An axially symmetric, torque-free rigid body, rotating and precessing, emits gravitational quadrupole radiation at two frequencies, $\omega$ and $2\omega$, corresponding to the $l=2\mathrm{}$, $m=1,2\mathrm{}$ spherical harmonics. We present explicitly the waveforms of the two polarizations at both frequencies. From observations of gravitational waves, one can derive information about the body's orientation and its precession amplitude. Electromagnetic radiation emitted by a spot fixed on the surface of the body arrives in pulses at a mean frequency $\Omega$ which is typically different from $\omega$. If the body is not axially symmetric but the amplitude of the precession is small, the gravitational radiation at the lower frequency $\omega$ is split into two frequencies on either side of the electromagnetic pulse frequency. We present explicit waveforms for the two polarizations in this case also.

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