Maxwell stress excitation of wire vibrations at difference and sum frequencies of electric currents in separate circuits.

Abstract

Oscillating electric currents through a wire under tension can excite transverse vibrational modes of the wire when a perpendicular static magnetic field is present and the frequency of the current is close to the natural frequency of the mode of interest. The excitation of the mode is associated with temporally oscillating Maxwell stresses on the wire, often also known as oscillating Lorentz forces. That excitation process is sometimes demonstrated in educational contexts. The investigation here concerns situations where a temporally oscillating magnetic field generated by oscillating electric currents in a cylindrical coil replaces the imposed perpendicular static magnetic field. The frequencies of the currents in the wire and in the coil are related to the frequency of the oscillating stress. In this experiment, this effect is documented for sum-frequency excitation (with input frequencies in the range of half that of the excited lowest vibrational mode of the wire) and the difference-frequency excitation (with input frequencies an order-of-magnitude larger than the mode frequency). This coupling may be useful when it is desirable to use only high-frequency currents. The experiment uses tone-burst stress excitation and a differential photodiode for detecting transverse low-amplitude wire oscillations. Signal envelopes decayed exponentially after the tone-burst.