Wednesday, 23 March 2016

Philip Morse's imaginary glass tube

I've been reading a lot of acoustics textbooks to try to overhaul my ideas about how acoustics can and should be taught in the twenty-first century and today I settled down with Philip Morse's Vibration and Sound (2nd ed. McGraw-Hill, 1948). Morse was really driving the subject: Leo Beranek's description of his first research project at MIT was that Morse had developed the idea of impedance as a way of characterising walls and wanted someone to measure it for the first time (sorry, I don't have the exact quote from his memoirs to hand; they're well worth reading too). No wonder Morse's own memoirs were called In at the Beginning; though I've not had a chance to read them yet.

There's lots about Vibration and Sound that shows how the attempt to explain flows from the attempt to understand; even though it's avowedly mathematical it's also full of thought-experiments. One that particularly struck me introduces wave motion on a stretched string, something I talk about a lot when lecturing on Musical Instrument Acoustics, both to engineers and musicians. What he imagined was a string passing through a glass tube bent into the shape of a plane curve with its ends co-axial. The string is under tension and is being wound from one spool to another at a constant speed, and it travels through the tube without friction (as in all the best mechanics textbook problems). He works out the centrugal force on a short curved section of string (which varies with the square of the string's speed) and the force on the side of the tube on the inside of the curve due to tension (which is independent of speed). He then shows that when the string is spooling at a particular speed the resultant force between string and tube will vanish and:
"...we can carefully break away the tube from around the string and leave the string moving with velocity c, still retaining the original form of the tube, a wave form standing still in space."
  1. Before we had tape recorders we had wire recorders, my father used one when he did his national service with the Royal Signals. Could they have inspired this? Their 'brief heyday', according to that article I just linked was from 1946 to 1954. My copy's a 2nd edition from 1948, the first was published in 1936. If anyone has a first edition could they tell me if this is in it?
  2. The tone implies that the calculation of the forces on the tube is an elementary matter. Maybe so for students drilled on endless mechanics sets but maybe less so now. Much as I like this example I don't know that it would help my students as much. In those days acoustics was a graduate subject, often for students who'd learned electronics in the army and were, like Philip Doak, studying on the GI Bill. It might make a nice exam question though.
  3. Someone's got to do this experiment, it would be so cool. Not with a glass tube but the wire could run between rollers which could be withdrawn once the wire's up to speed. Then you could adjust the tension and move the wave back and forth.