Question

A person going away from a factory on his scooter at a speed of 36 kmph listens to the siren of the factory. If the actual frequency of the siren is 700 hz and a wind is blowing along the direction of the scooter at 36 kmph, find the observed frequency heard by the person.
$\begin{aligned} & a)680Hz \\\ & b)510Hz \\\ & c)640Hz \\\ & d)600Hz \\\ \end{aligned}$

Answer 1

Find the speed of the scooter, speed of the wind blowing in the direction of scooter in mps mathematical unit. Next, use the doppler effect formula to find the frequency apparent using the actual frequency, speed of wind and scooter. The velocity of sound will be the sum of velocity of the sound and the velocity of the object, that is scooter.
Formula used:
${{f}^{1}}_{o}={{f}_{o}}(\dfrac{{{v}_{s}}+{{v}_{w}}-{{v}_{o}}}{{{v}_{s}}+{{v}_{w}}})$

Complete answer:
Let us convert the speed of scooter,
$\begin{aligned} & {{v}_{o}}=36\times \dfrac{5}{18} \\\ & {{v}_{0}}=10m{{s}^{-1}} \\\ \end{aligned}$
Let us find the speed with which the siren travels along the wind ,
As the speed of wind and scooter are in the same direction,
$\begin{aligned} & v=340+10 \\\ & \Rightarrow v=350m{{s}^{-1}} \\\ \end{aligned}$
According the doppler effect, the observed frequency is equal to,
$\begin{aligned} & {{f}^{1}}_{o}={{f}_{0}}(\dfrac{350-10}{350}) \\\ & {{f}^{1}}_{o}=700\times \dfrac{340}{350} \\\ & {{f}^{1}}_{o}=680Hz \\\ \end{aligned}$

So, the correct answer is “Option A”.

Additional Information:
The doppler effect is the change in frequency of a wave in relation to an observer who is moving relative to the view source. It is named after a physicist Christian doppler who described this phenomenon in 1842. The reason for the doppler effect is that when the source of the waves is moving towards the observer, the wave crest is emitted from a position closer to that of the previous crest for each you take slightly less time to receive lower than the previous view. Similar procedure goes to the recession.

Note:
The reason why the velocity of the scooter is negative in the doppler effect is because the scooter is travelling away from the siren in the above question. As it moves away, it gradually decreases, therefore it is taken as negative.