Doppler Effect Homework: Source Moving Away from Observer

In summary, the wavelength of the sound waves, as measured by the observer, would be λ + VT due to the movement of the source away from the stationary observer at speed V. This can be derived by considering two successive wavefronts leaving the source and the distance they have traveled towards the observer.
  • #1
thornluke
37
0

Homework Statement


A source of sound emits waves of wavelength λ, period T and speed v when at rest.
The source moves away from a stationary observer at speed V, relative to the observer. The wavelength of the sound waves, as measured by the observer is

A. λ + vT
B. λ - vT
C. λ + VT
D. λ - VT

Homework Equations


f' = f(v / (v±u) moving source
f' = f((v±u) / v) moving observer

The Attempt at a Solution


Since the source is moving away, it is safe to say assume that the frequency would be lower as the wavelengths emitted from the moving source would become more and more apart.

Therefore f' < f of moving source.

But up till here, I am lost...Please explain! I want to understand this question.

Cheers.
 
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  • #2
Well, if you know λ will be larger, that eliminates 2 answers. so the only question is whether λ will increase be vT or VT. Which makes more sense?
 
  • #3
superdave said:
Well, if you know λ will be larger, that eliminates 2 answers. so the only question is whether λ will increase be vT or VT. Which makes more sense?

C since v is the speed at rest, whilst V is the speed when the source is moving away.
Is it possible to explain this by deriving different equations to λ + VT?
 
  • #4
thornluke said:
C since v is the speed at rest, whilst V is the speed when the source is moving away.
v is the speed of sound when the source is at rest, V is the speed of the source.
A question for you: what is the speed of the sound, as judged by the listener, when the source is moving away?
Is it possible to explain this by deriving different equations to λ + VT?
I don't understand the question. Are you asking how to derive the formula λ + VT?
Consider two successive wavefronts leaving the source. The first leaves the source. After time T it has advanced vT (=λ) towards the listener. Meanwhile, the source is VT further away. So when the second leaves the source it is VT+vT behind its predecessor. They will stay that far apart all the way to the listener.
 
  • #5


The Doppler Effect is a phenomenon that describes the change in frequency of a wave as a result of relative motion between the source of the wave and the observer. In this scenario, the source is moving away from the observer at a speed V. This means that the distance between the source and the observer is increasing over time.

As the source moves away, the wavelength of the sound waves will increase, since the waves are being stretched out over a larger distance. This means that the frequency of the sound waves will decrease, since frequency and wavelength are inversely proportional (as one increases, the other decreases).

Using the equation f' = f((v±u) / v) for a moving observer, we can see that the frequency of the sound waves as measured by the observer (f') will be lower than the frequency emitted by the source (f). This is because the relative speed between the source and observer is now (v+V), where V is the speed of the source.

To determine the exact relationship between the wavelength and frequency, we can use the equation c = fλ, where c is the speed of the wave. We know that c = vT, since the source is at rest. Therefore, we can rearrange the equation to solve for wavelength:

λ = c / f

Substituting in the values for c and f' from the equation above, we get:

λ = (v+V)T / f'

Since we know that f' < f, we can see that the wavelength will be longer when measured by the observer, meaning that the answer is A. λ + vT. This is because the wavelength will increase by a factor of vT due to the relative motion between the source and observer.

I hope this explanation helps you understand the concept of the Doppler Effect and how it applies to this particular scenario. Let me know if you have any further questions.
 

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 wave source.

2. How does the Doppler Effect apply to homework?

In the context of homework, the Doppler Effect can be used to calculate the change in frequency or wavelength of a source moving away from an observer, which may be relevant in physics or astronomy assignments.

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

The formula for calculating the Doppler Effect is: Δf = f0 * (v ± vo) / (v ± vs), where Δf is the change in frequency, f0 is the original frequency, v is the speed of the wave, vo is the velocity of the observer, and vs is the velocity of the source.

4. What are some real-life examples of the Doppler Effect?

The Doppler Effect can be observed in various real-life situations, such as the change in pitch of a siren as an ambulance passes by, the change in frequency of a train whistle as it approaches and then passes, and the redshift of galaxies in astronomy.

5. How does the Doppler Effect homework relate to physics?

The Doppler Effect is a key concept in physics, as it helps to explain the observed changes in frequency and wavelength of waves in various situations. This understanding is essential in fields such as acoustics, electromagnetism, and fluid dynamics.

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