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3 years ago

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A train sounds its whistle as it approaches a tunnel in a cliff. The whistle produces a tone of 650 Hz and the train travels wit

h a speed of 21.2 m/s. Find the frequency heard by an observer standing near the tunnel entrance.

1 answer:

Alex777 [14]3 years ago

5 0

Answer: $f_{0}$ = 692.82Hz

Explanation: This question of ours is based on Doppler effect.The Doppler effect states that<em> if a source is producing sound at a specific frequency to an observer and there is a relative motion between the observer and the source, the frequency of sound perceived by the observer will be different from that of the original from the source. </em>

This represented mathematically below as

$f_{0} =\frac{v +v_{0} }{v -v_{s} } * f$

where

$f_{0}$ = observed frequency = ?

f = original frequency of sound source = 650Hz

v = speed of sound in air = 343m/s

$v_{0}$ = velocity of observer relative to the source = 0m/s ( the observer is standing, thus meaning he is not moving)

$v_{s}$ = velocity of sound source relative to the observer = 21.2m/s

by putting all of these in the formulae, we have that

$f_{0} = \frac{343 + 0}{343 -21.2} *650\\\\\\f_{0} = \frac{343}{321.8} * 650\\\\\\f_{0} = 692.98Hz$

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