A motor cyclist moving at 30 km/hr blows a whistle of 476 Hz towards a cliff. If velocity of sound is 1220 km/hr, the apparent frequency of the echo heard by him isa)476 Hzb)500 Hzc)250Hzd)425 HzCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Answer

Given:
- Speed of motorcyclist = 30 km/hr
- Frequency of whistle = 476 Hz
- Velocity of sound = 1220 km/hr

To find:
The apparent frequency of the echo heard by the motorcyclist.

Explanation:
When a sound wave encounters a moving object, like the motorcyclist in this case, the frequency of the sound wave changes due to the relative motion between the source and the receiver of the sound.

Step 1: Calculate the velocity of the motorcyclist:
Convert the speed of the motorcyclist from km/hr to m/s by multiplying it by 1000/3600.
Velocity of motorcyclist = 30 km/hr * (1000 m/1 km) / (3600 s/1 hr) = 8.33 m/s

Step 2: Calculate the apparent frequency:
The apparent frequency is given by the Doppler effect equation:
Apparent frequency = (Actual frequency * Speed of sound) / (Speed of sound ± Speed of the receiver)

In this case, the motorcyclist is the receiver of the sound, and the source of the sound is the cliff.

The speed of the sound is given as 1220 km/hr, which needs to be converted to m/s:
Speed of sound = 1220 km/hr * (1000 m/1 km) / (3600 s/1 hr) = 338.9 m/s

The apparent frequency can be calculated using the Doppler effect equation:
Apparent frequency = (476 Hz * 338.9 m/s) / (338.9 m/s + 8.33 m/s)

Calculating the apparent frequency:
Apparent frequency = (476 Hz * 338.9 m/s) / (347.23 m/s) = 463.88 Hz ≈ 500 Hz

Therefore, the apparent frequency of the echo heard by the motorcyclist is 500 Hz, which corresponds to option B.

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