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Junior Executive (ATC) Official Paper 3: Held on Nov 2018 - Shift 3

Option 1 : c

Junior Executive (ATC) Official Paper 1: Held on Nov 2018 - Shift 1

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__Concept:__

Doppler Effect: An increase or decrease in the frequency of sound, light, or other waves that are observed by the observer due to the movement of the source and observer towards (or away from) each other is known as Doppler Effect.

The apparent frequency heard by the observer is given by the formula:

\(f=f_0\left ( \frac{v-u_o}{v-u_s} \right )\)

where,

u0 = speed of observer with respect to the medium, considered positive (+) when it moves towards the source and **negative (-) when it moves away from the source.**

us = speed of source with respect to the medium, considered positive (+) when it moves towards the observer and **negative (-) when it moves away from the observer.**

__Calculation:__

Given, stationary source (us) = 0

Speed of light in medium = c = 3x10^{8} m/s

Speed of the observer (u0) = 0.86c m/s

Source frequency = (f0)

Apparent frequency (f') = ?

Apparent frequency,

\(f' = \frac{{\nu + {u_0}}}{{\nu - {u_s}}}{f_0}\)

Here us = 0

\(f' = \frac{{c+ {0.86c}}}{{}{{c}}}{f}=1.86f\)

Actual wavelength is:

\(λ=\frac{c}{f}\)

And apparent wavelength is given as:

\(λ'=\frac{c}{f'}=\frac{c}{1.86f}\)

It can be written as;

\(λ'=\frac{λ}{1.86}\)

Now, the speed of light appeared to the observer = λ'f'

\(=\frac{\lambda}{1.86}\times{1.86f} = c\)

1. When an observer is moving towards the stationary source of the sound, then the apparent frequency will be greater than the real frequency.

2. When the observer is stationary and the source is moving away from the observer, then the apparent frequency will be less than the real frequency.