A Photographic Method of Finding the Instantaneous Velocity of Spark Waves

The velocity of explosive sound waves, determined by early investigators, is briefly discussed, particularly the several experiments of Mach and his associates on the velocity of spark waves.A new and direct photographic method for finding spark wave velocity. A shadow of a sound wave produced by an electric spark near the center of a long light-tight rectangular box was cast on a dry plate at one end of the box by the light from a properly timed spark at the other end. A notched rim steel disk was rotated at a high and measured speed just in front of and parallel with the dry plate, the shadow of the disk covering but a narrow strip along one edge of the plate. Both the sound and light sparks cast notch shadows on the plate, the distance between the two shadows of the same notch giving the time interval between the sparks, and the sound wave picture the distance traversed by the wave in that interval. Plotting distance against time, the tangent to the curve at a given point gives the instantaneous velocity of the wave at that point. The formula used in calculating time intervals is derived and discussed.Velocity almost normal except near the spark. Measurements were made on two hundred and eighty plates, for waves from 0.32 cm. to 50 cm. in radius, for both heavy and thin sparks, and for disk edge speeds of almost two hundred meters per second. A wave velocity double the normal at 0.32 cm. from the spark axis decreased very rapidly with increasing distance and at 2 cm. from the source was only slightly above normal. At points relatively near the spark where the intensity of the expanding wave was still great, the velocity of waves from heavy sparks was greater than that from thin sparks. Reference is made to corroborative results obtained by the writer when using two other photographic methods.Sources of error in previous investigations eliminated by the photographic method. Previous investigators have found average and not instantaneous velocities. Since the velocity very close to the source is very high, average velocities run high. However, previous results have been entirely too high due to errors inherent in the experimental methods used. Attention is directed to several, the chief one being the use of tubes or "canals." The paper gives a photograph of a sound wave, a part of which has passed through a canal of the size used by Mach, the other part expanding freely into the space about the spark, showing the former wave thirty per cent faster than the latter---due to the lower average intensity of the expanding wave.