How a wave moves - conceptual physics question

An alumna of my Conceptual Physics Summer Institute was having some trouble with picturing the answer to this question from waves problem set 9.  She asked if I could help.  Of course!  This is an important but very difficult question which helps students understand how a wave moves along a string.

The question, which I've adapted from an old New York Regents physics exam: 

If you assign this, do NOT let students ask you questions!  Make them show their own personal understanding without you giving them hints.  I'd either give this as a quiz question to ensure it's students' own work; or allow collaboration among classmates so that they argue with one another, but can't in their minds simply appeal to the authority that "teacher said to think about <foo>" or "teacher said the answer is <bar>, so I'll make up some random bologna for my justification."  

And so, most students will get this wrong on first attempt.  Let them.  They need to struggle, to make their own mistakes such that they care about the solution you show them for a greater purpose than just getting a problem done.

How do I explain the answer?  I first put the PHET waves simulation on screen.  My students are familiar with this simulation, having played with it for 10 minutes as a previous assignment, and having seen it on screen a few times.

I set the simulation to "oscillate" and "no end," as in the screenshot below.  I turn the "damping" slider all the way off.  I tune the frequency slider to 1 Hz, meaning the wave has a period of 1 second.

I show the students that the wave moves to the right, while the pieces of the string move up and down.  (Of course I've shown this before!  I still need to show them again to set the context for this particular problem.)  I ask, how far does a wave crest travel in 1 second?

After a discussion, the class usually agrees that the wave travels one wavelength.  Great.  

Then I ask, how far does the wave crest travel in a tenth of a second?  Since we just discussed how far the crest travels in one second, they pretty quickly come up with 1/10 of a wavelength.  

But what does that mean for this particular problem?  Students still have a tough time connecting the top picture to the correct answer.  Many still think that since the wave moves 1/10 of a wavelength, that the wavelength itself is now much smaller, making the wave extra-squiggly.  I know, I know, this makes no sense to us as physics teachers; but that's a very frequent misconception.  Here's how I bust it.

I pause the simulation, and circle several positions, as in the picture on the problem set:

Then, I move the animation forward a few frames.  Everyone sees immediately what the new wave looks like (and that the wavelength hasn't changed!):

This is a good a-ha moment for the class!  It's not merely okay for most of the class to get something wrong on a quiz or on an assignment - it's on occasion absolutely necessary in order to advance the class's collective understanding.