Various properties of waves

I have a few waves questions I would really like to have addressed. I’ll post my logic/solution for each question and any feedback is welcome.

Q. 10: This one seems pretty straight forward but shouldn’t the units be 3.0 rad/m? Since x is in meters and we’re not changing the order of magnitude for any other variables, I don’t quite see how the units cancel out properly…I’d just like to confirm this.

Q. 20 and 21: This seems also pretty simply but I may be missing something here. To find instantaneous velocity is to take the derivative (find slope of tangent) at a point. Looking at the question like this, my answer for 20 would be E and 21 would be D. Am I missing something fundamental here?

Q. 31: This question also didn’t make complete sense to me. Looking at 3, the tension appears to be the greatest since there’s one string and 2 masses for which it must be keep up. 2 looks like the lowest and 1 is intermediate, since FT ~ v2. Once again, am I missing something big here?

Any help with these questions would be great! Thanks!

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