Solving the Doppler Effect for Ambulance Moving in Expressway

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The discussion focuses on calculating the frequency changes of an ambulance siren as it moves past an observer, considering the effects of wind. The ambulance travels at 60 km/hr with a siren frequency of 880 Hz, and the sound velocity in calm air is 340 m/s. An east wind of 5 m/s and a north wind of 5 m/s are analyzed for their impact on the observed frequencies at points A and B. The key challenge is understanding how the wind affects the sound waves, particularly for the frequency detected at point B, where the sound travels against the wind. The distances provided do not directly influence the frequency change but are relevant for visualizing the wave fronts.
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Homework Statement


An ambulance is moving in an expressway at a speed of 60km/hr from East to West(from A to B) as shown in the figure with a siren of 880Hz. Let the frequecies of the siren sound detected by an observer located at point O be Va and Vb as the ambulance just passes point A and B respectively.Point C is just to the North of O and OC=AC=BC=100m. Here the sound velocity in calm air is 340m/s.
i)Incase there is an east wind of 5m/s(18km/hr), what is the approximate value of (va/vb)-1
i)Incase there is a North wind of 5m/s(18km/hr),what is the approxiamate value of (va/vb)-1
attachment.php?attachmentid=59776&d=1371910117.png

Homework Equations


doppler effect
f'=(v+vs)/(v°-v)f

The Attempt at a Solution


I ignored the frequency values and concentrated on the ratios of change of frequency but I cannot comprehend how the frequency will change in the vb case.As for Va the wind will definitely reduce the frequency so that the ratio will be
(340+50/3+5)/340.
could someone help me on how the frequency for vb will change?
Do the distances given have any effect on the question?
 

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Hint:
When the wind is coming from the east, so the sound from B has to travel against the wind to get to O.
It can help to sketch in the whole wave-fronts.
 

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