# The Doppler Effect Revision Notes

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12.2The Doppler Effect

In these revision notes for The Doppler Effect, we cover the following key points:

• What happens to the wavelength and frequency of a wave when the source and the receiver are moving in respect to each other?
• What is the Doppler Effect in waves?
• How the Doppler Effect is applied in sound waves?
• How the Doppler Effect is applied in light waves?
• What is the general equation of the Doppler Effect in waves?

## The Doppler Effect Revision Notes

When a wave source is moving in a certain direction, the wavelength decreases in the moving direction and increases in the opposite side. This means the sound frequency also changes compared to the original frequency emitted by the source.

By definition, the effect of frequency change when the source and the detector are in relative motion to each other is known as the Doppler Effect.

There are three possible cases of source and detector movement in respect to each other. They are:

1. Detector moving, source stationary
2. Source moving, detector stationary
3. Both detector and source are moving

When the detector is moving and the source is stationary, we have

f = v + vd/v × f0

for the new frequency when the detector is moving towards the source and

f = v - vd/v × f0

for the new frequency when the detector is moving away from the source.

If the source is moving and the detector is stationary, we have

f = v/v - vs × f0

when the source is moving towards the stationary detector and

f = v/v + vs × f0

when the source is moving away from the stationary detector.

When combining all the above equations, we obtain the general Doppler Effect formula

f = v ± vd/v ± vs × f0

The signs are determined by considering the relative movement of source and receiver in respect to each other.

The Doppler Effect in light waves occurs in a similar way as in sound waves. The only difference is the introduction of a new factor, β = v/c in the formula of the new light frequency, where v is the relative speed of the moving object to the source and c is the speed of light in vacuum (c = 3 × 108 m/s). There are two possible cases in this regard:

1. When source and detector are separating from each other. The formula of frequency for the Doppler Effect in this case is:

f = f0 × √1 - β/1 + β

The new frequency will be lower than the original one. Therefore, a phenomenon known as "red-shift" does occur. It means the detected light frequency will shift towards the red part of visible light spectrum, as red light represents the part of the visible light spectrum with the lowest frequency.

2. When source and detector are approaching each other. In this case, we have:

f = f0 × √1 + β/1 - β

Obviously, the new frequency is higher than the original one. Therefore, a phenomenon known as "blue-shift" does occur. It means the detected light frequency will shift towards the blue part of visible light spectrum as blue light represents a part of the visible light spectrum with high frequency (it should have been violet, but violet belongs to the family of blue light).

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