   # Measurement of the frequency of the mains If a current is passed through a wire in a magnetic field then the wire will move. If this current is alternating, as in the mains supply, the wire will vibrate, the fundamental resonant frequency of vibration being equal to the frequency of the mains supply.

An a.c. supply is passed from a low-voltage transformer to a stretched wire placed between the poles of a strong magnet (Figure 1). The tension and/or length of the wire are adjusted until resonance occurs. The frequency of vibration and hence the frequency of the supply (fo) may then be found from the equation:

Frequency of the mains (fo) = [1/2L][T/m]1/2

Student investigation
If the wire on the sonometer is metal it can be used as a simple electric guitar. Set up the apparatus as shown in Figure 2, with the large magnet placed with its poles on either side of the sonometer wire. When the wire is plucked the movement of the wire in the magnetic field induces an e.m.f. in the wire. If this alternating e.m.f. is fed to an amplifier and speaker a note will be heard. Since the e.m.f. induced is proportional to the rate at which the magnetic flux is cut, how will the volume and pitch produced by the speaker be affected by the amplitude of the vibration of the wire?