The song of the singing rod

This paper discusses basic and advanced aspects of the sound radiated by the singing rod demonstration commonly used in physics courses to depict an example of longitudinal waves. Various methods of exciting these rods are discussed along with the issues associated with each method. Analysis of the sound radiated by various rods with small-signal and large-signal excitations is presented for four different rods. The small-signal sound radiation consists of a fundamental frequency and odd harmonics (each corresponding to a longitudinal mode) when the rod is held at its midpoint. Large-signal sound radiation is highly dependent on the rod's geometry. The large-signal sound can possess strong even harmonics and/or beating tones resulting from modal coupling of transverse bending modes and either subharmonic longitudinal modes or torsional modes. A detailed analysis of the sound radiation from a singing rod can provide excellent laboratory exercises or classroom demonstrations for advanced undergraduate or graduate level acoustics courses whose scope includes resonances of a bar.