14.1 Speed of Sound, Frequency, and Wavelength - Physics
Key Concepts
- Sound Waves: Disturbance of matter transmitted from a source outward; characterized by periodic waves causing simple harmonic motion.
- Pressure Regions:
- Compressions: High-pressure areas in the wave.
- Rarefactions: Low-pressure areas in the wave.
- Longitudinal Waves: Move through a medium in the same direction as wave propagation.
Properties of Sound Waves
- Amplitude: Decreases with distance; energy spreads over a larger area and is absorbed (e.g., eardrum).
- Compression and Rarefaction: Analogy to crests and troughs in transverse waves.
Speed of Sound
- Medium Dependence:
- Gases: Lower speed due to compressibility.
- Liquids/Solids: Higher speed due to rigidity.
- Temperature Influence: Speed varies with the medium's temperature, notably in gases.
- Misconceptions: Speed depends on rigidity and density; in solids, rigidity has a greater effect.
| Medium | Speed (m/s) |
|---|
| Air | 331 |
| Water (fresh) | 1480 |
| Steel | 5960 |
Sound Wave Characteristics
- Relation to Frequency & Wavelength:
- Formula: ( v = f \lambda )
- ( v ): Speed of sound, ( f ): Frequency, ( \lambda ): Wavelength.
- Speed is independent of frequency; all frequencies travel at nearly the same speed in a given medium.
- Inverse Relationship: Higher frequency results in shorter wavelength.
Applications and Phenomena
- Echolocation: Used by bats/dolphins; sound waves reflect to locate objects.
- SONAR Technology: Mimics echolocation for navigation underwater.
- Frequency Independence: Sound speed from a source remains constant despite frequency changes.
Experiments and Examples
- Voice as a Sound Wave: Observing changes in amplitude through paper.
- Practical Problems: Calculating wavelengths using given speed and frequency.
Worked Example
- Problem: Calculate wavelengths at audible extremes (20 Hz and 20,000 Hz) with sound speed 348.7 m/s.
- Using ( \lambda = \frac{v}{f} )
- For 20 Hz: 17m wavelength.
- For 20,000 Hz: 0.017m wavelength.
Conclusion
- Understanding speed and properties of sound waves is essential for applications in technology and everyday phenomena.
Additional Resources
Note: This summary is based on the OpenStax textbook chapter on the speed of sound, frequency, and wavelength.