Wave Motion 4 Question 8
8. A train is moving on a straight track with speed $20 ms^{-1}$. It is blowing its whistle at the frequency of $1000 Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is close to (speed of sound $=320 ms^{-1}$ )
(2015 Main)
(a) $12 \%$
(b) $6 \%$
(c) $18 \%$
(d) $24 \%$
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Answer:
Correct Answer: 8. (a)
Solution:
- Observer is stationary and source is moving.
During approach, $f _1=f \frac{v}{v-v _s}$
$$ =1000\left(\frac{320}{320-20}\right)=1066.67 Hz $$
During recede, $f _2=f\left(\frac{v}{v+v _s}\right)$
$$ =1000\left(\frac{320}{320+20}\right)=941.18 Hz $$
$\mid \%$ change in frequency $\mid=\left(\frac{f _1-f _2}{f _1}\right) \times 100 \approx 12 \%$
