Unit 6 Waves and Sound: Mechanical Waves, Sound, and Standing-Wave Resonance

Wave

A traveling disturbance that transfers energy and momentum from one place to another without permanently transporting matter.

Transverse wave

A wave in which the medium oscillates perpendicular to the direction the wave travels (propagates).

Longitudinal wave

A wave in which the medium oscillates parallel to the direction the wave travels; sound in air is a key example.

Amplitude

The maximum displacement from equilibrium (or maximum pressure/density variation for sound).

Wavelength (λ)

The spatial period of a repeating wave; the distance between repeating points (e.g., crest-to-crest or compression-to-compression).

Period (T)

The time for one full cycle of oscillation.

Frequency (f)

The number of cycles per second (Hz); related to period by f = 1/T.

Wave speed (v)

How fast the wave pattern moves through space; related by v = fλ and is set by the medium’s properties (in typical AP contexts).

Intensity (I)

Power delivered per area by a wave; I = P/A (for sound, tied to loudness).

Inverse-square law (spherical spreading)

For roughly uniform radiation in all directions, A = 4πr² so intensity decreases with distance as I = P/(4πr²) (doubling r makes I one-fourth).

Principle of superposition

When waves overlap, the resulting displacement equals the algebraic sum of the individual displacements.

Constructive interference

Interference where waves arrive in phase and produce a larger net amplitude (for equal-wavelength waves: Δr = mλ).

Destructive interference

Interference where waves arrive out of phase and reduce/cancel amplitude (for equal-wavelength waves: Δr = (m + 1/2)λ); energy is redistributed, not destroyed.

Path difference (Δr)

The difference in distances traveled by two waves to reach a point; determines whether interference is constructive (mλ) or destructive ((m + 1/2)λ).

Boundary reflection (fixed vs free end)

When a transverse wave reflects: at a fixed end the reflected pulse inverts (phase inversion); at a free end it does not invert.

Compression

In a sound (longitudinal) wave, a region of higher-than-average pressure/density.

Rarefaction

In a sound (longitudinal) wave, a region of lower-than-average pressure/density.

Bulk modulus (B)

A measure of how difficult a medium is to compress; for sound in fluids, larger B tends to increase speed (v = √(B/ρ)).

Density (ρ)

Mass per volume of a medium; for sound in fluids, larger ρ tends to decrease speed (v = √(B/ρ)).

Decibel (dB) sound level (β)

A logarithmic measure of sound intensity: β = 10 log10(I/I0), with I0 = 1.0×10⁻¹² W/m²; +10 dB means 10× intensity.

Resonance

Large-amplitude oscillations when a system is driven at (or near) one of its natural frequencies, making energy transfer especially efficient (limited by damping).

Beats

A loudness pulsing caused by superposition of two close frequencies; beat frequency fbeat = |f1 − f2|.

Doppler effect

A change in observed frequency due to relative motion between source and observer; approaching increases observed frequency, separating decreases it.

Standing wave

A stable pattern formed by interference of two waves of the same frequency and amplitude traveling in opposite directions, producing fixed nodes and antinodes.

Harmonic

A resonant mode in a standing-wave system; for many systems, frequencies are integer multiples of the fundamental (with open-closed pipes allowing only odd harmonics).