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A sound source is releasing a signal of constant frequency 330 Hz. f& $λ$ are frequency and wavelength observed by an observer. The velocity of sound in air is 330 $m s^{- 1}$ .
Column-I Column-II
P The observer & source move towards each other. 1 $λ = 1 m, f > 330 Hz$
Q
The observer and source are stationary, wind is
blowing towards source from observer.
2 $λ = 1 m, f = 330 Hz$
R
The source is stationary, wind is blowing from source to
observer and observer is moving away from the source.
3 $λ < 1 m, f > 330 Hz$
S
The source is stationary and observer is moving
towards source.
4 $λ = 1 m, f < 330 Hz$

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P $\to$ 3,Q $\to$ 2,R $\to$ 4,S $\to$ 2

P $\to$ 3,Q $\to$ 1,R $\to$ 4,S $\to$ 3

P $\to$ 3,Q $\to$ 2,R $\to$ 4,S $\to$ 1

P $\to$ 3,Q $\to$ none,R $\to$ 4,S $\to$ 1

answer is A.

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Detailed Solution

$λ = \frac{v}{f} = \frac{330}{330} = 1 m$

P : $A s s o u r c e a n d o b s e r v e r a r e m o v i n g t o w a r d s e a c h o t h e r f^{'} = f_{0} (\frac{u + u_{0}}{u - u_{s}})$

Frequency increases and wavelength decreases.

Q : $A s s o u r c e a n d o b s e r v e r a r e a t r e s t v_{O} = 0 a n d v_{S} = 0$

$w i n d i s b l o w i n g f r o m s o u r c e t o o b s e r v e r m o v i n g a w a y f r o m s o u r c e = f^{'} = f_{0} (\frac{u + u_{w} + u_{0}}{u + u_{w} - u_{s}}) = f_{0}$

Frequency remain same and wavelength also remain same.

R : $O b s e r v e r i s m o v i n g t o w a r d s s t a t i o n a r y s o u r c e = f^{'} = f_{0} (\frac{u + u_{w} - u_{0}}{u + u_{w}})$

Frequency decreases and wavelength remain same.

S : $f^{'} = f_{0} (\frac{u + u_{0}}{u})$

Frequency increases and wavelength remain same.

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