【正文】 nked in a very close manner with the coding method for the informational munication, with the pass band of the receiving and radiating elements in the apparatus, with the spatial characteristics of the ultrasonic munication channel, and with the measuring accuracy.Let us dwell on the questions of general importance for ultrasonic ranging in air, name: on the choice of a carrier frequency and the amount of acoustic power received.An analysis shows that with conical directivity diagrams for the radiator and receiver, and assuming that the distance between radiator and receiver is substantially smaller than the distance to the obstacle, the amount of acoustic power arriving at the receiving area for the case of reflection from an ideal plane surface located at right angles to the acoustic axis of the transducer es to （1）where Prad is the amount of acoustic power radiated, B is the absorption coefficient for a plane wave in the medium, L is the distance between the electroacoustic transducer and the test me, d is the diameter of the radiator (receiver), assuming they are equal, and c is the angle of the directivity diagram for the electroacoustic transducer in the radiator.Both in Eq. (1) and below, the absorption coefficient is dependent on the amplitude and not on the intensity as in some works [1], and therefore we think it necessary to stress this difference.In the various problems of sound ranging on the test members of machines and structures, the relationship between the signal attenuations due to the absorption of a plane wave and due to the geometrical properties of the sound beam are, as a rule, quite different. It must be pointed out that the choice of the geometrical parameters for the beam in specific practical cases is dictated by the shape of the reflecting surface and its spatial distortion relative to some average position.Let us consider in more detail the relationship between the geometric and the power parameters of acoustic beams for the most mon cases of ranging on plane and cylindrical structural members.It is well known that the directional characteristic W of a circular piston vibrating in an infinite baffle is a function of the ratio of the piston39。s diameter to the wavelength d/λ as found from the following expression: (2)Where Jl is a Bessel function of the first order and α is the angle between a normal to the piston and a line projected from the center of the piston to the point of observation (radiation).From Eq.(2)it is readily found that a t w ot oo n e reduction in the sensitivity of a radiator with respect to sound pressure will occur at the angle（3）For angles α≤.(3)can be simplified to （4） where c is the velocity of sound in the media and f is the frequency of the radiated vibrations.It follows from Eq.(4)that when radiating into air where c=330 m/sec, the necessary diameter of the radiator for angle of the directivity diagram at the level of pressure taken with respect to the axis can be found to be （5）Where d is in cm, f is in kHz, and α is in degrees of angle.Curves are shown in plotted from Eq.(5)for six angles of a radiator39。s directivity diagram.The directivity needed for a radiator is dictated by the maximum distance to be measured and by the spatial disposition of the test member relative to the other structural members. In order to avoid the incidence of signals reflected from adjacent members onto the acoustic receiver, it is necessary to provide a small angle of divergence for the sound beam and, as far as possible, a smalldiameter radiator. These two requirements are mutually inconsistent since for a given radiation frequency a reduction of the beam39。s divergence angle requires an increased radiator diameter.In fact, the diameter of the sonicated spot is controlled by two variables, name: the diameter of the radiator and the divergence angle of the sound beam. In the general case the minimum diameter of the sonicated spot D min on a plane surface normally disposed to the radiator39。s axis is given by （6）where L is the least distance to the test surface.The specified value of D min corresponds to a radiator with a diameter （7）As seen from Eqs.(6)and(7), the minimum diameter of the sonieated spot at the maximum required distance cannot be less than two radiator diameters. Naturally, with shorter distances to the obstacle the size of the sonicated surface is less.Let us consider the case of sound ranging on a cylindrically shaped object of radius R. The problem is to measure the distance from the electroacoustic transducer to the side surface of the cylinder with its various possible displacements along the X and Y axes. The necessary angleαof the radiator39。s directivity diagram is given in this case by the expression （8）Where α is the value of the angle for the directivity diagram, Y max is the maximum displacement of the cylinder39。s center from the acoustic axis, and L min is the minimum distance from the center of the electroacoustic transducer to the reflecting surface measured along the straight line connecting the center of the number with the center of the transducer.It is clear that when measuring distance, the running time of the information signal is controlled by the length of the path in a direction normal to the cylinder39。s surface, or in other words, the measure distance is always the shortest one. This statement is correct for all cases of specular reflection of the vibrations from the test surface. The simultaneous solution of Eqs.(2)and(8)when W= leads to the fol