Acoustic quality factor and energy losses in cylindrical pipes

The quality factor Q of a damped oscillator equals 2π times the ratio of stored energy to the energy dissipated per cycle. This makes Q a sensitive probe of energy losses. Using modest equipment, we measured the acoustical Q for a set of cylindrical pipes having the same resonant frequency, but different diameters D. The graph of Q vs D could be well fitted with two parameters, one of which corresponds to energy loss via radiation from the ends of the pipe, and the other to thermal and viscous losses very close to the pipe wall. The wall loss parameter was quite constant no matter where the pipes were located, but the radiative loss parameter varied significantly with location inside a room, suggesting that room reflections affected the sound radiated from the pipe. This study offers valuable insights at no great expense, and could be the basis of an upper-division undergraduate laboratory experiment.