A wave is a disturbance that propagates through space and time, transferring energy from one place to another without any net transport of matter. Waves are characterized by their wavelength, frequency, and speed. Two main types of waves are distinguished by the direction in which the medium's disturbance occurs relative to the direction of propagation. In transverse waves, the oscillations are perpendicular to the direction of wave travel, as in light or waves on a string. In longitudinal waves, the oscillations are parallel to the direction of travel, as in sound. For all waves, the speed equals the product of frequency and wavelength, with \(v = f\lambda\).
Sound travels through gases, liquids, and solids as a longitudinal wave. In an ideal gas, its speed is given by \(v = \sqrt{\gamma P/\rho}\) or, equivalently, \(v = \sqrt{\gamma RT/M}\), where \(\gamma\) is the ratio of specific heats, \(P\) is pressure, \(\rho\) is density, \(T\) is absolute temperature, and \(M\) is the molar mass. In air at 20 °C, the speed of sound is approximately 343 m/s. When a source of sound and an observer move relative to each other, the observed frequency shifts. This is the Doppler effect, described by \(f' = f(v \pm v_o)/(v \pm v_s)\), where the signs depend on whether the observer or source is moving toward or away from the other. The familiar change in pitch of a passing siren is a common example.
Oscillatory motion of a particular kind is called simple harmonic motion, or SHM. In SHM, the restoring force on an object is directly proportional to the displacement from equilibrium and points back toward it, giving \(F = -kx\). The corresponding acceleration is \(a = -\omega^2 x\), where \(\omega\) is the angular frequency. A simple pendulum, when its amplitude is small, is an excellent approximation to SHM, and its period depends only on its length and the local gravitational acceleration, with \(T = 2\pi\sqrt{L/g}\). Notably, the period of a simple pendulum is independent of the mass of the bob and, for small oscillations, of the amplitude.