👂Acoustics Unit 1 – Introduction to Acoustics and Sound Waves

What's Acoustics All About?

• Acoustics is the scientific study of sound, including its generation, transmission, and effects
• Encompasses various disciplines such as physics, engineering, architecture, and music
• Investigates how sound waves interact with different materials and environments
• Explores the perception of sound by humans and animals, including psychoacoustics
• Applies knowledge to design spaces with optimal acoustic properties (concert halls, recording studios)
• Develops technologies for sound reproduction, noise control, and acoustic measurements
• Plays a crucial role in fields like telecommunications, medical imaging, and underwater navigation

The Basics of Sound Waves

• Sound waves are longitudinal pressure waves that propagate through a medium (air, water, solids)
• Generated by vibrating objects, causing compression and rarefaction of the surrounding medium
• Characterized by properties such as frequency, wavelength, and amplitude
• Frequency determines the pitch of the sound, measured in Hertz (Hz)
  • Higher frequencies produce higher-pitched sounds, while lower frequencies produce lower-pitched sounds
• Wavelength is the distance between two consecutive compressions or rarefactions, inversely related to frequency
• Amplitude corresponds to the loudness of the sound, determined by the maximum displacement of the medium particles
  • Measured in decibels (dB), a logarithmic scale that accounts for the wide range of audible sound pressures

How Sound Travels

• Sound waves require a medium to propagate, as they are mechanical waves
• In gases, sound travels faster in lighter molecules (helium) compared to heavier ones (carbon dioxide)
• Speed of sound in air is approximately 343 meters per second at room temperature (20°C)
• In liquids and solids, sound travels faster due to the closer proximity of molecules
  • Speed of sound in water is about 1,480 meters per second, while in steel, it can reach 5,960 meters per second
• Sound waves experience attenuation (decrease in amplitude) as they travel through a medium
• Attenuation is caused by factors such as absorption, scattering, and geometric spreading
• Temperature, humidity, and wind can also affect the propagation of sound waves in air

Measuring Sound: Frequency and Amplitude

• Frequency is the number of oscillations or cycles per second, expressed in Hertz (Hz)
  • Audible frequency range for humans is approximately 20 Hz to 20,000 Hz (20 kHz)
• Amplitude is the maximum displacement of the medium particles from their equilibrium position
• Sound pressure level (SPL) is a logarithmic measure of the effective sound pressure relative to a reference value
  • Measured in decibels (dB), with 0 dB corresponding to the threshold of human hearing (20 µPa)
• Loudness is the subjective perception of sound pressure, influenced by factors like frequency and duration
• Sound intensity is the power carried by sound waves per unit area, expressed in watts per square meter (W/m²)
  • Related to sound pressure level by the formula: $I = \frac{p^2}{\rho c}$, where $p$ is sound pressure, $ρ$ is the medium density, and $c$ is the speed of sound

Sound Properties: Reflection, Refraction, and Diffraction

• Reflection occurs when sound waves bounce off a surface, following the law of reflection
  • Angle of incidence equals the angle of reflection
• Refraction happens when sound waves bend as they pass through mediums with different densities or temperatures
  • Snell's law describes the relationship between the angles of incidence and refraction: $\frac{\sin θ_1}{v_1} = \frac{\sin θ_2}{v_2}$
• Diffraction is the bending of sound waves around obstacles or through openings
  • Depends on the size of the obstacle or opening relative to the wavelength of the sound
  • Low-frequency sounds (long wavelengths) diffract more easily than high-frequency sounds (short wavelengths)
• Interference occurs when two or more sound waves interact, resulting in constructive (amplification) or destructive (cancellation) interference
• Standing waves can form in enclosed spaces due to the superposition of incident and reflected waves
  • Characterized by nodes (minimal displacement) and antinodes (maximal displacement) at specific locations

Intro to Room Acoustics

• Room acoustics studies the behavior of sound in enclosed spaces
• Reverberation is the persistence of sound after the source has stopped, caused by multiple reflections
  • Reverberation time (RT60) is the time it takes for the sound pressure level to decrease by 60 dB after the source stops
• Early reflections arrive within 50-80 milliseconds of the direct sound and contribute to speech intelligibility and musical clarity
• Late reflections arrive after the early reflections and contribute to the overall reverberant sound field
• Sound absorption is the process by which sound energy is converted into heat, reducing reflections
  • Absorption coefficients (α) describe the fraction of incident sound energy absorbed by a material, ranging from 0 (perfect reflection) to 1 (perfect absorption)
• Room modes are standing waves that occur at specific frequencies, determined by the room dimensions
  • Modal density increases with frequency, leading to a more diffuse sound field at higher frequencies

Real-World Applications of Acoustics

• Architectural acoustics: Designing spaces with optimal acoustic properties for speech intelligibility, musical performance, or noise control
  • Examples include concert halls, theaters, classrooms, and open-plan offices
• Environmental acoustics: Studying the impact of noise on human health and wildlife, and developing strategies for noise mitigation
  • Noise barriers, sound insulation, and urban planning considerations
• Underwater acoustics: Using sound waves for communication, navigation, and imaging in aquatic environments
  • Sonar systems, marine mammal studies, and oceanographic research
• Biomedical acoustics: Applying acoustic principles to medical diagnosis and therapy
  • Ultrasound imaging, lithotripsy (breaking up kidney stones), and high-intensity focused ultrasound (HIFU) for tumor treatment
• Musical acoustics: Investigating the physics of musical instruments and the perception of musical sounds
  • Instrument design, tuning, and virtual acoustics for digital music production

Key Formulas and Calculations

• Speed of sound: $v = \sqrt{\frac{K}{\rho}}$, where $K$ is the bulk modulus and $ρ$ is the medium density
  • In air: $v = 331.3 + 0.606T$ (m/s), where $T$ is the temperature in °C
• Wavelength: $λ = \frac{v}{f}$, where $v$ is the speed of sound and $f$ is the frequency
• Sound pressure level (SPL): $L_p = 20 \log_{10} \left(\frac{p}{p_0}\right)$ (dB), where $p$ is the sound pressure and $p_0$ is the reference pressure (20 µPa)
• Sound intensity level (SIL): $L_I = 10 \log_{10} \left(\frac{I}{I_0}\right)$ (dB), where $I$ is the sound intensity and $I_0$ is the reference intensity ($10^{-12}$ W/m²)
• Reverberation time (Sabine formula): $RT60 = \frac{0.161V}{A}$, where $V$ is the room volume (m³) and $A$ is the total absorption (m²)
  • Total absorption: $A = \sum_{i=1}^{n} S_i \alpha_i$, where $S_i$ is the surface area of material $i$ and $α_i$ is its absorption coefficient
• Doppler effect: $f_o = f_s \left(\frac{v \pm v_o}{v \mp v_s}\right)$, where $f_o$ is the observed frequency, $f_s$ is the source frequency, $v$ is the speed of sound, $v_o$ is the observer velocity (+ if moving towards the source), and $v_s$ is the source velocity (+ if moving away from the observer)