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The police car with its 300-Hz siren is moving away from the warehouse at a speed of 16.0 m/s . . . What frequency does the driver of the police car hear reflected from the warehouse?. . Use 344m/s for the speed of sound in air.

Verified Answer :

frequency heard by listener: fl = ? 
frequency of source: fs = 300 Hz 
velocity of listener: vl = 16 m/s 
velocity of source: vs = 0 
velocity of sound in air: c = 344 m/s 

fl = fs [(c – vl)/c] = 300[(344-16)/344]
        =286.04 Hz

Answer;

= 286.05 Hz

Explanation;

We can use or employ the Doppler equation:

fl = fs[(c±vl)/(c-/+vs)

where,

  • frequency heard by listener: fl = ?
  • frequency of source: fs = 300 Hz
  • velocity of listener: vl = 16 m/s
  • velocity of source: vs = 0
  • velocity of sound in air: c = 344 m/s

The source will be the origin of the reflected signal (i.e.the

warehouse). So that, velocity of source: vs = 0

The listener is the policeman moving away from the source

with velocity: vl = 16 m/s

Therefore, the Doppler equation. becomes:  

fl = fs [(c – vl)/c]

= 300[(344-16)/344]

= 286.04 Hz

where, fl is the frequency of the reflected sound heard by

the police officer.

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