8.2 Attenuation of sound in different media

Sound attenuation is a crucial concept in acoustics, affecting how sound travels through different media. It involves absorption, which converts sound energy to heat, and scattering, which redirects sound waves. Various factors like material properties, frequency, temperature, and pressure influence attenuation.

Calculating sound attenuation in air involves complex equations considering classical absorption and relaxation processes. Transmission loss measures sound intensity reduction through media, affected by impedance mismatches and material properties. Environmental factors like temperature, humidity, and pressure significantly impact attenuation, creating intricate propagation patterns.

Attenuation of Sound in Different Media

Factors of sound attenuation

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• Absorption mechanisms convert sound energy into heat
  • Classical absorption occurs due to viscosity and heat conduction
  • Molecular relaxation involves energy transfer between molecules' translational and internal modes
  • Thermal conduction dissipates sound energy through temperature gradients
  • Viscosity causes friction between fluid layers, damping sound waves
• Scattering redirects sound energy from its original path
  • Reflection bounces sound waves off surfaces (ocean floor)
  • Refraction bends sound waves as they pass through media with different properties (thermoclines in oceans)
  • Diffraction allows sound to bend around obstacles (hearing around corners)
• Material properties influence sound propagation
  • Density affects the speed and impedance of sound waves
  • Elasticity determines how easily a material deforms under sound pressure
  • Porosity impacts absorption through increased surface area (acoustic foam)
• Frequency dependence shows higher frequencies attenuate more rapidly (birdsong vs thunder)
• Temperature effects alter molecular behavior and sound speed
• Pressure effects change medium density and sound propagation
• Composition of the medium affects absorption and scattering properties (salt water vs fresh water)

Calculation of air sound attenuation

• Attenuation coefficient measures sound intensity loss per unit distance (dB/m or Np/m)
• Stokes-Kirchhoff classical absorption equation: $\alpha_{cl} = \frac{\omega^2}{2\rho c^3}(\frac{4}{3}\mu + \mu_B + \frac{\kappa(\gamma-1)}{C_p})$ Considers viscosity, thermal conductivity, and specific heat
• Relaxation processes contribute to attenuation
  • Oxygen relaxation dominates at frequencies below 2 kHz
  • Nitrogen relaxation becomes significant above 20 kHz
• Total attenuation coefficient sums individual contributions: $\alpha_{total} = \alpha_{cl} + \alpha_{O_2} + \alpha_{N_2}$
• Sound intensity decay follows exponential law: $I = I_0 e^{-\alpha x}$ Describes intensity reduction over distance
• Atmospheric absorption calculated using ISO 9613-1 standard Accounts for temperature, humidity, and pressure effects

Transmission loss in media

• Transmission loss measures reduction in sound intensity through a medium
• Impedance mismatch causes reflection and transmission at interfaces
  • Reflection coefficient determines amount of reflected energy
  • Transmission coefficient indicates energy passed through interface
• Mass law predicts transmission loss for simple partitions: $TL = 20 \log_{10}(fm) - 42$ dB Where f is frequency and m is mass per unit area
• Coincidence effect occurs when bending wavelength matches sound wavelength
• Stiffness-controlled region dominates at low frequencies
• Resonance effects create peaks and dips in transmission loss curve
• Multi-layer systems analyzed using transfer matrix method Accounts for multiple reflections and transmissions between layers

Environmental effects on attenuation

• Temperature effects alter sound propagation
  • Speed of sound increases with temperature (331 m/s at 0℃, 343 m/s at 20℃)
  • Molecular relaxation changes affect absorption
• Humidity effects impact attenuation
  • Water vapor content alters absorption characteristics
  • Relaxation frequency shifts with changing humidity
• Pressure effects modify sound propagation
  • Density changes affect sound speed and impedance
  • Mean free path alterations influence molecular collisions
• Combined effects on attenuation coefficient vary with frequency and conditions
• Seasonal and diurnal variations create complex attenuation patterns
• Atmospheric layering impacts sound propagation
  • Temperature inversions can create sound channels
  • Wind gradients cause refraction and shadow zones