AL

Sound and Its Measurement – Key Vocabulary

Learning Objectives

  • 2.1 Describe sound waves and their common attributes; express how these characteristics are measured.
  • 2.2 Explain core inter-relationships among sound measurements; perform simple calculations (priority = grasping concepts > manipulating equations).
  • 2.3 Identify different reference systems for the decibel and specify when each is appropriate.
  • 2.4 Differentiate physical acoustics from psychoacoustics.
  • 2.5 State the reasons for audiometer calibration and list, in general terms, what calibration entails.

Fundamentals of Sound

  • Sound is generated whenever molecules vibrate and is carried through a medium (gas, liquid, or solid) as a pressure wave.
  • Two broad descriptive domains:
    • Physical acoustics – frequency, intensity, wavelength, velocity, etc. (exists independent of human hearing).
    • Psychoacoustics – pitch, loudness, sound quality, localization (requires human perception).

Molecular Motion & Elasticity

  • Elasticity = “springiness” of a substance; increases as inter-molecular distance decreases. ⇒ Solids > liquids > gases in elasticity.
  • Brownian motion = rapid, random movement of air particles; particle velocity rises with temperature (thermal energy).

Wave Mechanics

  • Waves consist of alternating regions of compression (condensation) and rarefaction.
  • Key parameters:
    • Frequency f (cycles/s; Hz).
    • Period T (time for one cycle); f=\frac{1}{T}.
    • Amplitude (maximum displacement).
    • Phase (angular position within a cycle; 0^{\circ}–360^{\circ}).

Types of Waves

  • Transverse – particle motion ⟂ wave motion.
    • Examples: water ripples, guitar strings, stadium waves, electromagnetic waves, seismic S-waves.
  • Longitudinal – particle motion ∥ wave motion (sound waves, seismic P-waves, clapping, vibrating drumheads, tsunami waves, woofer output).
  • Sinusoidal – mathematical description of simple harmonic motion; foundation of acoustics.

Sine Waves & Pure Tones

  • Each sinusoidal cycle contains one compression and one rarefaction.
  • A pure tone = vibration at one and only one frequency.

Vibration (Oscillation)

  • Repetitive back-and-forth mechanical motion; graphically represented as a sine wave.

Frequency & Periodic Variables

  • Measured in hertz \text{(Hz)}: cycles per second.
  • Determining factors:
    • Length ↑ ⇒ f ↓
    • Mass ↑ ⇒ f ↓ (lower pitch for larger vocal folds).
    • Stiffness/Tension ↑ ⇒ f ↑.

Amplitude & Intensity

  • Amplitude = wave height; psychophysical correlate = loudness.
  • Greater amplitude ⇒ greater intensity (louder sound).

Resonance

  • Resonant (natural) frequency = rate at which a mass vibrates most easily; maximal magnitude & slowest decay.
  • Illustrative example: crystal glass shattering when exposed to its resonant frequency at sufficient amplitude.

Sound Velocity

  • Speed of sound increases with medium density and with temperature/humidity.
    • Typical air value: v \approx 344\,\text{m/s} (≈ 1,130 ft/s).
  • Instantaneous velocity = velocity at a specific moment within the wave.

Wavelength

  • \lambda = \frac{v}{f} (where \lambda = wavelength, v = velocity, f = frequency).
  • Inverse relationship: f ↑ ⇒ \lambda ↓.

Interference

  • When ≥2 waves coexist their instantaneous amplitudes algebraically sum.
    • Constructive (reinforcement) vs. destructive (cancellation) interference depends on frequency, intensity, and phase relationships.

Beats

  • Two tones with small frequency separation (e.g., 1,000 Hz & 1,003 Hz) produce periodic amplitude modulations at the difference frequency (3 Hz) perceived as beats.

Complex Sounds

  • Real-world sounds rarely pure; they comprise multiple sine components.
  • Speech is a highly complex sound.
  • Fourier analysis decomposes any complex wave into its sinusoidal components.
  • Fundamental frequency (F{0}) = lowest component of a periodic complex. • Periodic complex – repeats over time (has F{0}).
    • Aperiodic complex – random, no F_{0} (perceived as noise).
  • Harmonics/Overtones = integer multiples of F_{0}.
  • In speech, resonant energy peaks in the spectrum are formants.

Sound Intensity, Force, Pressure, Work, Power

  • Intensity I = force per unit area; obeys inverse-square law (intensity ∝ \frac{1}{r^{2}}).
  • Force (Newtons, N): greater force ⇒ higher amplitude.
  • Pressure (Pascals, Pa): P \propto F for fixed area.
  • Work (Joules, J): W = F \times d (force × distance moved).
  • Power (Watts, W): rate of energy expenditure; common measure of acoustic magnitude.

Acoustic Impedance Z

  • Opposition a medium presents to sound transmission.
    • Units: Ohms (Ω).
  • Z increases with density.
  • Components:
    • Resistance (friction).
    • Reactance (frequency-dependent):
    – Mass reactance (dominates high frequencies).
    – Stiffness reactance (dominates low frequencies).

The Decibel (dB)

  • Logarithmic unit expressing a ratio:
    \text{dB} = 10 \log{10} \left(\frac{I{\text{meas}}}{I{\text{ref}}}\right) or 20 \log{10} \left(\frac{P{\text{meas}}}{P{\text{ref}}}\right).
  • 0\,\text{dB} ≠ “no sound”; it means measured intensity = reference.
  • Doubling intensity (+100 %) ⇒ +3 dB, not ×2 dB.
  • Reference scales:
    • dB IL (Intensity Level) – physical intensity reference.
    • dB SPL (Sound Pressure Level) – physical pressure reference; used in calibration & acoustics.
    • dB HL (Hearing Level) – psychophysical reference based on average normal thresholds (18–25 yr olds); varies with frequency.
    • dB SL (Sensation Level) – referenced to an individual’s threshold.
    – Example: threshold 20 dB HL, presentation 60 dB HL ⇒ 40 dB SL.

Hearing Level & Audiometer Calibration

  • ANSI establishes audiometric reference levels (audiometric zero = 0\,\text{dB HL}).
  • Clinical audiometers typically cover -10\,\text{dB HL} to 110\,\text{dB HL}.
  • Calibration ensures output intensities match ANSI reference values.

Equal Loudness Contours

  • Show dB SPL required across frequencies to achieve equal perceived loudness (measured in phons).
  • Mid-frequencies (≈ 3 kHz) need less SPL for equal loudness than very low or very high frequencies.

Psychoacoustic Attributes

  • Pitch ⇔ frequency (mel scale accommodates intensity effects).
    • Hearing loss alters pitch perception.
  • Loudness ⇔ intensity (phon & sone scales; affected by frequency).
  • Localization – relies on inter-aural intensity & phase cues; requires two healthy ears.
  • Masking – elevation of threshold for one sound due to presence of another (masker).

Diagnostic Audiometer

  • Measures hearing via:
    • Air-conduction pure tones.
    • Bone-conduction pure tones.
    • Speech audiometry (words/sentences).
  • Transducers: supra-aural earphones, insert earphones, bone vibrator, loudspeakers (sound field).
  • Controls independently select frequency and intensity.

Sound Measurement Instruments

  • Pure-Tone Audiometer – basic screenings.
  • Speech (Clinical) Audiometer – full diagnostic battery; includes recorded/live-voice speech & sound-field capability.
  • Sound Level Meter (SLM): hand-held mic-based device recording \text{dB SPL}. Audiological uses:
    • Verify test-booth ambient noise < ANSI maximum permissible levels.
    • Calibrate audiometer outputs (earphone couplers: 6\,\text{cm}^3 supra-aural, 2\,\text{cm}^3 insert; artificial mastoid for bone).
  • Weighting networks:
    • A-weighting (dBA): mimics ear’s risk contour; OSHA compliance.
    • C-weighting (dBC): flat 30–10,000 Hz; explosions, engines.

Noise Exposure Guidelines

  • Cumulative damage risk grows with time + level.
  • Common thresholds (NIH “It’s a Noisy Planet”, 2019):
    • ≤70 dBA – generally safe indefinitely.
    • 85 dBA – potentially harmful after a few hours.
    • 100 dBA – harmful after ≈14 min.
    • 110 dBA – harmful after ≈2 min.

Acceptable Ambient Noise for Audiometry

  • ANSI (1999) lists maximum permissible sound-booth levels; stricter for supra-aural earphones than insert earphones.
  • Clinicians must monitor and document room noise during testing.

Key Equations & Relationships

  • f = \frac{1}{T} (period ↔ frequency).
  • \lambda = \frac{v}{f} (wavelength).
  • \text{dB} = 10 \log{10} \big(\frac{I}{I0}\big) = 20 \log{10} \big(\frac{P}{P0}\big).
  • Inverse-square law: I \propto \frac{1}{r^{2}}.
  • Work: W = F \times d.

Practical & Ethical Implications

  • Accurate calibration safeguards diagnostic validity & patient safety.
  • Understanding psychoacoustics guides hearing-aid fitting, noise-control policy, & communication-disorder therapies.
  • Noise-exposure education (e.g., OSHA, NIH campaigns) mitigates lifelong hearing-loss risk.