A Source of Sound S Emitting Waves of Frequency 100 Hz and an Observer
This scenario presents a basic setup for exploring the concepts of sound waves and the Doppler effect. Let's break down the elements and their implications:
The Sound Source (S)
- Frequency (f) = 100 Hz: This means the source produces 100 sound waves per second. Higher frequencies correspond to higher pitch.
- Wave Propagation: Sound waves travel outwards from the source as compressions and rarefactions in the medium (air, water, etc.)
The Observer
- Position: The observer's position relative to the source is crucial. Their relative motion (whether they are moving towards or away from the source) will determine the perceived frequency of the sound.
The Doppler Effect
The Doppler effect describes the change in frequency of a wave (like sound) as the source and observer move relative to each other.
- Moving Source, Stationary Observer: If the source is moving towards the observer, the sound waves are compressed, leading to a higher perceived frequency (higher pitch). Conversely, if the source is moving away, the waves are stretched, leading to a lower perceived frequency (lower pitch).
- Stationary Source, Moving Observer: If the observer is moving towards the source, the perceived frequency increases. If the observer is moving away, the perceived frequency decreases.
- Both Moving: The Doppler effect applies when both the source and the observer are moving. The relative velocity between them determines the change in perceived frequency.
Formula for the Doppler Effect
The Doppler effect for sound can be described by the following formula:
f' = f(v ± v<sub>o</sub>) / (v ± v<sub>s</sub>)
Where:
- f' is the observed frequency
- f is the emitted frequency
- v is the speed of sound in the medium
- v<sub>o</sub> is the velocity of the observer (positive if moving towards the source, negative if moving away)
- v<sub>s</sub> is the velocity of the source (positive if moving towards the observer, negative if moving away)
Example
Let's say the source is emitting sound at 100 Hz and is stationary. The observer is moving towards the source at 10 m/s. The speed of sound in air is approximately 343 m/s.
Using the formula:
f' = 100 (343 + 10) / (343 + 0) ≈ 103 Hz
The observer will perceive a frequency slightly higher than the emitted frequency due to their motion towards the source.
Conclusion
The scenario of a sound source emitting waves and an observer highlights the fundamental principles of sound wave propagation and the Doppler effect. Understanding the Doppler effect is crucial in fields like astronomy, medicine, and engineering.
