The Doppler effect describes the change in frequency or wavelength of a wave due to the relative motion between the source of the wave and an observer. This effect can be observed for various types of waves, including sound waves.
When the source of sound and the observer are in motion relative to each other, the frequency of the sound perceived by the observer can differ from the actual frequency emitted by the source. The Doppler effect equation for sound waves is given by:
f' = (v + vo) / (v + vs) * f
Where:
- f' is the observed frequency of the sound,
- f is the actual frequency emitted by the source,
- v is the speed of sound in the medium,
- vo is the velocity of the observer (positive if moving towards the source, negative if moving away),
- vs is the velocity of the source (positive if moving away from the observer, negative if moving towards).
In this equation, the observed frequency (f') is determined by the ratio of the sum of the speed of sound and the observer's velocity to the sum of the speed of sound and the source's velocity, multiplied by the actual frequency emitted by the source (f).
If either the observer or the source is stationary (velocity is zero), the equation simplifies. For example, if the observer is stationary and the source is moving, the equation becomes:
f' = v / (v + vs) * f
Similarly, if the source is stationary and the observer is moving, the equation becomes:
f' = (v + vo) / v * f
These equations illustrate how the motion of the source or observer affects the observed frequency of the sound. If the observer is moving towards the source, the observed frequency will be higher (higher pitch). If the observer is moving away from the source, the observed frequency will be lower (lower pitch).