Honors Standing Wave Lab

The majority of these were bad to awful, and most are being returned without grades. Here are some samples of why.

1) Purpose. Almost every lab is designed to confirm something we proposed as an hypothesis. You have been told this many times, most recently with your pendulum labs where you proved omega = sqrt(g/L) without most of you realizing you did it. In this case I spent more than a period trying to establish that, c (wave speed) of a transverse wave is given by c= sqrt(Ftension/(Mass per meter). We then discussed standing waves and established the hypothesis that a standing wave must contain n/2 wavelengths (i.e.n/2 lambdas), where n was any whole number. From this and the fact that a loop was half a wavelength we got number of loops = 2L/lambda

using lambda = cT = c/f we get number of loops (i.e. n loops)= 2L/(c/f) or number of loops =2 Lf/c which can be rewritten as c= 2Lf/number of loops. Substituting sqrt(Ftension/(mass per meter) for c and squaring both sides and then multiplying by (mu i.e. Mass/meter) gives you an expression for the Ftension required for n loops.

Proving the bold equations are correct are what the purpose of this lab was. Vague statements such as exploring relationships or determining relationships applicability are useless if the relationships you are trying to demonstrate are not stated. Most of you blindly quoted FT = 4L^2F^2(mu i.e. mass/meter)/ n loops with no explanation of where it came from. If you are going to use something like that, derive it and show you understand where it comes from and what it mean, or its just a formula that a child can plug numbers into and get answers.

2) Understanding of math is a rare commodity around here. Here are some typical bits of math from your labs:

"We proved 4L^2F^2(mass/meter, or mu))/ n loops is a correct equation." No equal sign, no indication at all of what it is supposed to equal, but still you were sure it was a correct equation.

"The speed = sqrt(FT/mu) therefore doubling the FT will increase c by 1/3."

"The speed is given by mu c^2 = FT/mu therefore doubling FT would quadruple c"

"Since lambda = cT increasing c by 1/3 increase lambda by 1/4"

By now the fact that you do not know that that the Sqrt( 2FT/mu) = sqrt(2) x (sqrt(FT/mu) is a scandal. Doubling FT alters c by a factor of the sqrt of 2 or 1.414. The new c = 1.414 x the old one and since lambda = cT = c/f, then if cnew is 1.414 c old then lambda new is 1.414 lambda old.

Graphing and slope is still a mystery to many of you. Graphs should be titled as vertical coordinate vs horizontal. Many of you labeled your lambdas as c and your c s as lambda. The slope of c vs lambda is f. You should have made this graph and your slope would have come out close to 60, the frequency supplied by the oscillator. Some of you graphed c calculated from c=sqrt(FT/mu) vs (sqrt(FT/mu) and came up with the not very surprising result that slope =1.

You were supposed to graph c calculated or ideal from c= sqrt(FT/mu) vs c measured from c = lambda (measured) x frequency known = (2Lstring /n loops) x 60. Then a slope = 1 would mean our equations was right.

Discussion sessions are not supposed to be just answers to questions. Just providing minimal answers to questions is the work of a child and will earn 20 points off in the future. At the very least the percent difference between ideal and measured should be discussed.

Conclusions should state concrete results, confirming or denying the validity of those identified in the Purpose while citing the evidence for your conclusion.

Silly words and thoughts continue to be common. One group told me that the number of half periods that pass from a wave passing through a node and returning to the node would have to be odd to keep the node moving. Nodes have no displacement and do not move. In a standing wave all nodes and antinodes maintain their locations. The string moves up and down at an antinode but the location of the antinode does not change. This why they are called standing waves NOT traveling waves. The number of half periods must even by the the way because the outgoing wave after passing through the node is reflected from a fixed end as an inverted wave and it if comes back to the node an even number of periods later it will be just in time to cancel the displacement caused by another outgoing (uninverted) wave; exactly what you need to have a node.

Fix these up and do your next labs as if you know why you are doing them and as if you know a little mathematics.