Glossary

8.2 Attenuation of sound in different media

3 min read•july 24, 2024

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, , , and pressure influence attenuation.

Calculating sound attenuation in involves complex equations considering classical absorption and relaxation processes. measures sound intensity reduction through media, affected by impedance mismatches and material properties. Environmental factors like temperature, , 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
    • 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 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: αcl=ω22ρc3(43μ+μB+κ(γ−1)Cp)\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: αtotal=αcl+αO2+αN2\alpha_{total} = \alpha_{cl} + \alpha_{O_2} + \alpha_{N_2}
  • Sound intensity decay follows exponential law: I=I0e−αxI = 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=20log⁡10(fm)−42TL = 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

Key Terms to Review (20)

Absorption attenuation: Absorption attenuation refers to the reduction in the intensity of sound waves as they pass through a medium due to energy being absorbed by that medium. This phenomenon is significant in understanding how sound interacts with various materials, influencing the propagation and quality of sound across different environments.
Air: Air is a mixture of gases that make up the Earth's atmosphere, primarily composed of nitrogen, oxygen, and smaller amounts of other gases like carbon dioxide and argon. It plays a crucial role in sound propagation, as the density and temperature of air significantly affect how quickly sound waves travel through it and how sound is absorbed or diminished as it travels through different media.
Beer-Lambert Law: The Beer-Lambert Law describes the relationship between the attenuation of light as it passes through a medium and the properties of that medium, specifically concentration and path length. In acoustics, this concept is crucial for understanding how sound is absorbed and scattered in different media, impacting sound intensity and quality as it travels through various materials.
Decibel: A decibel is a logarithmic unit used to measure the intensity of sound, specifically in relation to a reference level. It provides a way to quantify sound levels, making it easier to understand the differences in loudness and intensity. By using this scale, we can compare sounds of different amplitudes, determine sound pressure levels, and understand how sound behaves in various environments.
Density: Density is defined as the mass of a substance per unit volume, often expressed in kilograms per cubic meter (kg/m³). This fundamental property of materials plays a crucial role in understanding how sound travels through different media, influencing factors such as speed, impedance, refraction, attenuation, and applications in imaging and testing technologies.
Elastic Modulus: Elastic modulus is a measure of a material's ability to deform elastically when a force is applied, quantified as the ratio of stress to strain. This property is crucial in understanding how different materials respond to stress, which directly influences factors like the speed of sound through those materials and how sound attenuates as it travels.
Frequency: Frequency is the number of occurrences of a repeating event per unit time, commonly measured in hertz (Hz), where one hertz equals one cycle per second. It directly affects various aspects of sound, such as pitch, wave behavior, and the way sound interacts with different media.
Geometric attenuation: Geometric attenuation refers to the decrease in sound intensity that occurs as sound waves spread out from a source over distance, primarily due to the increase in surface area that the sound energy is distributed over. This phenomenon highlights how the sound pressure level diminishes as the distance from the source increases, illustrating the inverse square law where sound intensity decreases with the square of the distance from the source. Understanding geometric attenuation is essential when analyzing how sound behaves in various media and environments.
Humidity: Humidity refers to the amount of water vapor present in the air. It plays a crucial role in the propagation of sound waves, as the presence of moisture in the air can significantly affect how sound travels. Higher humidity levels can lead to an increase in the speed of sound, as water vapor is less dense than the nitrogen and oxygen that make up most of the air we breathe.
Inverse Square Law: The inverse square law states that the intensity of a physical quantity, such as sound or light, diminishes in proportion to the square of the distance from its source. As you move away from the source, the energy spreads over a larger area, leading to a decrease in intensity that is inversely related to the square of the distance. This concept is crucial for understanding how sound waves propagate through different environments, how they are measured, and how they attenuate as they travel.
Longitudinal Waves: Longitudinal waves are a type of mechanical wave where the particle displacement is parallel to the direction of wave propagation. These waves are characterized by compressions and rarefactions, allowing sound to travel through different media, impacting various phenomena such as refraction, diffraction, and attenuation.
Microphone array: A microphone array is a set of multiple microphones arranged in a specific geometric configuration to capture sound from various directions and improve audio quality. By using multiple microphones, this setup can enhance sound localization, provide spatial audio information, and reduce noise from unwanted sources. Microphone arrays are particularly useful in applications like teleconferencing, recording, and surveillance where clear sound capture is essential.
Neper: The neper is a logarithmic unit used to measure ratios, particularly in the context of sound attenuation and electrical signals. It is defined as the natural logarithm of a ratio of two values, commonly representing power or intensity levels, which allows for easy calculation of exponential changes in sound pressure levels or signal strength when sound travels through different media. The neper is especially relevant in acoustics as it provides a direct way to express how sound diminishes as it moves through various materials.
Solid materials: Solid materials are substances characterized by a definite shape and volume, consisting of closely packed particles that can vibrate but cannot move freely. This structure allows solids to transmit sound waves efficiently, making them important for understanding how sound is attenuated in various media. Their properties influence the speed of sound, attenuation levels, and the way sound interacts with different environments.
Sound Insulation: Sound insulation refers to the ability of a material or structure to reduce the transmission of sound from one area to another. It plays a critical role in managing sound levels within buildings and environments, ensuring that noise is kept at acceptable levels to maintain comfort and functionality. The effectiveness of sound insulation can vary depending on the material properties, frequency of the sound, and the construction techniques used, making it essential for controlling unwanted noise in various contexts.
Spectrum analyzer: A spectrum analyzer is an electronic device that measures and displays the frequency spectrum of signals. By analyzing the amplitude of frequencies within a signal, it helps visualize how sound behaves as it travels through different media, revealing how various materials can attenuate sound waves at specific frequencies.
Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance, directly affecting the speed at which sound travels through different media. As temperature increases, the particles move more vigorously, which allows sound waves to propagate faster. This concept connects to various phenomena in acoustics, including how sound bends when moving through different temperatures and states of matter.
Transmission Loss: Transmission loss refers to the reduction in sound energy as it passes through a medium or between different media, impacting how much sound is perceived on the other side. This concept is critical for understanding how sound behaves in different environments, as it determines how effectively sound travels and how much of it is absorbed or reflected at interfaces between materials with varying acoustic properties.
Transverse waves: Transverse waves are a type of wave where the oscillation of the medium is perpendicular to the direction of the wave's travel. These waves exhibit unique behaviors such as reflection, refraction, and diffraction when interacting with different materials, and they play a significant role in various physical phenomena.
Water: Water is a vital liquid substance that exists in three states: solid (ice), liquid, and gas (vapor). It plays a crucial role in various physical processes, including sound propagation and attenuation. In the context of sound, water's properties significantly influence how sound waves travel and lose energy as they move through it, affecting their speed, wavelength, and intensity.
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