  Mach’s first important scientific contribution was over the recently discovered ‘Doppler theory’. In 1841, Christian Doppler noticed that sound changes in frequency as a source moves toward and away from an observer. By 1845 he had generalized this to include all wave phenomena, including light. Two prominent physicists, Petzval and Ångström, challenged Doppler. Mach devised a simple apparatus that demonstrated that the Doppler effect was real, at least for sound. A six-foot tube with a whistle at one end was mounted so as to rotate in a vertical plane. When the listener stood in the plane of the axis of rotation no changes in pitch could be heard. But if the observer stood in the plane of rotation, fluctuations in pitch that corresponded to the speed of rotation could be heard. The application of this work to Doppler effects with light remained controversial, but Mach is regarded as one of the first to realize the possibility of studying a star’s spectrum to understand its movements [see Blackmore 1972: 17–19; Swoboda 1974: 20–75].