A wave carries a disturbance through a medium. In a transverse wave particles move perpendicular to propagation; in a longitudinal wave they move parallel to it. Follow the highlighted particle to distinguish particle oscillation from the traveling pattern.
The traveling-wave phase advances along the medium as time passes. Frequency sets the oscillation rate and wavelength sets the spatial repetition. Together they determine the propagation speed.
Where pulses overlap their displacements add algebraically. They then pass through with their original shapes in a linear medium. A pulse reflected at a fixed end inverts; a free-end reflection remains upright.
Two opposite traveling waves form a standing pattern with fixed nodes. Both fixed ends must be nodes, so only wavelengths 2L/n fit. Higher tension raises all harmonic frequencies; greater linear density lowers them.
An open end allows air displacement while a closed end constrains it. Two open ends support every integer harmonic; one closed end supports only odd harmonics. The mode index counts allowed modes, not necessarily harmonic number.
Nearby tones alternate between constructive and destructive interference. The loudness envelope repeats at the difference frequency. The signed envelope has twice the intensity-peak spacing because positive and negative peaks both correspond to loud sound.
Sound propagation depends on a gas’s adiabatic compressibility and density. In an ideal gas their pressure dependence cancels, leaving temperature, molar mass and heat-capacity ratio. Warm or light gases transmit sound faster.
An approaching source compresses the wavefront spacing and raises observed frequency. An approaching observer meets wavefronts faster. Their velocities enter different parts of the sound Doppler formula because the medium defines a preferred frame.