Derivation of Doppler effect?

Question

Answer

The derivation of the Doppler Effect equations is the most straightforward by starting with wavelength. The Doppler Effect equations for the change in wavelength or in frequency as a function of the velocity of the wave source and/or observer can be determined though simple and logical derivations.

Answer

Answer

Derivation of Doppler Effect:

Concept:

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 is commonly observed in sound waves, light waves, and other types of waves.

Key Formula:

The formula for the Doppler effect in terms of frequency is given by:

$$ f' = f \left( \frac{v + V_o}{v + V_s} \right) $$

where:
- $ f' $ is the observed frequency
- $ f $ is the emitted frequency
- $ v $ is the speed of the wave in the medium
- $ V_o $ is the velocity of the observer
- $ V_s $ is the velocity of the source

Derivation:

1. Let's consider a source emitting waves with frequency $ f $ and speed $ V_s $ and an observer moving towards the source with velocity $ V_o $.

2. The observer will receive waves with frequency $ f' $ due to the relative motion of the source and the observer.

3. By applying the principle of superposition and considering the relative velocities, we can derive the formula for the observed frequency as mentioned above.

4. This formula accounts for the change in frequency observed by the moving observer and is known as the Doppler effect.

Conclusion:

The Doppler effect is a fundamental concept in wave physics that explains the change in frequency or wavelength of waves due to the relative motion of the source and the observer. It has applications in various fields such as astronomy, meteorology, and medical imaging.

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