observer : f01 =[ vs /( vs - vx )].fs ...........(1)

Condition 2 when source passes observer    : f02 = [vs /( vs + vx) ].fs ............(2)

eq(1) : eq (2) we get : f01 / f02 = ( vs + vx )/( vs - vx )

                                 7/6 = ( 340 + vx ) / ( 340 - vx )

solve this equation get vx = 26.15 m/s

Part b : ft = 320 hz    ;    fc = 510 hz   ;   vs = 340 hz

1) train is source and car is observer

   fc1 = [( vs + vc ) /( vs + vt)].ft

   fc1 = [(340 +40)/(340+20)].320

   fc1 = 337.78 hz

2) car is source and train is observer

    ft1 = [( vs + vt) / (vs + vc )].fc

    ft1 = [(340 + 20)/(340 + 40)].510

    ft1 = 483.16 hz

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