Glossary - The Physics of Waves

Terms as they are used in this book. Cross-references point into the chapters where the idea is introduced.

Absorptive amplitude: The imaginary part of a complex driven-oscillator amplitude. It is largest at resonance and measures the part of the response in phase with the driving force’s power input. See Chapter 2.
Angular frequency $\omega$: Radians per unit time. Related to the ordinary frequency $\nu$ (cycles per unit time) by $\omega = 2\pi\nu$ .
Dispersion relation: An algebraic relation between $\omega$ and $k$ (or $k^2$ ) that a traveling or standing wave in a given medium must satisfy. It depends on the infinite system, not on the boundary conditions. See Chapter 5.
Elastic amplitude: The real part of a complex driven-oscillator amplitude; the part of the displacement in phase with the driving force.
Group velocity: The velocity of the envelope of a wave packet, $v_g = d\omega/dk$ . Distinct from the phase velocity $v_\varphi = \omega/k$ . See Chapter 10.
Impedance: For a traveling wave, the ratio of the driving force (or voltage) to the resulting velocity (or current). Continuity of force and displacement at a junction is conveniently expressed in terms of impedances. See Chapter 8.
Irreducible solution: A solution of a linear, time-translation-invariant equation that merely rescales under a shift of the time origin, $z(t+a)=h(a)z(t)$ . For the systems in this book these are complex exponentials. See Chapter 1.
Linearity: Superposition: if $x_1$ and $x_2$ are solutions, so is $A x_1 + B x_2$ . Small oscillations of a conservative system about a stable equilibrium are linear.
Local interactions: Each degree of freedom couples only to its neighbors, not to distant parts of the system. Together with linearity and translation invariance, this produces waves.
Normal mode: A motion in which every coordinate oscillates at a single frequency. In a linear system the general free motion is a superposition of normal modes. See Chapter 3.
Phase velocity: The velocity of a surface of constant phase, $v_\varphi = \omega/k$ .
Polarization: The pattern of the two (or more) transverse components of a wave, for example linear or circular. See Chapter 12.
Time translation invariance: The equations of motion do not change if the origin of time is shifted. If $x(t)$ is a solution, so is $x(t+a)$ .
Translation invariance: The infinite system looks the same after a discrete (or continuous) shift in space. This is what makes $e^{ikx}$ a useful building block for waves.