3.5 Doppler Effect

3.5 Doppler Effect

Definition:

The Doppler Effect refers to the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. It is commonly observed in sound waves but also applies to electromagnetic waves, such as light.

Doppler Effect in Sound:

- **Approaching Source:** If the source of sound is moving towards the observer, the observed frequency increases, and the wavelength decreases.
- **Receding Source:** If the source of sound is moving away from the observer, the observed frequency decreases, and the wavelength increases.

The change in observed frequency f' is given by:
f' = f(v ± vo)/(v ∓ vs)

where:
- f is the actual frequency of the source,
- v is the speed of sound in the medium,
- vo is the speed of the observer relative to the medium,
- vs is the speed of the source relative to the medium,
- The signs depend on the direction of motion (approaching or receding).

Example Problem:

A car honks its horn at a frequency of 500 Hz as it approaches a stationary observer. If the car is moving at 20 m/s and the speed of sound in air is 340 m/s, what is the frequency heard by the observer?

Solution:

Using the Doppler Effect formula for an approaching source:
f' = f(v + vo)/v = 500 Hz × (340 m/s + 20 m/s)/340 m/s ≈ 529 Hz
The frequency heard by the observer is approximately 529 Hz.