368 



PHOTOGRAPHY OF SOUND WAVES. 



iiiu- the rcrtcction of u i)lane wave in ii spherical mirror. The eoii.struc- 

 tion is shoAvn in tiu". 1!'. 



A IK' is the iniiTor, AOC the plane wave. Around points on ABC 

 as centers (lesci-il)e circles tan*;ent to the wave. These circles will he 

 enveloped l>y anothei- suiiace, ADPj, ))elow the mirroi* (the orthogonal 

 surface). If we erect normals on this surface, we have the I'eflccted 

 rays: and if we measui'c off ecpial distances on the normals, we have 

 tile rellected wa\"e front. By drawing- tlie orthogonal surface we avoid 

 the complication of having to measure otl' the distances around a 

 corner. The orthogonal surface is an epicycloi<l formed by the rolling 

 of a circle of a diameter e(]ual to the radius of curvature of the mir- 



ror on tlie mirror's surface, and normals can be erected bv drawing the 

 arc FG (the path of the center of the generating circle) and descril)- 

 ing circles of diameter BE around various points on it. A line joining 

 the point of intersection of one of these circles with the epicycloid 

 and the point of tangency with the mirror will, when producc^d, give 

 a reflected ray: for example, JK produced for circle described around 

 H. The construction once prepared, the series of wave-front pictures 

 can be very quickly made. Three or four sheets of paper are laid 

 under the construction, and holes are punched through the pile by 

 means of a pin, at equal distances along each ra^- (measured from the 

 orthogonal surface). 



