physics//wave

A wave is a disturbance that travels through a medium or a field and carries energy from one place to another while the medium itself stays where it is, and it is how most remote measurement works: a sensor sends a wave out, or waits for one, and reads what the trip did to it. Sound, ultrasound, radio, light and the ripples on a pond are all waves, and the same few quantities describe every one of them.

A wave is a disturbance that travels through a medium or a field and carries energy from one place to another while the medium itself stays where it is, and it is how most remote measurement works: a sensor sends a wave out, or waits for one, and reads what the trip did to it. Sound, ultrasound, radio, light and the ripples on a pond are all waves, and the same few quantities describe every one of them.

Each point of the medium oscillates about its rest position (an oscillator repeated in space), and the pattern moves on. Three numbers fix the pattern. The frequency fff is how many oscillations a point makes per second; the wavelength λ\lambdaλ is the distance between two crests; the speed ccc is how fast a crest travels, and it is set by the medium, not by the source. They are tied by

c=f λ.c = f\,\lambda .c=fλ.

Sound in air at 20 °C travels at 343 m/s, so a 343 Hz tone has a wavelength of one metre and a 34.3 kHz tone one centimetre.

The wavelength is the size of the smallest thing a wave can resolve.

To see finer detail, raise the frequency; the price, in every medium, is that higher frequencies are absorbed sooner and reach less far.

The medium sets the speed and the source sets the frequency. When a wave passes from air into water the frequency stays the same and the wavelength stretches with the speed; this is why a scanner that assumes one speed for the whole body misplaces echoes from tissue where the true speed differs.

At a boundary between two media part of the wave reflects and part goes on, in proportions set by how different the media are; for sound that difference is the acoustic impedance, and every echo-based instrument is built on it.

Motion between the source, the reflector and the receiver shifts the frequency that arrives, which is the Doppler effect and the way waves measure speed rather than distance.

The mechanical wave this notebook develops is sound, with its high-frequency branch, ultrasound.