Our high school student is thinking about waves on a string, and isconfused once

Question

Our high school student is thinking about waves on a string, and isconfused once again. He knows the formula for wave velocity: wavevelocity equals wavelength times frequency. What he's confusedabout is the interpretation of that equation.

Your job in this essay is to give that interpretation. Your answershould include two things: 1. A physical reason why the wavevelocity should depend solely on the string itself, not on (say)how quickly someone moves one end of the string up and down tocreate the waves. 2. A verbal reason why (for example) thewavelength must get shorter if the person making the waves moveshis hand up and down more quickly (you can't just pointto the wave velocity equation and say "as frequency goes up,wavelength must go down"). Justifications for why this is so wouldbe much appreciated.

Explanation / Answer

Here are some pointers for your essay. Why/how does the disturbance travel along a string? - string is under tension - displacement of bit of string from equilibrium position (ie aswave pulse goes past) causes extra tension - the amount of extra tension caused by the displacement is relatedto the elasticity of the string - this tension causes the restoring force (so more tension makes afaster wave speed) - OTOH the finite mass of the string gives it inertia, resistsrestoring force. (this will slow the wave speed) -how frequently the disturbance is made doesn't come into thephysics in any way. Part 2 -speed of wave along string is constant. - the string goes up (at your hand) when your hand goes up, downwhen your hand goes down - these disturbances travel along string at wave speed. - if string made to go up and down more quickly (higher frequency)then distrubance doesn't have time to get away from you as far bythe time you bring your hand down again - so wavelength isn't as long. Hope this helps

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