Glossary

1.3 Sound wave characteristics and behavior

3 min read•july 24, 2024

Sound waves are fascinating phenomena that shape our auditory world. They travel through various media, each with unique properties affecting propagation speed and behavior. Understanding how sound waves move and interact is crucial for grasping acoustics fundamentals.

, , and play key roles in how we perceive sound. These processes explain why sound behaves differently in various environments, from echoes in large rooms to muffled voices through walls. The adds another layer, explaining changes in moving sound sources.

Sound Wave Propagation and Behavior

Propagation of sound waves

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  • characteristics
    • Compression and rarefaction alternate regions of high and low pressure propagate through
    • Particle displacement parallel to wave direction oscillates back and forth along propagation axis
  • Speed of sound in different media
    • Air: approximately 343 m/s at 20℃ varies with temperature and humidity
    • Water: approximately 1480 m/s at 20℃ faster due to higher density and incompressibility
    • Solids: varies widely, generally faster than liquids or gases (steel ~5000 m/s, wood ~3300 m/s)
  • Factors affecting sound propagation
    • Temperature increases speed of sound in gases (air ~+0.6 m/s per ℃)
    • Density higher density typically increases speed (mercury vs water)
    • Elasticity of the medium more elastic materials transmit sound faster (steel vs rubber)
  • Impedance
    • Resistance to sound wave propagation measures how easily sound travels through medium
    • Relationship: Z=ρcZ = \rho c, where ρ\rho is density and cc is speed of sound determines reflection and transmission at boundaries
  • Transmission between media
    • Impedance mismatch greater difference leads to more reflection (air-water interface)
    • Energy transfer and reflection at boundaries partial transmission and reflection occur at interfaces

Reflection and refraction of sound

  • Reflection
    • Occurs when sound waves encounter a boundary bounce back from surfaces
    • Angle of incidence equals angle of reflection follows law of reflection
    • Specular vs diffuse reflection smooth surfaces produce specular, rough surfaces produce diffuse
  • Refraction
    • Change in wave direction due to speed change bends as it enters new medium
    • Snell's law: sin⁡θ1sin⁡θ2=v1v2\frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} relates angles of incidence and refraction to wave speeds
    • Temperature gradients causing sound refraction in air creates mirages and sound shadows
    • Bending of waves around obstacles or through openings allows sound to "bend" around corners
    • each point on wavefront acts as new source of wavelets
    • Relationship between and obstacle size more pronounced for wavelengths similar to or larger than obstacle
    • Constructive and destructive interference waves add or cancel based on phase
    • Standing waves and resonance form in enclosed spaces (musical instruments, room modes)

Sound wave attenuation factors

  • Attenuation
    • Reduction in amplitude over distance sound becomes weaker as it travels
    • Causes: geometric spreading, , energy dissipates and spreads out
  • Absorption
    • Conversion of sound energy to heat materials dampen sound vibrations
    • Porous materials and their effectiveness (acoustic foam, fiberglass)
    • Absorption coefficient measures fraction of incident sound energy absorbed
  • Factors influencing attenuation and absorption
    • dependence higher frequencies generally attenuate more rapidly
    • Material properties (density, porosity, stiffness) affect absorption characteristics
    • Thickness of absorbing materials thicker materials typically absorb more effectively
  • Transmission loss
    • Measures sound reduction through barriers or partitions
    • Mass law for single-layer partitions doubling mass increases TL by ~6 dB
  • Reverberation time
    • Sabine formula: T60=0.161VAT_{60} = \frac{0.161V}{A} relates room volume to absorption
    • Relationship to room acoustics and absorption longer RT in reflective spaces, shorter in absorptive

Doppler effect in acoustics

  • Doppler effect principle
    • Apparent change in frequency due to relative motion perceived pitch changes
    • Formula: f′=fc±vrc±vsf' = f\frac{c \pm v_r}{c \pm v_s} calculates observed frequency
  • Scenarios
    1. Stationary source, moving observer pitch increases as observer approaches, decreases as recedes
    2. Moving source, stationary observer pitch increases as source approaches, decreases as recedes
    3. Both source and observer moving combined effect of both motions
  • Applications
    • Traffic speed measurement police radar guns use Doppler shift
    • Medical ultrasound (blood flow measurement) detects flow velocity and direction
    • Radar systems measure target speed and direction
    • Astronomical observations (redshift/blueshift) determine celestial object motion
  • Limitations and considerations
    • Medium motion effects wind can influence Doppler shift in air
    • Relativistic Doppler effect at high velocities requires special relativity corrections

Key Terms to Review (18)

Absorption: Absorption refers to the process by which sound energy is taken in by a material rather than being reflected or transmitted. This phenomenon is crucial in understanding how sound waves behave when they encounter different surfaces, influencing both the quality of sound in a space and the effectiveness of soundproofing materials. By absorbing sound, materials can reduce echo and improve clarity, playing a vital role in acoustics and sound management.
Attenuation: Attenuation refers to the reduction in strength or intensity of a sound wave as it travels through a medium. This decrease in sound energy can occur due to various factors, including absorption, scattering, and geometric spreading. Understanding attenuation is crucial for analyzing sound wave characteristics, evaluating ultrasonic imaging methods, and studying the physics of ultrasonic waves in different applications.
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.
Diffraction: Diffraction is the bending and spreading of waves when they encounter an obstacle or pass through an opening. This phenomenon is essential for understanding how sound behaves in various environments, influencing aspects such as wavelength, frequency, and wave interactions with boundaries and media.
Doppler Effect: The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. This phenomenon can significantly alter our perception of sound and light, influencing how we understand wave properties, sound characteristics, and applications in various technologies such as medical imaging and ultrasonic waves.
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.
Hertz: Hertz is the unit of frequency that measures the number of cycles per second of a periodic wave, such as sound. It connects to various aspects of wave behavior, including how changes in frequency affect pitch, the relationship between frequency and wavelength, and how sound behaves in different media. Understanding hertz is crucial for analyzing sound characteristics, including infrasound and ultrasonic waves, which exist outside the range of human hearing but have significant applications in various fields.
Huygens' Principle: Huygens' Principle states that every point on a wavefront can be considered a source of secondary wavelets, which spread out in all directions at the same speed as the original wave. This concept helps to explain various phenomena related to wave behavior, such as reflection, refraction, and diffraction, by allowing us to visualize how waves propagate through space and interact with obstacles.
Interference: Interference refers to the phenomenon that occurs when two or more waves superimpose, leading to a combination of their amplitudes. This can result in constructive interference, where waves combine to produce a larger amplitude, or destructive interference, where waves cancel each other out. Understanding interference is crucial for comprehending how sound waves behave, how standing waves are formed, how low-frequency sounds propagate, and how beats occur when waves interact.
Longitudinal wave: A longitudinal wave is a type of wave where the displacement of the medium is parallel to the direction of the wave's travel. This characteristic allows sound waves, which are fundamentally longitudinal, to transmit energy through various media by compressing and rarefying the particles in the medium. The behavior and properties of longitudinal waves are essential for understanding sound wave characteristics, how sound propagates through different materials, and how standing waves are formed in mediums like air, water, or solids.
Loudness: Loudness is the subjective perception of sound intensity, which relates to how we experience sound rather than its physical measurement. It varies based on sound wave characteristics, including amplitude and frequency, and plays a critical role in applications across different fields such as acoustics. Understanding loudness helps in designing spaces like concert halls, where the experience of sound is influenced by factors such as reverberation time and the equal-loudness contours that describe how humans perceive different frequencies at varying loudness levels.
Medium: In the context of acoustics, a medium is a substance through which sound waves travel. This can include gases, liquids, and solids, each affecting how sound is transmitted based on their physical properties. The medium plays a crucial role in determining sound wave characteristics, including speed, wavelength, and how sound interacts with obstacles.
Pitch: Pitch is the perceptual attribute of sound that allows it to be classified as higher or lower in frequency. It is closely related to the frequency of a sound wave, where higher frequencies correspond to higher pitches, and lower frequencies relate to lower pitches. Understanding pitch involves various aspects like wavelength, sound wave behavior, and how humans perceive these auditory signals.
Reflection: Reflection is the process by which sound waves bounce off a surface and return into the medium from which they originated. This phenomenon is crucial in understanding how sound behaves in different environments, impacting how we perceive sound through echoes and other acoustic phenomena.
Refraction: Refraction is the bending of sound waves as they pass from one medium to another, caused by a change in their speed. This phenomenon is crucial for understanding how sound behaves in different environments, influencing aspects like wavelength, frequency, and the overall propagation of sound in various applications.
Scattering: Scattering refers to the redirection of sound waves when they encounter an obstacle or inhomogeneity in the medium through which they are traveling. This phenomenon is crucial in understanding how sound interacts with various materials and environments, affecting wave behavior such as reflection, absorption, and transmission. Scattering plays a significant role in sound wave characteristics, focusing effects, low-frequency propagation, and ultrasonic wave behavior.
Transverse Wave: A transverse wave is a type of wave in which the oscillations or vibrations occur perpendicular to the direction of the wave's travel. This characteristic is important in understanding how different types of waves, including sound waves, behave and interact with their environments. Transverse waves exhibit distinct behaviors such as polarization and the formation of standing waves, making them essential in studying various acoustic phenomena.
Wavelength: Wavelength is the distance between successive peaks or troughs of a wave, which determines its frequency and energy characteristics. Understanding wavelength is crucial as it relates directly to how sound behaves in different environments, including reflection, diffraction, and interference. Additionally, wavelength plays a vital role in various applications such as ultrasonic imaging and the Doppler effect.
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