A note on abnormalities in the travel time of a wave between two extensive apertures

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Abstract
It is a common practice to attempt to measure the velocity of mechanical waves in a solid by putting two circular coaxial plane electromechanical transducers on two parallel faces distance R apart and measuring the time for transmitting a sudden disturbance to travel from one to the other, the assumption being made that the velocity c is R/t. Apart from other difficulties which are encountered in such an experiment there is a fundamental source of error due to a peculiar integration effect when each transducer, as is usually the case, is very many wavelengths across and a train of sinusoidal waves is employed : the apparent time of travel of the wave when plotted against distance is not a smooth curve but has steps in it. It will be appreciated that the arrival of the wave as a whole must be delayed compared with the time R/c, because some of the energy must proceed by a path longer than R from the tip of one transducer obliquely across to a point on the other transducer and this results in an angle of lag of the received wave which is a function of the geometry of the system, the wavelength and the transducer diameter or aperture 2a.

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