Transverse wave problem

[big man]

The transverse displacement (in cm) of a taut string carrying a sinusoidalwave is measured at points along its length close compared to the wavelength of the wave, and at time intervals small compared with the period of the wave. The results are: SEE ATTACHMENT

Determine the values a,b,c,d, the speed of and direction of the wave, and the amplitude of the wave.


This is the question that I'm having trouble with and I'd appreciate any help here, but first this is what I was thinking:

To determine a,b,c and d I thought that the ratios of the tranverse displacements would be the same. So you would calculate a as follows:

a = [(8.08)/(10.40)]*5.68
b = [(12.62)/(10.40)]*5.68

c and d would be calculated in a similar manner. However, I'm not entirely sure that it's correct.

As for the speed and direction of the wave I don't really have a clue. For the speed of the wave I was trying to use the particle velocity relationship:

particle velocity = dy/dt = c*(dy/dx)

So c = (dy/dt)*(dx/dy)

The problem here is that with my method for calculating the values of a,b,c and d, the displacements (y) are different over the same time interval, which means that I don't get a consistent value for the particle velocity. Also with how the question is setup you can't find the change in the distance along the string with a change in the transverse displacement.

Any help would be great.
Thanks :)

Edit: OK I fixed the table, but if you can't see the word document just let me know.

[Integral]

You are told that this is a sinusoidal wave. What is the most general description of a wave that you are given? It should look something like

S(x,t) = A Sin(bx + ct)

What you need to do is to use the information given to find the A ,b and c in the above expression.
What mathematical tools do you have at your disposal?

[big man]

Yeah I had the sinusoidal bit, but I figured that you'd need to solve for the speed and direction first to then be able to solve for amplitude.

What do you mean by tools exactly?
We don't use any maths programs or anything like that, we just have a summary sheet of important results regarding transverse waves.

[big man]

I was also wondering if there are any books that are particularly good university text books that cover the "Particles and Waves" topics like SHM, transverse wave motion and longitudinal wave motion and that maybe use different approaches (ie Lagrangian, hamiltonian & Newtonian).

Thanks

[big man]

Well I've handed in the little that I did be it right or wrong :smile:

However, if any of you have time it would be cool to still work through this problem 'cause at least then I would know how to approach questions like this.

Thanks Integral for the initial post as well.

[big man]

***bump*** anyone up for discussing any aspect of this question? :lol: