Question

The change in frequency due to Doppler's effect does not depend on

• A. The speed of the source
• B. The speed of the observer
• C. The frequency of the source
• D. Separation between the source and the observer

Answer 1

The correct option is D

Separation between the source and the observer

The explanation for the correct option

In the case of option D,

1. Doppler's effect is the apparent variation in frequency between when sound or light waves leave a source and when they reach an observer, which is induced by the observer's and the wave source's relative velocity.
2. The frequency due to the Doppler effect is,
   $f=f_0\frac{\left(V\pm V_0\right)}{\left(V\pm V_s\right)}$
3. The frequency does not depend on the separation between the source and the observer.
4. The frequency of the real source does not vary.
5. Only the wavelength changes for the traveling observer (at the source), whereas both frequency and wavelength change for the stationary observer (as a result of the doppler shift).

The explanation for the incorrect options:

In the case of option A,

1. When the source moves faster than the waves, the Doppler effect occurs.
2. A distinct phenomenon occurs when the source moves at the same or faster speed as the wave.
3. Thus, option A is incorrect.

In the case of option B,

1. The effect is amplified as the relative speed increases.
2. When there is relative motion between the observer and the source, the Doppler effect happens not only for sound but for any wave.
3. Thus, option B is incorrect.

In the case of option C,

1. The Doppler effect isn't responsible for the frequency shift.
2. The temporal Doppler effect is the cause of this. The frequency emitted by the source, according to Special Relativity, redshifts as the object accelerates. However, it is suitable.
3. This is precisely what occurs with GPS satellite clocks. The clock slows down as they move faster.
4. Thus, option C is incorrect.

Hence, option D is the correct answer.