Sonars and echo sounders are frequently calibrated using echoes from spheres of copper or tungsten carbide at spot frequencies in narrow frequency bands. Modern transducers require methods for calibration of broader frequency bands. In this paper a method is presented and applied to two commercial transducers centred at 120 kHz and 200 kHz, respectively. A demand for accurately known parameters of the calibration spheres was recognized. A method for determining compressional and shear wave speeds in such spheres is demonstrated, using dominant dips in the echo spectra in combination with computed form functions, and an inversion scheme based on the Nelder-Mead simplex algorithm. The wave speeds of 4 tungsten carbide spheres and 9 copper spheres were determined. The copper spheres ageing from 30 years to recent were examined for possible evidence of age effects, and none were found. Suspending the spheres in mono filament nylon cages requires soaking in water for at least 5 hours to obtain stable echoes. This time is not affected by dipping the spheres in detergent solutions. Finally, an approximate method to find the magnitude of the transducer transfer functions is demonstrated.