"Then comes my fit(the perfect circle) again"
Ivor Catt 24jan00
Howie FRS, head of the Cavendish, said to me; "Physical reality is composed of sine waves." Thus, the question as to whether the word "wave" means "sine wave" or "any wave" is meaningless for him. As with the ancients' commitment to the circle, today's commitment to the sine wave (which actually is the circle, somewhat camouflaged) has held back science right through the twentieth century. This problem recurs in the theory of the violin string, and in many other places.
"Vibrations and waves",
by A. P. French, M.I.T., pub. Nelson 1965/79.
[p167] In a stringed instrument such as a piano, the string is struck once at some chosen point. At the moment of impact, and for a brief instant thereafter, the string is sharply pushed aside near this point, and its shape is nothing like a sine curve. Shortly thereafter, however, it settles down to a motion which is a simple superposition of the fundamental and a few of its lowest harmonics. It is a physically very important fact that these vibrations can occur simultaneously and to all intents independently of one another. [There follows an experiment whose results are falsely alleged to prove that any movement is the sum of sine waves. In reality, it is only shown that the movement is the sum of reciprocating waves, for example see fig. 7 in my 1996 book "Electromagnetism".]
[p161] Our discussions in this chapter will not be limited to vibrating strings. If they were, one might well question their importance. After all, who, apart from a segment of the musicians' community, depends on stretched strings for making a living? [Here we see how relatively (economically) unimportant music was in world culture in 1965.] The fact is, though, that through a full analysis of this almost absurdly elementary physical system - through an understanding of its dynamics, its natural vibrations, its response at different frequencies - we are introduced to results and concepts that have their counterparts throughout the realm of physics, including electromagnetic theory, quantum mechanics, and all the rest.