physics//wave//sound

2026-10-02

Sound is a pressure wave: a travelling pattern of compressions and rarefactions in a gas, a liquid or a solid, and it is what microphones, sonar, parking sensors and medical scanners send or listen for. In air and water it is longitudinal (the particles move back and forth along the direction of travel); a solid can also carry shear waves, which fluids cannot.

Its speed depends only on the medium, on how stiff it is against compression and how dense it is:

c=K/ρ,c = \sqrt{K/\rho},c=K/ρ,

where KKK is the bulk modulus and ρ\rhoρ the density. Stiffness wins over weight, which is why sound is faster in water than in air and faster again in metal: about 343 m/s in dry air at 20 °C, 1481 m/s in fresh water at the same temperature, and about 5120 m/s in iron.

The speed is the ruler of every echo instrument. A sonar or a scanner measures time and converts it to distance with an assumed ccc; an error in that assumption is an error in every distance it reports. In air the speed also rises with temperature, by about 0.6 m/s per degree, so an ultrasonic range sensor that ignores the temperature misreads distance by roughly 2 mm per metre for every degree it is off.

Human hearing covers roughly 20 Hz to 20 kHz, and the upper limit falls with age. Above it lies ultrasound, the same physics at wavelengths short enough to image.

What fraction of a sound wave crosses a boundary, and what fraction comes back as an echo, is decided by the acoustic impedance of the two sides, which is why sound in air barely enters water and why a scanner needs gel.

Sound fades with distance for two reasons that a measurement has to separate: spreading, which dilutes the same energy over a larger area, and absorption by the medium, which turns it into heat and grows with frequency.