The change in frequency of a sound wave with distance can be explained through the concept of the Doppler effect. The Doppler effect describes the change in frequency of a wave, including sound waves, as perceived by an observer when the source of the wave and/or the observer is in relative motion.
When a sound source is moving towards an observer, the sound waves get compressed, resulting in a higher frequency or pitch. This is known as a "blue shift" or "positive Doppler shift." Conversely, when a sound source is moving away from an observer, the sound waves get stretched, resulting in a lower frequency or pitch. This is known as a "red shift" or "negative Doppler shift."
The formula for calculating the observed frequency (f) of a sound wave in relation to the source frequency (f0) and the relative velocity (v) between the source and the observer is given by:
f = (v + vo) / (v + vs) * f0
Where:
- f is the observed frequency.
- f0 is the source frequency.
- v is the velocity of sound in the medium.
- vo is the velocity of the observer relative to the medium.
- vs is the velocity of the source relative to the medium.
In most cases, the velocity of the observer relative to the medium is negligible compared to the velocity of sound, so it can be disregarded, simplifying the formula to:
f = (v + vs) / v * f0
This formula allows you to calculate the observed frequency based on the source frequency and the relative velocity between the source and the observer.
It's important to note that the Doppler effect is dependent on the relative motion between the source, the observer, and the medium. If either the source or the observer is stationary, the observed frequency will be equal to the source frequency. Additionally, the Doppler effect applies to any type of wave, not just sound waves, including light waves and electromagnetic waves.