Praxis Audiology (5343)

Sound is a propagated disturbance of particles in an elastic medium. Air particles oscillate around a rest position, producing alternating regions of condensation (increased pressure) and rarefaction (decreased pressure); the particles do not travel with the wave. Sound requires a medium with mass (inertia) and elasticity (stiffness), and its speed depends on the medium: about 343 m/s in air at 20 °C (often rounded to 340 m/s), roughly 1,480 m/s in water, and faster still in solids such as bone.

The simplest vibration is simple harmonic motion, whose pressure-time waveform is a sinusoid (pure tone). A sinusoid is fully described by three properties: frequency, amplitude, and starting phase. Every other sound can be described as a sum of sinusoids (Fourier analysis).

THE SINUSOID: AMPLITUDE, PERIOD, AND PHASE

RMS amplitude of a sinusoid = 0.707 x peak amplitude.

Two cycles of a pure tone. Amplitude is measured from rest to peak; peak-to-peak is twice the peak amplitude; one period spans 360 degrees of phase.

Frequency (f): cycles per second, in hertz (Hz). Perceptual correlate is pitch. Normal human range is about 20 to

Wavelength is inversely related to frequency.

Amplitude: magnitude of displacement or pressure, expressed as peak, peak-to-peak, or root-mean-square (RMS). Perceptual correlate is loudness. Sound level meters and audiometers express RMS values. Phase: the point in the cycle, in degrees (0–360°). Two equal tones 180° apart cancel completely; tones in phase reinforce. A time delay converts to phase as (delay / period) × 360°: a 0.25-ms delay of a 1000-Hz tone equals 90°.

Wavelength has clinical consequences. The head casts an acoustic shadow mainly for high frequencies, whose wavelengths are short relative to head size. Reflected pure tones in a booth create standing waves with fixed level peaks and nulls, so sound-field testing uses warble tones or narrowband noise.

Simple periodic Sinusoid Single line

Line spectrum: f0 plus harmonics

Vowels, square wave, voiced speech

Complex aperiodic No repetition Continuous spectrum

In a complex periodic sound, the fundamental frequency (f0) is the lowest component and the repetition rate of the waveform; harmonics are integer multiples of f0 (a 200-Hz f0 has harmonics at 400, 600, 800 Hz). Shorter signals have broader spectra: the briefer the stimulus, the greater its spectral splatter. This time-frequency trade-off explains why a click is an excellent synchronizing stimulus for the ABR but has poor frequency specificity, and why tone bursts used for frequency-specific ABR have rise-fall times of a few cycles.

Every object has a natural (resonant) frequency at which it vibrates with the least opposition. A tube closed at one end, such as the external auditory canal closed by the tympanic membrane, resonates at a quarter wavelength: f = c/4L. With an adult canal length of about 2.5 cm, f ≈ 343/(4 × 0.025) ≈ 3,400 Hz; the measured ear canal resonance is generally cited near 2,500–3,000 Hz because the canal is not a rigid uniform tube. The concha adds a resonance near 5 kHz. Together, the open ear produces a gain of roughly 15–20 dB in the 2–4 kHz region (the real-ear unaided response, REUR). Occluding the canal with an earmold removes this natural gain (insertion loss), which hearing aid fittings must restore.

Impedance (Z) is total opposition to energy flow, measured in ohms. It has a frequency-independent resistance (R) component (friction) and a frequency-dependent reactance: mass reactance (Xm) increases with frequency, and stiffness (compliant) reactance (Xs) decreases with frequency. Z = √[R² + (Xm − Xs)²]. At the resonant frequency Xm = Xs, reactance cancels, and only resistance remains. Admittance (Y) is the reciprocal of impedance, with conductance

Link pathology to the impedance component it changes.

Stiffness-dominated system (normal middle ear at 226 Hz): stiffness reactance governs low frequencies. Otosclerosis and ossicular fixation add stiffness and affect low frequencies most. Mass-related pathology (fluid, cholesteatoma mass, thickened TM) affects high frequencies more. Normal adult middle ear resonance is roughly 800–1,200 Hz; increased stiffness raises it and added mass or