2.1 Principles of Sound and Acoustics

Sound waves are the foundation of audio production. Understanding their properties and behavior is crucial for creating quality recordings and mixes. From propagation to reflection, refraction, and absorption, these principles shape how we perceive and manipulate sound.

Frequency, amplitude, phase, and wavelength are key concepts in audio. They determine pitch, loudness, and tonal quality, influencing everything from microphone placement to speaker design. Mastering these fundamentals is essential for effective music production and recording.

Sound Wave Properties

Propagation and Behavior

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• Sound waves propagate through mediums as longitudinal pressure waves causing particle compressions and rarefactions
• Speed of sound varies based on medium properties (temperature, humidity, density)
• Reflection bounces sound waves off surfaces following the law of reflection (angle of incidence equals angle of reflection)
• Refraction bends sound waves passing between mediums with different densities altering direction and speed
• Diffraction allows sound waves to bend around obstacles or spread through openings depending on wavelength and obstacle size
• Absorption converts sound energy into heat energy when interacting with materials
  • Different materials have varying absorption coefficients across frequencies
  • Affects reverberation time and overall room acoustics
• Interference occurs when multiple sound waves interact
  • Constructive interference amplifies sound
  • Destructive interference cancels sound

Advanced Concepts

• Standing waves form in enclosed spaces when incident and reflected waves combine
  • Create areas of high and low pressure (nodes and antinodes)
  • Influence room acoustics and speaker placement
• Doppler effect changes perceived frequency as source or listener moves
  • Approaching source increases perceived frequency
  • Receding source decreases perceived frequency
• Resonance amplifies sound at specific frequencies in enclosed spaces
  • Determined by room dimensions and shape
  • Can cause uneven frequency response in listening environments

Frequency, Amplitude, Phase, and Wavelength

Fundamental Concepts

• Frequency measures wave cycles per second in Hertz (Hz)
  • Directly relates to perceived pitch
  • Human hearing range spans approximately 20 Hz to 20 kHz
• Amplitude represents maximum wave displacement from equilibrium
  • Correlates to perceived loudness
  • Measured in decibels (dB) for sound pressure levels
• Phase indicates waveform position relative to reference point
  • Measured in degrees or radians
  • Affects sound quality and stereo imaging
• Wavelength spans distance between consecutive wave peaks
  • Inversely proportional to frequency
  • Calculated using speed of sound and frequency ($\lambda = c/f$)

Relationships and Applications

• Speed of sound equation: $c = f \times \lambda$
  • c = speed of sound (m/s)
  • f = frequency (Hz)
  • λ = wavelength (m)
• Harmonics represent integer multiples of fundamental frequency
  • Contribute to timbre and tonal quality
  • Even harmonics (2f, 4f, 6f) often produce "warmer" sounds
  • Odd harmonics (3f, 5f, 7f) can add "edge" or "brightness"
• Fourier theorem states complex waveforms decompose into simple sine waves
  • Enables spectral analysis and synthesis techniques
  • Forms basis for many audio processing algorithms

Sound Pressure Level vs Loudness

Sound Pressure Level (SPL)

• SPL measures effective sound pressure relative to reference value
  • Expressed in decibels (dB)
  • Reference pressure typically 20 μPa (threshold of human hearing)
• Decibel scale logarithmic nature
  • 10 dB increase represents tenfold intensity increase
  • 3 dB increase doubles sound intensity
  • 6 dB increase doubles sound pressure
• Common SPL values
  • 0 dB: Threshold of hearing
  • 60 dB: Normal conversation
  • 90 dB: Loud music
  • 120-140 dB: Threshold of pain

Perceived Loudness

• Loudness subjectively measures sound intensity perception
  • Not directly proportional to SPL
  • Influenced by frequency, duration, and spectral content
• Fletcher-Munson curves (equal-loudness contours) illustrate loudness perception variations
  • Show reduced sensitivity to low and high frequencies
  • Explain need for loudness compensation in audio systems
• Phon scale measures perceived loudness
  • 1 phon equals 1 dB SPL at 1 kHz
  • Accounts for frequency-dependent loudness perception
• Factors affecting loudness perception
  • Temporal integration combines sound energy over time
  • Auditory masking occurs when louder sounds obscure quieter ones
  • Binaural summation increases perceived loudness for sounds from multiple directions

Direct Sound vs Reflections

Direct Sound Characteristics

• Direct sound travels straight from source to listener without reflections
  • Arrives first providing crucial source location and characteristic information
  • Determines initial timbral and spatial perception
• Importance in stereo imaging and sound localization
  • Interaural time differences (ITD) and interaural level differences (ILD) cues
  • Precedence effect (Haas effect) prioritizes direct sound for localization
• Critical distance marks point where direct and reverberant sound energies equalize
  • Influences microphone placement and listening positions
  • Affects clarity and definition of recorded or reproduced sound

Early Reflections and Reverberation

• Early reflections reach listener shortly after direct sound (within 50-80 ms)
  • Contribute to perceived spaciousness and source width
  • Enhance or degrade sound quality depending on timing and direction
• Reverberation persists after original sound stops due to multiple reflections
  • Characterized by reverberation time (RT60)
    • Time for sound to decay by 60 dB after source stops
    • Optimal RT60 varies by room use (music, speech, etc.)
  • Initial time delay gap (ITDG) between direct sound and first reflection
    • Affects perceived intimacy and clarity
    • Shorter ITDG increases sense of closeness to source
• Room modes (standing waves) occur at specific frequencies
  • Determined by room dimensions
  • Can cause uneven frequency response and sound coloration
  • Addressed through acoustic treatment and speaker/listener positioning