On edge-tones (I)

Abstract

An edge-tone is heard when a stream of air issuing from a slit or hole strikes a sharp edge, or surface bounded by sharp edges. A brief description is given of previous work, and it is shown that the eddies which give rise to edge-tones conform to a simple Karman vortex-system. On the assumptions (1) that the distance a from the edge to the slit is always equal to l, the distance between two eddies in the same row, and (2) that tone is destroyed when the edge - when moved across the jet towards still air - crosses the line of eddy centres, one can measure h/l, where h is the separation of the eddy-rows, directly from measurements of the boundaries for tone. From the experiments it is found that at low pressures and with wide slits h/l, for air, = 0.276, which may be compared with v. Karman's prediction of 0.283 for an infinite system in a perfect fluid. If the edge is moved towards the slit, h, the separation of the eddy-rows, must decrease proportionally. The experiments show that when the eddies are formed very close to the edges of the slit, and therefore in a field of high velocity-gradient at right angles to the direction of motion, they are deflected towards the middle, or principal, plane of the jet. The amount of this deflection increases very rapidly as a approaches a0, at which distance tone can only be obtained when the edge lies in the principal plane. The experiments show that with wide slits, when a = a0, then l=a0; h = 0.67d, where d is the width of the slit. The minimum distance for tone, a0, varies with the velocity v, and the width of the slit. The results suggest an equation of dynamic similarity: B(ν/vd) = (a0/d)2 - 1.50 where B is a number (about 2,000 for air) and v is the coefficient of kinematic viscosity. By considering the acceleration that produces the deflection, an expression of somewhat similar form can be obtained theoretically. The tonal boundaries in the region of simple tone approach two straight-line asymptotes, equally inclined to the principal plane, which converge at a point 0 near the plane of the slit. If a and a0 denote the distance of the edge and the minimum distance for tone respectively from 0, the total separation, y, of the two boundaries at any distance a is given by the equation: y = (h/l)ā - (h/l)ā0 exp[-m2(ā2 - ā02)] where 1/m is approximately equal to d, when the slit is very wide. The measurements of the frequency of the tone and the deductions made from them will form the subject of a subsequent communication.