Waves and Sound

Gives the displacement of a medium particle at position x and time t for a harmonic wave travelling in the positive x direction.

Relates wave propagation speed to frequency, wavelength, angular frequency, and angular wave number.

Calculates the propagation speed of a transverse wave on a string under tension T with linear mass density μ.

Expresses the mass per unit length of a uniform circular wire in terms of its mass, length, density, and radius.

Calculates the speed of longitudinal waves through a fluid of bulk modulus B or a solid rod of Young's modulus Y.

Calculates the speed of sound in an ideal gas under Laplace's adiabatic assumption as a function of temperature.

Calculates the resultant amplitude when two sinusoidal waves of identical frequency superpose with phase difference φ.

Gives the displacement relation of a standing wave formed by the superposition of two identical oppositely directed travelling waves.

Gives the separation between consecutive nodes (or antinodes) and between a node and its adjacent antinode.

Gives the fundamental frequency and higher harmonics for transverse standing waves on a string fixed at both ends.

Gives all integer harmonic resonant frequencies for an air column in a pipe open at both ends.

Gives the odd harmonic resonant frequencies of an air column in an organ pipe closed at one end.

Relates the first two resonance tube lengths to sound wavelength and Rayleigh end correction for a pipe of radius r.

Calculates the number of periodic waxing and waning of sound intensity heard per second from two slightly detuned sources.

Gives the apparent frequency perceived by an observer moving at speed v_o relative to a source moving at speed v_s in air.