Sound waves are mechanical vibrations that travel through matter. They're characterized by frequency, wavelength, and amplitude, which determine pitch and loudness. Understanding these properties is crucial for grasping how sound behaves in different environments.

Sound propagation varies in gases, liquids, and solids due to their unique properties. This affects how we perceive sound and design noise control solutions. Concepts like acoustic impedance, reflection, and absorption play key roles in managing sound in various settings.

Sound Wave Properties

Characteristics of Sound Waves

• Sound waves are mechanical waves that require a medium to propagate (air, water, solids)
• Characterized by frequency, wavelength, and amplitude
• Frequency is the number of oscillations or cycles per unit time, measured in Hertz (Hz)
  • Human audible frequency range: 20 Hz to 20 kHz
  • Examples: 100 Hz (low-pitched sound), 1000 Hz (medium-pitched sound), 10000 Hz (high-pitched sound)
• Wavelength is the distance between two consecutive points of a wave that are in phase (crests, troughs)
  • Inversely proportional to frequency
  • Examples: 20 Hz sound wave in air has a wavelength of ~17 m, 20 kHz sound wave in air has a wavelength of ~1.7 cm
• Amplitude is the maximum displacement of a wave from its equilibrium position
  • Related to energy and intensity of the sound wave
  • Higher amplitude results in louder sound
  • Examples: Whispering (low amplitude), normal conversation (medium amplitude), shouting (high amplitude)

Speed of Sound

• The speed of sound in a medium is determined by the medium's properties (density, elasticity)
• In air at 20°C, the speed of sound is approximately 343 m/s
• Speed of sound varies with temperature
  • Increases by ~0.6 m/s per degree Celsius increase in temperature
  • Examples: Speed of sound in air at 0°C is ~331 m/s, at 30°C is ~349 m/s
• Speed of sound is different in various media
  • Examples: ~1,500 m/s in water, ~5,000 m/s in steel

Sound Propagation in Media

Propagation in Gases, Liquids, and Solids

• Sound propagation is the transmission of sound waves through a medium (gas, liquid, solid)
• In gases (air), sound waves propagate as longitudinal waves
  • Particles oscillate parallel to the direction of wave propagation
  • Speed of sound depends on temperature, humidity, and pressure
  • Examples: Sound propagation in Earth's atmosphere, sound propagation in helium gas (faster than in air)
• In liquids (water), sound waves also propagate as longitudinal waves
  • Speed of sound in water is ~1,500 m/s (4.3 times faster than in air)
  • Examples: Sound propagation in oceans, sound propagation in liquid nitrogen
• In solids, sound waves can propagate as both longitudinal and transverse waves
  • Speed of sound is generally higher than in gases and liquids due to stronger intermolecular bonds and elastic properties
  • Examples: Sound propagation in steel (~5,000 m/s), sound propagation in diamond (~12,000 m/s)

Acoustic Impedance and Reflection

• Acoustic impedance of a medium is the product of its density and the speed of sound in that medium
• Impedance mismatch between two media can cause reflection and transmission of sound waves at the interface
• Reflection occurs when a sound wave encounters a boundary between two media with different acoustic impedances
  • Some of the wave's energy is reflected back into the original medium
  • The angle of reflection equals the angle of incidence
  • Examples: Echo (reflection of sound waves from a large surface), sonar (reflection of sound waves used for underwater navigation)
• Transmission occurs when a portion of the sound wave's energy passes through the boundary into the second medium
  • The amount of transmitted energy depends on the impedance mismatch between the media
  • Examples: Sound transmission through walls (partial reflection and transmission), sound transmission from air to water (most energy is reflected due to large impedance mismatch)

Sound Pressure Levels and Decibels

Sound Pressure Level (SPL) and Decibels (dB)

• Sound pressure level (SPL) is a logarithmic measure of the effective pressure of a sound relative to a reference value (threshold of human hearing, 20 µPa)
• SPL is expressed in decibels (dB) and is calculated using the formula: SPL = 20 log10 (p / p0)
  • p is the measured sound pressure
  • p0 is the reference pressure
• The decibel scale is logarithmic
  • An increase of 10 dB corresponds to a tenfold increase in sound pressure and a perceived doubling of loudness
  • Examples: 60 dB is 10 times the sound pressure of 50 dB, 80 dB is 100 times the sound pressure of 60 dB
• Common sound pressure levels:
  • 0 dB: Threshold of hearing
  • 60 dB: Normal conversation
  • 100 dB: Jackhammer at 1 meter
  • 120 dB: Threshold of pain
  • Examples: Rustling leaves (~20 dB), vacuum cleaner (~70 dB), live rock concert (~110 dB)

Weighted Decibel Scales (dBA, dBC)

• Weighted decibel scales (dBA, dBC) account for the frequency-dependent sensitivity of human hearing
• dBA is commonly used for environmental noise measurements
  • Emphasizes frequencies around 1-6 kHz, where human hearing is most sensitive
  • Examples: Traffic noise measurements, workplace noise assessments
• dBC is used for low-frequency noise assessment
  • Applies less attenuation to low frequencies compared to dBA
  • Examples: Bass-heavy music, industrial machinery noise

Sound Reflection, Absorption, and Diffraction

Reflection and Absorption

• Reflection occurs when a sound wave encounters a boundary between two media and some of the wave's energy is reflected back into the original medium
  • The angle of reflection equals the angle of incidence
  • Examples: Sound reflection from walls in a room, sound reflection from the surface of a lake
• Absorption is the process by which sound energy is converted into heat as it propagates through a medium or encounters a surface
  • Porous materials (acoustic foam, fiberglass) are effective at absorbing sound
  • Examples: Sound absorption by carpeting in a room, sound absorption by acoustic panels in a recording studio
• The absorption coefficient of a material is the fraction of incident sound energy absorbed by the material
  • Ranges from 0 (perfect reflection) to 1 (perfect absorption)
  • Examples: Concrete has a low absorption coefficient (~0.02 at 500 Hz), acoustic foam has a high absorption coefficient (~0.9 at 500 Hz)

Diffraction

• Diffraction is the bending of sound waves around obstacles or through openings when the wavelength is comparable to or larger than the size of the obstacle or opening
  • Allows sound to propagate around corners and barriers
  • Examples: Sound diffraction around a corner in a hallway, sound diffraction through an open door
• The Fresnel number is a dimensionless parameter that relates the size of an obstacle or opening to the wavelength of the sound wave and the distance between the source and the obstacle
  • Helps predict the extent of diffraction
  • Smaller Fresnel numbers indicate more diffraction
  • Examples: Low-frequency sounds (large wavelengths) diffract more easily around obstacles than high-frequency sounds (small wavelengths)