JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Waves & Sound

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When a car is approaching the observer, the frequency of horn is 100 Hz . After passing the observer, it is 50 Hz . If the observer moves with the car, the frequency will be

\frac{X}{3} Hz

where

x =

____

Answer: 200

Solution

Using the Doppler effect:

Approaching:

f_{1} = 100 = f_{0} (\frac{C}{C - v _{s}})

Receding:

f_{2} = 50 = f_{0} (\frac{C}{C + v _{s}})

Dividing:

\frac{f _{1}}{f _{2}} = 2 = \frac{C + v _{s}}{C - v _{s}}

2 C - 2 v_{s} = C + v_{s}

v_{s} = \frac{C}{3}

Substituting back:

100 = f_{0} \times \frac{C}{C - C /3} = f_{0} \times \frac{3}{2}

f_{0} = \frac{200}{3}

Therefore,

x = 200

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Integer answer

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