Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A speed motorcyclist sees a traffic jam ahead of him. He slows down to $36 \text{ km/h}$ . He finds that traffic has eased and a car moving in front of him at $18 \text{ km/h}$ is honking at a frequency of $1392 \text{ Hz}$ . If the speed of sound is $343 \text{ m/s}$ , the frequency of the honk as heard by him will be

$1332 \text{ Hz}$

$1372 \text{ Hz}$

$1412 \text{ Hz}$

$1454 \text{ Hz}$

Step-by-Step Solution

Identify the Given Data: Velocity of the observer (motorcyclist), $v_o = 36 \text{ km/h} = 36 \times \frac{5}{18} \text{ m/s} = 10 \text{ m/s}$ . Velocity of the source (car), $v_s = 18 \text{ km/h} = 18 \times \frac{5}{18} \text{ m/s} = 5 \text{ m/s}$ . Actual frequency of the honk, $f = 1392 \text{ Hz}$ . Speed of sound, $v = 343 \text{ m/s}$ .
Determine the Relative Motions: The motorcyclist is behind the car. Both are moving in the same direction.

The observer (motorcyclist) is moving towards the source, which tends to increase the apparent frequency. Thus, the numerator in the Doppler formula will be $(v + v_o)$ .
The source (car) is moving away from the observer, which tends to decrease the apparent frequency. Thus, the denominator will be $(v + v_s)$ .

Apply the Doppler Effect Formula: The apparent frequency $f'$ is given by: $f' = f \left( \frac{v + v_o}{v + v_s} \right)$ Substitute the values into the formula : $f' = 1392 \left( \frac{343 + 10}{343 + 5} \right)$ $f' = 1392 \left( \frac{353}{348} \right)$ $f' = 4 \times 353 = 1412 \text{ Hz}$ Therefore, the frequency of the honk heard by the motorcyclist is $1412 \text{ Hz}$ .

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