A train is moving with a speed of \(10 m/s\) towards a platform and blows a horn with frequency \(400 Hz\). Find the frequency heard by a passenger standing on the platform. Take speed of sound = \(310 m/s\).
- 405 Hz
- 425 Hz
- 380 Hz
- 413 Hz
The Correct Option is D
Approach Solution - 1
The frequency heard by the passenger on the platform will be different from the actual frequency of the horn due to the Doppler effect, which is the change in frequency of a wave in relation to an observer who is moving relative to the source of the wave.
The formula for the frequency observed due to Doppler effect is:
\(f' = f \frac{(v + u)}{ (v + vs)}\)
Where:
f = actual frequency of the horn
f' = frequency observed by the passenger
v = speed of sound
u = speed of the train towards the platform
vs = speed of the passenger towards the train (assumed to be zero in this case)
Given,
actual frequency of horn, f = 400 Hz
speed of sound, v = 310 \(\frac{m}{s}\)
speed of train, u = 10 \(\frac{m}{s}\)
speed of the passenger towards the train, vs = 0
Substituting these values in the formula, we get:
\(f' = 400\frac{(310 + 10)}{ (310 + 0)}\)
f' = 413 Hz (approx)
Therefore, the frequency heard by the passenger on the platform is 413 Hz (Option D).
Answer. D
Approach Solution -2
\(f' = f[\frac{(v-v0)}{(v-vs)}]\)
\(f' = 400[\frac{(310-0)}{(310-10)}]\)
\(f' = \frac{4}{3}(310)Hz\)
\(f' ≃ 413 Hz\)
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Concepts Used:
Doppler Effect
The Doppler effect is a phenomenon caused by a moving wave source that causes an apparent upward shift in frequency for observers who are approaching the source and a visible downward change in frequency for observers who are retreating from the source. It's crucial to note that the impact isn't caused by a change in the source's frequency.
The Doppler effect may be seen in any wave type, including water waves, sound waves, and light waves. We are most familiar with the Doppler effect because of our encounters with sound waves