Chapter 9: Formula Reference — Waves and Sound
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A wave is a disturbance that transfers energy from one point to another without a net transfer of matter. Sound is a mechanical, longitudinal wave that requires a material medium (solid, liquid, or gas) to travel and cannot propagate through a vacuum — a fact frequently tested in exams. This section covers the basic wave relations and the physics of sound.
9.1 Basic Wave Relations
Quantity | Formula | Symbols & SI Units |
|---|---|---|
Wave equation | v = fλ | v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m) |
Time period | T = 1/f | T = time period (s) |
Speed of a transverse wave on a string | v = √(T/μ) | T = tension in string (N), μ = mass per unit length (kg/m) |
Speed of sound in a gas (Newton–Laplace) | v = √(γP/ρ) | γ = ratio of specific heats, P = pressure (Pa), ρ = density (kg/m³) |
9.2 Sound
Concept | Detail |
|---|---|
Nature of sound | Longitudinal mechanical wave; requires a medium; cannot travel through vacuum |
Speed of sound in air (0°C, at sea level) | ≈ 331 m/s (approx. 332–343 m/s at room temperature) |
Order of speed of sound | Fastest in solids, slower in liquids, slowest in gases (generally: solid > liquid > gas) |
Audible range for humans | 20 Hz to 20,000 Hz (20 kHz) |
Infrasonic sound | Frequency below 20 Hz (inaudible to humans; e.g. used by elephants, whales) |
Ultrasonic sound | Frequency above 20,000 Hz (inaudible to humans; used in SONAR, medical ultrasound, bats' echolocation) |
Doppler Effect | Apparent change in frequency of a wave due to relative motion between source and observer |
Echo | Reflected sound heard distinctly; requires the reflecting surface to be at least about 17 m away (minimum time gap of about 0.1 s for the human ear to distinguish it from the original sound) |
Resonance | Phenomenon where a system driven at its natural frequency vibrates with maximum amplitude |
Loudness | Depends on amplitude of the sound wave (and intensity) |
Pitch | Depends on frequency of the sound wave |
Intensity of sound (unit) | Measured in decibel (dB), a logarithmic unit |
9.3 Doppler Effect Formula
Case | Formula |
|---|---|
General Doppler formula | f' = f × (v ± v₀)/(v ∓ vₛ) |
Symbols | f' = apparent frequency, f = actual (source) frequency, v = speed of sound, v₀ = speed of observer, vₛ = speed of source |