Hearing Science Exam Pt 2

What are the two types of waves?

Transverse and Longitudinal

How do particles move in a transverse wave?

Perpendicular to wave propagation

How do particles move in a longitudinal wave?

Parallel to wave propagation (compression and rarefaction)

Define frequency.

Number of cycles per second (Hz)

Define wavelength.

Distance between successive points of similar phase

Define period.

Time for one cycle = 1/f

Define phase.

Relative timing position within a cycle (0°–360°)

Define amplitude.

Maximum displacement from equilibrium

List properties of a medium.

Mass, Density, Elasticity

What does elasticity determine?

How well a medium returns to original shape

What does density affect?

Speed and impedance of sound

State Hooke’s Law.

F = −k x (restoring force is proportional to displacement)

Define stiffness and compliance.

Stiffness = k (↑ restoring force); Compliance = 1/k

List Newton’s three laws.

1) Inertia 2) F = m a 3) Action = Reaction

What is inertia?

Resistance to change in motion

Differentiate scalar and vector quantities.

Scalar = magnitude only; Vector = magnitude + direction

Define acceleration.

Change in velocity / time

Define force.

Mass × acceleration

Define pressure.

Force / area (Pascals)

Define momentum.

Mass × velocity

Define kinetic energy.

½ m v²

Define potential energy.

Stored energy due to position

Define work.

Force × distance

Speed of sound in air?

≈ 343 m/s (at 20 °C)

What is a complex wave?

Sum of two or more sine waves

Periodic vs Aperiodic?

Periodic = repeats; Aperiodic = random (no repetition)

Describe a sawtooth wave.

Contains all harmonics; amplitude ∝ 1/n

Describe a square wave.

Odd harmonics only; amplitude ∝ 1/n

Describe a triangular wave.

Odd harmonics only; amplitude ∝ 1/n² (smoother)

Describe a pulse wave.

Single burst or short on–off cycles

Define reflection.

Wave bounces off surface

Define refraction.

Change in direction when entering different medium

Define diffraction

Bending of wave around barrier or through opening

Define interference

Two waves combine to reinforce or cancel

Constructive vs Destructive interference?

Constructive = in-phase → ↑ amplitude; Destructive = 180° out of phase → cancel

Define standing wave.

Result of interference between incident and reflected waves

Define node and antinode.

Node = no motion; Antinode = max motion

Define harmonics and overtones.

Harmonic = integer multiple of f₀; Overtone = 2nd, 3rd etc. harmonic

Define beats.

Amplitude fluctuation from two close frequencies (beat frequency = difference)

Define resistance.

Opposition to motion due to friction (R = F/v)

Define power.

Work / time (W = J/s)

Define impedance (Z)

Total opposition to sound flow = √(R² + (Xₘ–Xₛ)²)

Define acoustic impedance.

ρ × c (density × speed of sound)

What are the 3 components of impedance?

Resistance, Mass Reactance, Stiffness Reactance

Mass reactance formula?

Xₘ = 2πf m

Stiffness reactance formula?

Xₛ = 1 / (2πf C)

As frequency ↑

→ Xₘ ? Xₛ ? → Xₘ ↑ Xₛ ↓

Define resonant frequency.

→ fᵣ where Xₘ = Xₛ → impedance minimum

Below fᵣ which dominates?

Stiffness

Above fᵣ which dominates?

Mass

Simplified relation between impedance, density, elasticity?

Z ≈ √(ρ × elasticity)

How are filters relevant to human anatomy?

Ear canal, vocal tract, middle ear act as acoustic filters and resonators

List filter types and functions.

Low-pass = passes low f; High-pass = passes high f; Band-pass = range; Band-stop = notch

Define cutoff frequency.

Point where output drops 3 dB (half-power)

Define resonance.

When input frequency matches natural frequency → max amplitude

Formula for open–open tube resonance.

fₙ = n c / 2L

Formula for open–closed tube resonance.

fₙ = (2n − 1) c / 4L

Example of open–open tube.

Flute, /vowels/

Example of open–closed tube

Ear canal, clarinet

Fundamental frequency of 2.5 cm ear canal.

≈ 3400 Hz (3.4 kHz)

Reference intensity.

10⁻¹² W/m²

Reference pressure.

20 µPa (2 × 10⁻⁵ Pa)

Equation for dB IL.

10 log (Ix/Ir)

Equation for dB SPL.

20 log (px/pr)

Why 20 log for pressure?

Because I ∝ p²

0 dB means?

Equal to reference level (threshold of hearing)

Doubling intensity

Δ? → +3 dB

Doubling pressure

Δ? → +6 dB

Negative dB means?

Below reference threshold

Inverse square law formula.

I₂ = I₁ · (r₁/r₂)²

Doubling distance changes dB by?

−6 dB

Can you add dB values directly?

No — convert to intensity first

Rule for adding equal sources

+3 dB

Rule for difference 0–1 dB.

Add 3 dB to higher

Rule for difference 2–3 dB

Add 2 dB to higher

Rule for difference 4–7 dB.

Add 1 dB to higher

Rule for difference ≥ 8 dB.

Add 0 dB (no change)

Example: Two 80 dB sources.

Combined = 83 dB

Ten identical sources @ 80 dB.

100 + 10 log 10 = 110 dB

Define inverse square law conditions.

Applies only to direct sound, not reflections