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Waves

Question

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?

Zero

0.5 %

5 %

20 %

Solution

20 %

Given:-

$\Rightarrow ν_{o} = \frac{ν}{5} \Rightarrow ν_{o} = \frac{320}{5} \Rightarrow ν_{o} = 64 m / s$

When observer moves towards the stationary source then

$n' = (\frac{ν + ν_{o}}{ν}) n n' = (\frac{320 + 64}{320}) n n' = (\frac{384}{320}) n n' = \frac{384}{320}$

Hence percentage increase

$(\frac{n' - n}{n}) = (\frac{384 - 320}{320} \times 100) = (\frac{64}{320} \times 100) % (\frac{n' - n}{n}) = 20 %$