Radiation from plane sound sources

Starting from Rayleigh's formula for the radiation from plane sound sources, the established relation is derived between the directivity of a source and its Fourier transform. As it is quite often easy to obtain a good estimate for the Fourier transform, it is not too difficult to find an approximation for the radiation pattern. In the case of short (bending) waves the radiation depends on the amplitude and the wavelength; it can be shown, however, that the boundary conditions and the envelope of the source vibrations also have a considerable influence. Therefore in principle 'small changes' in the vibration pattern can have a large effect on the directivity and the total radiated power. It is also shown that additional damping of bending waves practically does not increase the radiation.