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Chapter 17: Q56P (page 509)

An ambulance with a siren emitting a whine at 1600Hzovertakes and passes a cyclist pedaling a bike at 2.44m/s. After being passed, the cyclist hears a frequency of 1590Hz. How fast is the ambulance moving?

Short Answer

Expert verified

The ambulance is moving at 4.61m/s

Step by step solution

01

The given data

  1. The frequency of the siren is, f = 1600Hz.
  2. The speed of the cyclist is, vD = 2.44m/s.
  3. Frequency of the siren heard by the cyclist is, f' = 1590Hz.
02

Understanding the concept of the Doppler Effect

Inserting the given values in the formula obtained from Doppler’s effect, we can find the speed of the ambulance.

Formula:

The frequency that is received by the listener as per the Doppler Effect,

f'=f(v+vD)(v+vs) …(i)

03

Calculation of the speed of ambulance

We know that the speed of sound is v = 343m/s

Using the formula of equation (i) and substitute all the value in this equation, the speed of the ambulance is given as:

1590Hz=1600Hz×343m/s+2.44m/s343m/s+vsvs=4.6125m/s=4.61m/s

Therefore, the speed of the ambulance is 4.61m/s.

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