Doppler Effect- small question on formula setup.

In summary, the problem involves using the Doppler effect formula to find the velocity of a moving car based on changes in frequency observed while passing a parked car. After setting up the equation using the given frequencies and the speed of sound, the formula can be rearranged to solve for velocity by setting the change in frequency equal to 95 Hz. The final solution will give the velocity at which the car is driving.
  • #1
Muntaballs
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0

Homework Statement



The security alarm on a parked car goes off and produces a frequency of 958 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 95 Hz. At what speed are you driving?



Homework Equations


Doppler effect formula:
F=Fo [(Vsound- Vobserver)/(Vsound-Vsource)]




The Attempt at a Solution



This should be an easy problem but I just don't know how to setup the equations. I need to find the velocity, but I don't know how to solve for V.

863=958 [(343-V)/(343-0)]

How do I solve for Velocity? I don't know how to rearrange the formula so that V is isolated on one side of the equation... Please help?
 
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  • #2
Use the formula twice. Once for the higher f observed when moving toward the source. Again for the lower f observed when moving away. Write that the higher f minus the lower f = 95. It is straightforward to solve that for v.
 

FAQ: Doppler Effect- small question on formula setup.

1. What is the formula for calculating the Doppler Effect?

The formula for the Doppler Effect is: fobs = fsource (v ± vobs) / (v ± vsource), where fobs is the observed frequency, fsource is the source frequency, v is the speed of sound/waves, vobs is the observed velocity, and vsource is the source velocity.

2. How does the Doppler Effect work?

The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It occurs because of the compression or stretching of the waves as the source and observer move closer or further apart.

3. What is the difference between the Doppler Effect for sound and light?

The main difference between the Doppler Effect for sound and light is the medium through which the waves travel. Sound waves need a medium (such as air or water) to travel through, while light waves can travel through a vacuum. Additionally, the speed of sound is much slower than the speed of light, so the Doppler Effect for sound is more noticeable in everyday situations.

4. How is the Doppler Effect used in real life?

The Doppler Effect has many practical applications in real life, such as in weather forecasting (using Doppler radar), in medical imaging (using Doppler ultrasound), and in astronomy (to measure the speed and distance of celestial bodies). It is also used in everyday situations, such as hearing the change in pitch of a siren as an ambulance passes by.

5. Can the Doppler Effect be observed with stationary objects?

Technically, the Doppler Effect requires the source or observer to be in motion. However, it can also be observed with stationary objects if the medium through which the waves travel is moving, such as a stationary person hearing the change in frequency of a sound wave caused by wind blowing towards them.

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