Solving the Doppler Effect for Ambulance Moving in Expressway

In summary, the conversation discusses the Doppler effect and its application in calculating the frequency ratio of a siren sound detected by an observer located at point O in different wind conditions. The frequency ratio is calculated using the formula f'=(v+vs)/(v°-v)f, where v is the wind velocity and vs is the sound velocity in calm air. When there is an east wind of 5m/s, the approximate value of (va/vb)-1 is (340+50/3+5)/340. However, the effect of the wind on the frequency of sound from point B is not clear. The distances given in the question may have an effect on the calculation, and sketching the wave-fronts may help
  • #1
Asla
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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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  • #2
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.
 

1. What is the Doppler Effect?

The Doppler Effect is the change in frequency of a wave when there is relative motion between the source of the wave and the observer. This results in a perceived change in the pitch or frequency of the sound.

2. How does the Doppler Effect apply to an ambulance moving in an expressway?

When an ambulance is moving in an expressway with its siren on, the sound waves emitted from the siren are compressed in front of the ambulance and stretched behind it due to the relative motion between the ambulance and the observer. This results in a higher pitch sound in front of the ambulance and a lower pitch sound behind it.

3. How can the Doppler Effect be solved for an ambulance moving in an expressway?

To solve the Doppler Effect for an ambulance moving in an expressway, the formula v = fλ can be used, where v is the speed of the ambulance, f is the frequency of the siren, and λ is the wavelength of the sound wave. This can be used to calculate the change in frequency of the sound wave as it moves towards and away from the observer.

4. What are the variables that affect the Doppler Effect for an ambulance moving in an expressway?

The variables that affect the Doppler Effect for an ambulance moving in an expressway include the speed of the ambulance, the frequency of the siren, and the distance between the ambulance and the observer. The speed and distance of the ambulance can be used to calculate the change in frequency, while the frequency of the siren remains constant.

5. How is the Doppler Effect for an ambulance moving in an expressway useful?

The Doppler Effect for an ambulance moving in an expressway can be useful in determining the speed of the ambulance and its direction of travel. It can also help other drivers on the road to be aware of the presence of the ambulance and make way for it to pass. Additionally, it can aid emergency responders in reaching their destination more efficiently and potentially saving lives.

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