- #1

bkraabel

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## Homework Statement

You and a friend each have one rope. You tie the two ropes together and stand as far apart as possible, each holding one end of the new longer rope and pulling to put it under tension. You then begin moving your arm in such a way as to produce a harmonic wave with a wavelength of 1.0 m. Your friend looks at the waves as they reach her arm. Is it possible that she measures a wavelength of (a) 0.8 m, (b) 1.0 m, or (c) 1.2 m?

## Homework Equations

For standing wave with BOTH ends fixed: [itex]\lambda=\frac{2 \ell}{n-1}[/itex] where [itex]n[/itex] is the number of nodes (including the node at each end) and [itex]\ell[/itex] is the length of the rope.

If one end of the rope is driven, this end is an antinode, so the wavelength would be so you get [itex]\lambda/4+(n-1)\lambda/2=\ell[/itex] , which simplifies to [itex]\lambda=\frac{4\ell}{2n-1}[/itex]

We also have the following relation between wave speed [itex]c[/itex], frequency and wavelength: [itex]c=\lambda f[/itex].

## The Attempt at a Solution

I assume the friend does not more her arm, so her end of the rope is a node. Your end of the rope is an antinode. The friend "looks at the waves as they reach her arm." What does that mean? She measures the wave speed? Frequency? Amplitude? All of those? Does she count the nodes between the two ends of the rope? That would seem to not be consistent with "looking at the waves as they reach her arm." So I assume she measures wavespeed and frequency and calculates wavelength. If she does that correctly, she should get the correct wavelength, so the answer would be

(a) no, (b) yes, (c) no

However, others argue (I don't know why) that the answer is

(a) yes, (b) yes, (c) yes

My question is: What argument(s) can you give to support the second answer (all yes)??

Thanks for any ideas.