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Q. The frequency of echo will be ____$Hz$ if the train blowing a whistle of frequency $320\, Hz$ is moving with a velocity of $36\, km / h$ towards a hill from which an echo is heard by the train driver. Velocity of sound in air is $330 \, m / s$.

JEE MainJEE Main 2022Waves

Solution:

The hill will be a secondary source.
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$f _1=$ frequency of the car w.r.t. the hill $f_1=\left(\frac{v}{v-v_s}\right) f=\left(\frac{330}{320}\right) \times 320=330 Hz$
$f _2=$ Frequency of the sound reflected by hill w.r.t. the car (echo)
$f _2=\left(\frac{ v + v _0}{ v }\right) f _1=\frac{(330+10)}{330} \times 330=340\, Hz$