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Name: Duane
Status: other
Age: N/A
Location: IL
Country: N/A
Date: N/A


Question:
Assume one had a circular guitar string (continuous) tightly strung around three fixed pulleys, one of which is driven by a motor. If the string was plucked between the non-motorized two fixed pulleys if would vibrate with a given wave form and frequency (motor off). What would the wave form and frequency (still confined between these two fixed pulleys) look like if the motor was then started causing the string to circulate at a fixed velocity.



Replies:
Dear Duane,

The frequency of the vibration of the guitar string would be the same since the density of the string and the tension would be unchanged, but the wave form would be quite different. The exact form would be complex and difficult to calculate.

For example if the string speed were the same as the speed of wave propagation along the string, the wave moving opposite to the string motion would actually be stationary and the wave moving in the direction of the string would appear to move twice as fast. In this case, there would be no standing wave so the sound would be much muted.

If the string were moving at 2/3 the speed of the wave along the string, the wave moving in the direction of the string would have twice the wavelength of the wave moving in the other direction (work it out!). The result might be some strange sounds!

The standing wave depends on the constructive interference of the waves moving in opposite directions after being reflected from the ends of the string. If a wave does not move along the string, it cannot interfere with the other wave. It might be fun to build such an apparatus and try to make music with it. If you should be so ambitious, I would greatly appreciate hearing about what you have done and learned!

Best, Dick Plano, Professor of Physics emeritus, Rutgers University



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