Are Units for Phase Calculations in Wave Problems Accurately Applied?

[MathewsMD]

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 F_T ~ v². Once again, am I missing something big here?

Any help with these questions would be great! Thanks!

 

[kontejnjer]

For Q10, you're right, the units should be rad/m.

For Q20 and Q21, try to imagine what happens to point P as the wave moves to the right. The waves are traverse in both cases, so a point "on" the wave cannot by definition have a longitudinal velocity component, just a traverse component, hence it can only go up or down.

As for Q31, I don't see any sort of picture so I can't really help out much.

 

[MathewsMD]

for q10, you're right, the units should be rad/m.

For q20 and q21, try to imagine what happens to point p as the wave moves to the right. The waves are traverse in both cases, so a point "on" the wave cannot by definition have a longitudinal velocity component, just a traverse component, hence it can only go up or down.

As for q31, i don't see any sort of picture so i can't really help out much.

q. 31

 

[kontejnjer]

If you haven't done so already, draw free body diagrams for all the cases depicted. You can then figure out the tensions in all of them. Notice that case 1 and 3 are equivalent because the forces on both ends of the rope are the same (in the first case, the wall must exert a force equal in magnitude to that of the weight of the block, otherwise it wouldn't be in equilibrium anymore).