The sonometer itself consists of a wire stretched between two supports or bridges on a wooden sounding box. The tension of the string may be varied either by a screw or by hanging weights on one end of it. The length of the vibrating wire can be changed using a small wooden support that can be moved along under the wire.
The purpose of the sounding box is to make a larger mass of air vibrate and so amplify the very small sounds produced by the vibrating string itself. If a string which is stretched between two fixed points is plucked at its center, vibrations produced and it move out in opposite directions along the string. Because of this, a transverse wave travels along the string. The same principle is applied in stringed instruments such as the guitar or cello.
This video explains how to find the relation between frequency and resonant length, and that between resonant length and tension.