There is Rayleigh's expression for the sound field excited by a transmitter. However, since that is two-dimensional integral expression, it is difficult to solve it analytically expect special cases such as the sound pressure on the axis of a disk transmitter. Then, the nearfield of a disk transmitter was calculated numerically with a digital computer. It seems that it takes much time to get the result with good precision by the method. If the Rayleigh's expression is transformed into one-dimensional integral, it can be computed easily. One of one-dimensional integral expressions is presented here. This is the integral of the quantity, which is the function related to the wave form of transmitted signal multiplied by the ring function related to the shape and dimension of a transmitter, of the distance from an observing point to the area element of the transmitter. Therefore, it is useful for the numerical calculation of the sound pressure at an observing point due to various transmitted signals. The expression (1) is Rayleigh's equation. This is transformed into the expression (7), in which R(r) named as ring function is determined with the shape of vibrating surface and an observing point. In Fig. 2, the locus of the points to which distance is r from the observing point is a circle. R(r) is the rate of the arc length contained within the vibrating surface to whole circle as shown in Fig. 2. Fig. 6 is a flow chart for the calculation of the sound field of a disk transmitter. Fig. 7 shows the result of the calculation about a circular concave transmitter excited with continuous sinusoidal signal. In another example, a signal is applied to a disk transmitter so that the vibrating velocity of disk surface is as shown on the right bottom of Fig. 10. Then, Fig. 10 (1)-(6) show the pressure wave form at each point in Fig. 9.
