Sound waves carry energy, and intensity measures how much energy flows through an area. This topic explores how we quantify sound intensity and relate it to our perception of loudness.

We'll learn about the decibel scale, which helps us compare vastly different sound intensities. We'll also dive into how our ears and brains process sound, affecting our perception of loudness.

Sound Intensity and Energy Transfer

Defining Sound Intensity

• Sound intensity measures sound energy transmitted through unit area per unit time (W/m²)
• Directly proportional to sound source power
• Inversely proportional to surface area of sound spread
• Follows inverse square law decreases as square of distance increases
• Vector quantity with magnitude and direction perpendicular to wavefront
• Energy transfers through compression and rarefaction of medium (air) as wave propagates

Relationship to Power and Energy

• Power of sound source represents total energy emitted per unit time (watts)
• Related to intensity by surface area sound passes through
• Sound intensity (I) calculated using formula: $I = P / (4πr²)$
  • P = power of sound source
  • r = distance from source
• Examples of sound intensities:
  • Whisper: $10^{-10}$ W/m²
  • Normal conversation: $10^{-6}$ W/m²

Calculating Sound Intensity Levels

Decibel Scale Basics

• Logarithmic scale expresses wide range of intensities humans perceive
• Sound intensity level (β) in decibels calculated using: $β = 10 \log_{10}(I/I_0)$
  • I = measured intensity
  • I₀ = reference intensity (typically $10^{-12}$ W/m² for air)
• Reference intensity I₀ corresponds to threshold of human hearing at 1000 Hz (0 dB)
• Each 10 dB increase represents tenfold increase in sound intensity
• Each 3 dB increase approximately doubles intensity

Applying the Decibel Scale

• Compare sound intensities using difference in dB levels: $Δβ = β_2 - β_1 = 10 \log_{10}(I_2/I_1)$
• Convert intensity levels back to absolute intensities: $I = I_0 × 10^{(β/10)}$
• Examples of sound intensity levels:
  • Quiet library: 30 dB
  • Normal conversation: 60 dB
  • Rock concert: 110 dB

Loudness and Frequency Dependence

Understanding Loudness Perception

• Subjective perception of sound intensity influenced by physical properties and human hearing
• Relationship between perceived loudness and sound intensity approximately logarithmic
• Equal-loudness contours (Fletcher-Munson curves) illustrate loudness perception variation with frequency
• Human ears most sensitive to frequencies between 2000 and 5000 Hz

Measuring Loudness

• Sound pressure level (SPL) closely related to sound intensity
• Often used interchangeably in practical applications
• Measured in dB relative to reference pressure of 20 μPa
• Phon scale quantifies loudness level
  • 1 phon defined as loudness of 1000 Hz tone at 1 dB SPL
  • Equal-loudness contours show lines of equal phon values across frequencies
• Loudness perception follows Stevens' power law: $L ∝ I^{0.3}$
  • L = perceived loudness
  • I = sound intensity

Factors Affecting Loudness Perception

Human Auditory System

• Anatomy includes outer, middle, and inner ear structures
• Basilar membrane in cochlea performs frequency analysis of incoming sounds
• Different regions respond to different frequencies (tonotopic organization)
• Auditory masking occurs when perception of one sound affected by presence of another
• Temporal integration affects loudness perception
  • Longer duration sounds generally perceived as louder than shorter sounds of same intensity

Psychoacoustic Factors

• Critical band theory explains how auditory system groups frequencies for loudness perception
• Affects perception of complex sounds and noise
• Binaural loudness summation sound presented to both ears perceived as louder than to one ear
• Loudness adaptation and fatigue occur with prolonged exposure
  • Can lead to temporary or permanent changes in loudness perception and hearing sensitivity
• Examples of psychoacoustic effects:
  • Cocktail party effect ability to focus on single conversation in noisy environment
  • Pitch circularity perception of continuously ascending or descending pitch (Shepard tone)