C.5.1 Understanding the Doppler effect

The Doppler Effect: Frequency Shift Due to Relative Motion

1. Imagine standing by a road as a car speeds past.
2. The sound of the engine is high-pitched as it approaches, but drops suddenly as it moves away.
3. This change in pitch is a classic example of the Doppler effect.

Why Does the Frequency Change?

To understand the Doppler effect, we need to consider two scenarios:

1. Stationary Source and Moving Observer
2. Moving Source and Stationary Observer

Stationary Source and Moving Observer

1. When a source is stationary, it emits wavefronts that spread out evenly in all directions.
2. If the observer is moving towards the source, they encounter wavefronts more frequently, resulting in a higher observed frequency.
3. Conversely, if the observer is moving away, they encounter wavefronts less frequently, leading to a lower observed frequency.

Moving Source and Stationary Observer

1. When the source is moving, the wavefronts are compressed in the direction of motion and stretched in the opposite direction.
2. This causes the wavelength to decrease in front of the source and increase behind it.

Wavefront Representation: Visualizing the Doppler Effect

Stationary Source and Moving Observer

1. In this scenario, the wavefronts are concentric circles centered around the stationary source.
2. If the observer moves towards the source, they encounter wavefronts more frequently, resulting in a higher observed frequency.
3. If the observer moves away, they encounter wavefronts less frequently, leading to a lower observed frequency.

Moving Source and Stationary Observer

1. When the source is moving, the wavefronts are no longer concentric.
2. Instead, they are compressed in the direction of motion and stretched in the opposite direction.
   • Observer in Front of the Source: The wavefronts are closer together, resulting in a higher frequency and shorter wavelength.
   • Observer Behind the Source: The wavefronts are farther apart, leading to a lower frequency and longer wavelength.

The Doppler Effect for Light: Redshift and Blueshift

• The Doppler effect also applies to light waves.
• However, because the speed of light is so much greater than everyday speeds, the effect is only noticeable when the relative velocity is a significant fraction of the speed of light.

Redshift and Blueshift

• Redshift:
  • If a light source is moving away from the observer, the observed wavelength increases, and the frequency decreases.
    • This is called a redshift because the light shifts towards the red end of the spectrum.
• Blueshift:
  • If the source is moving towards the observer, the observed wavelength decreases, and the frequency increases.
    • This is called a blueshift because the light shifts towards the blue end of the spectrum.

Approximate Doppler Formula for Light

When the speed of the source or observer is much smaller than the speed of light, the change in frequency $\mathrm{\Delta }f$ can be approximated by:

$$\mathrm{\Delta }f\approx f\left(\frac{v}{c}\right)$$

Here, $v$ is the relative speed, and $c$ is the speed of light.

Reflection and Self-Assessment

The Doppler effect is a powerful concept that reveals how relative motion affects the waves we observe, from the sound of a passing car to the light from distant galaxies.