 Copyright © 2012 by Paul Niquette. All rights reserved. |
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 locks necessarily depend on harmonic
oscillators for accurately measuring the passage
of -- well, time. The familiar sound of ticking and
tocking characterizes the application of a gravity
pendulum. Likewise the clicking of a clock
or watch, which exploits precise vibrations of a balance
spring. Modern time pieces use electronic
devices referenced to a quartz
crystal oscillator for the job.Electric clocks in the early 20th century exploited the alternating current in the mains power, which is accurately maintained by utility companies on the power grid. In most parts of the world, that frequency is 50 cycles per second (now called Hertz, abbrev. Hz). The Americas use 60 Hz. So what happens if one takes an electric clock transported from, say, Sunnyvale and plugs it into an electrical outlet in Jugon-les-Lacs? Of course one would dare not do such a thing! Well-traveled solvers know that an American appliance cannot be directly plugged into an electrical outlet in France. There's a serious problem with the voltage.
If his clock did not blow up in his hands when he plugged it in, the puzzle-master must have known enough to use an adapter that included a 2:1 step-down transformer. However, he apparently forgot about the difference in power-line frequency. onnected to an
American power source at 60 Hz, the clock will register
a total of 1,944,000 electrical cycles between midnight
and 9:00 AM (9 x 60 x
60). Registering the same number of cycles at 50
Hz, will take longer -- indeed 20% longer (100 x
60 / 50). The alarm will sound at 10:48 AM. The clock in the puzzle will indicate 9:00 AM, and, should the puzzle-master not consult his watch and discover his error, he would blithely assume he has an hour until the beginning of his French lesson and thus will arrive as late as...
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