Doppler effect and relative motion

In summary, there is a question about the Doppler effect and relative motion involving a whistle with a frequency of 1200 Hz traveling south at 30.0 m/s and an observer traveling north at 18.0 m/s. Using the equation f=(v/v+vs)fs, the apparent frequency was calculated to be 1051 Hz. However, it was pointed out that this equation is incorrect for this scenario. The correct equation should include both velocities of the source and observer and take into account the direction of the observer's velocity.
  • #1
trulyfalse
35
0
Hello everyone! I need some help with a Doppler effect/relative motion question.

Homework Statement


A whistle with a frequency of 1200 Hz is traveling south at a velocity of 30.0 m/s. You are traveling north away from the whistle at a speed if 18.0 m/s. If the speed of sound is 340 m/s, what is the apparent frequency of the whistle as heard by you? (Answer: 1044 Hz)

Homework Equations


f=(v/v+vs)fs

The Attempt at a Solution


Relative to myself, the train is moving at a speed of 48 m/s south and therefore away from me. Using the aforementioned equation I calculated frequency at 1051 Hz. Is the answer key wrong or am I missing something?
 
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  • #2
The equation you have used is incorrect for the case when both source and observer are moving. Can you check in your notes or book for the correct one? It will have both speeds in it, vo and vs. You will also need to note that the velocity of the observer vo in the equation you should find will be negative if he's moving away from the source.
 

1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. This effect can be observed in various types of waves, such as sound waves, light waves, and water waves.

2. How does the Doppler effect relate to relative motion?

The Doppler effect is directly related to relative motion. It occurs when there is a difference in the speed or direction of motion between the source of the wave and the observer. The relative motion between the two determines the amount of frequency or wavelength shift observed.

3. What are some real-life examples of the Doppler effect?

The Doppler effect can be observed in everyday situations, such as the change in pitch of a siren on a moving ambulance as it passes by, the change in the color of a star as it moves away from or towards Earth, and the change in frequency of a train horn as it approaches and passes by a stationary observer.

4. How is the Doppler effect used in science and technology?

The Doppler effect has many practical applications in science and technology. It is used in radar and sonar systems to determine the speed and direction of moving objects. It is also used in medical imaging techniques, such as ultrasound, to create images of internal structures and detect abnormalities.

5. Can the Doppler effect be observed in all types of waves?

Yes, the Doppler effect can be observed in all types of waves, including electromagnetic waves, mechanical waves, and water waves. However, the amount of frequency or wavelength shift may vary depending on the type of wave and the relative motion between the source and observer.

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