Unit
- Sound waves: Sound propagates as longitudinal pressure waves through elastic media (air, water, solids). The wave consists of alternating compressions and rarefactions traveling at a speed determined by the medium's density and elasticity.
- Frequency and wavelength: Frequency (Hz) is the number of cycles per second; human hearing ranges from 20 Hz to 20,000 Hz. Wavelength equals wave speed divided by frequency, governing how sound interacts with obstacles and openings.
- Amplitude and sound pressure: Amplitude relates to the magnitude of pressure variation. Sound pressure level (SPL) is measured in decibels (dB) as a logarithmic ratio relative to the reference pressure of 20 micropascals.
- Inverse square law: In free field conditions, sound pressure decreases by 6 dB for each doubling of distance from a point source. This principle is fundamental for predicting sound propagation in open spaces.
- Phase and interference: When two sound waves meet, they combine constructively (amplitude increase) or destructively (amplitude reduction) depending on their phase relationship. Phase differences cause standing waves and comb filtering effects.
- Impedance and transmission: Acoustic impedance is the product of medium density and sound speed. Changes in impedance at boundaries cause partial reflection and transmission of sound energy.
- Timbre and harmonics: Most sounds are complex waves composed of a fundamental frequency plus integer multiples (harmonics). The relative strength of harmonics determines an instrument's timbre or tonal quality.
- Decibel scale: The decibel scale compresses a huge dynamic range (from threshold of hearing to pain) into manageable numbers. A 10 dB increase represents a tenfold increase in sound intensity, perceived as roughly doubling loudness.
- Diffraction and scattering: When a sound wave encounters an obstacle or aperture, it bends around edges and spreads into shadow zones. Diffraction is strongest when the wavelength is comparable to or larger than the obstacle size, enabling sound to wrap around corners and barriers.
- Reverberation and decay: In enclosed spaces, sound persists after the source stops due to multiple reflections from surfaces. The reverberation time (RT60) is the interval required for the sound level to decay by 60 dB, a key parameter for room acoustics design.
- Absorption and attenuation: Porous materials and resonators convert sound energy into heat via viscous and thermal losses. Absorption coefficients (0 to 1) quantify how much incident energy is absorbed per surface, reducing reflected sound and controlling reverberation.
Code Example
Python
import numpy as np
# Calculate sound pressure level in dB
p = 0.1 # RMS sound pressure in Pa
p_ref = 20e-6 # reference pressure
spl = 20 * np.log10(p / p_ref)
print('SPL = {:.1f} dB'.format(spl))
# Compute wavelength at 1 kHz in air (c=343 m/s)
f = 1000
c = 343
wavelength = c / f
print('Wavelength = {:.2f} m'.format(wavelength))This Python snippet computes SPL from RMS pressure and calculates wavelength using the wave equation. The numpy library handles the logarithmic calculation efficiently.
Quick Revision
- Sound is a longitudinal pressure wave with frequency, amplitude, and phase properties.
- SPL is measured on a logarithmic decibel scale referenced to 20 µPa.
- Inverse square law governs free-field sound propagation.
- Impedance mismatches cause partial reflection and transmission at boundaries.