Frequency of sound received by an observer

[PSN03]

Homework Statement

A source and an observer are situated on two perpendicular tracks as shown in the figure the observer is at rest and source is moving with a speed 50m/s the source emits sound waves of frequency 90Hz which travel in the medium with velocity 200m/s the frequency of sound heard by observer when the source crosses the origin is

Relevant Equations

By dopler's equation we know that
f'=f(v±vo/v±vs)
Where
f'= new frequency
vo=velocity of observer
vs=velocity of source
v=velocity of sound

My thought process was this,
They are asking us to find the frequency of sound received by observer when the source reaches at origin. According to me when the source reaches origin there would be no component of source's velocity in the direction of observer, hence vs=0
vo=0 since the observer is stationary

Therefore by the formula I should get the answer as
f'=f(v±0/v±0)
=f
Hence no change in frequency should be observed. But my answer is wrong.
Lease tell me where am I going wrong?

 

[BvU]

How close is the observer to the crossing point of the tracks ?

 

[TSny]

Hence no change in frequency should be observed. But my answer is wrong.
Lease tell me where am I going wrong?

It takes time for the sound to travel from the source to the observer. At the instant when the source crosses the origin, the observer is hearing the sound that was emitted by the source at an earlier time (when the source was not yet at the origin). Some geometry will come into play. So, you need a good sketch of the situation.

 

[PSN03]

It takes time for the sound to travel from the source to the observer. At the instant when the source crosses the origin, the observer is hearing the sound that was emitted by the source at an earlier time (when the source was not yet at the origin). Some geometry will come into play. So, you need a good sketch of the situation.

Yes...I got it later. Thanks for your help and I feel so stupid for forgetting such a simple point.

 

[BvU]

No need to feel stupid. My first reaction was like yours. I wonder if the actual problem statement mentions something of a distance between observer and crossing point ?

 

[PSN03]

No need to feel stupid. My first reaction was like yours. I wonder if the actual problem statement mentions something of a distance between observer and crossing point ?

I guess the distance is enough for our answer to come right, though it isn't mentioned.