In-Depth Notes on Sound and Digital Audio Concepts

WHAT IS SOUND?

• Sound is a mechanical wave that requires a medium to propagate.

  • Oscillates through space and deforms the medium.

  • Air, made up of many particles, is the medium for sound propagation.

SOUND PROPAGATION

• Creating Sound:

  • Actions like plucking a string, hitting a drum, or clapping hands cause air pressure changes.

• Pressure Changes:

  • Compression: Increased pressure above ambient atmospheric pressure.

  • Rarefaction: Decreased pressure below ambient atmospheric pressure.

  • Ears detect these changes and convert them into electrical signals interpreted as sound.

THE EAR

• Outer Ear: Funnels sound into the ear canal.

• Middle Ear: Eardrum vibrates in response to sound waves.

• Inner Ear: Transmits vibrations to cochlea, stimulating hair cells.

• Auditory Nerve: Carries signals to the brain for interpretation.

PROPERTIES OF SOUND

• Speed of Sound:

  • Speed sound travels through air, affected by density and elasticity.

  • Speed changes with temperature, humidity, and altitude.

  • Average speed is $343 ext{ m/s}$ at $20^{ ext{°C}}$ and sea level.

• Amplitude:

  • Measures intensity or magnitude of a sound wave.

  • Higher amplitude = louder sound; lower amplitude = quieter sound.

• Frequency:

  • Rate of oscillation measured in Hertz (Hz).

  • Higher frequency = higher pitch; lower frequency = lower pitch.

  • Human hearing range: $20 ext{Hz} - 20,000 ext{Hz} (20 ext{kHz})$.

• Period:

  • Time to complete a cycle: $T = rac{1}{ ext{frequency}}$.

  • For $200 ext{Hz}$ sound, period is $0.005 ext{s}$.

• Wavelength:

  • Length of sound wave: $ext{wavelength} \ ( ext{λ}) = rac{ ext{velocity}}{ ext{frequency}}$.

  • For a $200 ext{Hz}$ signal, wavelength is approximately $1.715 ext{ m}$.

• Phase:

  • Current position within a cycle, measured in degrees (360° = complete cycle).

• Constructive & Destructive Interference:

  • Constructive: Same polarity amplitudes increase total sound;

  • Destructive: Opposing amplitudes can cancel each other.

WAVEFORM CHARACTERISTICS

• Sine Tones: Only single frequency with no harmonics.

• Timbre: Quality or character of sound, determined by total frequency content (descriptor terms like ‘brassy’, ‘dull’).

  • Fundamental Frequency: Primary pitch; harmonic series includes integer multiples of the fundamental.

SOUND VISUALIZATION

• Amplitude/Time, Amplitude/Frequency, Frequency/Time:

  • Various visual formats show sound characteristics in different dimensions.

TIME IN SOUND

• Envelope:

  • Describes sound characteristics over time:

  • Attack: Initial onset;

  • Decay: Decrease in amplitude post-attack;

  • Sustain: Steady amplitude;

  • Release: Amplitude decreases to silence.

• ADSR: Common model for envelope representation.

INTENSITY AND LOUDNESS

• Intensity: Measured based on pressure, different from loudness (perceived intensity).

• Decibel Scale: Logarithmic measure; every increase of 10 dB means tenfold intensity increase.

• Thresholds:

  • Decibels' impact on human ear perception ranging from threshold of hearing (0 dB) to pain threshold (10 W/m²).

DIGITAL AUDIO

• Conversion: Audio is digitized through analog-to-digital conversion (ADC).

• Sampling: Capture sound by measuring amplitudes at intervals; higher sample rates lead to better quality.

• Sample Rate: 44.1kHz is standard for CDs; based on Nyquist Theorem.

• Bit Depth: Defines dynamic range and resolution; standard values are 16-bit, 24-bit, and 32-bit float.

CLIPPING

• Occurs when audio exceeds maximum levels in digital format; results in distortion.

RECAP

• Key Concepts: Amplitude, Frequency, Phase, Timbre, Envelope (ADSR), Intensity, Loudness, Digital Audio, Sampling, Bit Depth, Clipping.