# Amplitude at various points on a string

1. Dec 3, 2011

### forestmine

1. The problem statement, all variables and given/known data

A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 192m/s and a frequency of 240 Hz. The amplitude of the standing wave at an antinode is .4cm.

Calculate the amplitude at points ont he string a distance of (i) 40cm, (ii) 20cm, and (iii)10 cm from the left end of the string.

2. Relevant equations

A*sin(kx)sin(ωt)
k=2$\pi$/λ
λ=v/f

3. The attempt at a solution

I'm assuming I need to use the equation for the position along a wave, given as A*sin(kx)sin(ωt). I'm thinking I need to set it up so that my only unknown is A. I started by solving for λ and then k. From there, I can find ω. I'm not sure, however, how to continue without knowing my time t. Also, when it says that the amplitude of the standing wave is .4cm, does that entail my maximum amplitude, and therefore all of the amplitudes I come up with should be points within this max displacement? And even if I have a given t, I still don't quite understand how to use the standing wave equation. In this form in particular, its solution entails the position, so is it simply A*sin(kx)sin(ωt)=the position at those given conditions.

Any direction would be greatly appreciated.

2. Dec 3, 2011

### Spinnor

First you might come up with the proper k such that you get the wave in this link,

http://gbhsweb.glenbrook225.org/gbs/science/phys/mmedia/waves/harm3.html

I think you can assume .4cm = A, what else could it be?

I get .8m for lamda. Let sin(wt) = 1 and plug in your values of x.

Hope this helps.

Edit, if some values come back negative I'm not sure if they should be reported as positive or negative.

Last edited: Dec 3, 2011
3. Dec 3, 2011

### forestmine

I also get .8 for λ.

But I still don't understand how to compute each of the amplitudes. I'm assuming I should use Asin(kx)sin(ωt), but if I plug in the given amplitude of .4 cm, then what variable am I solving for?

Also, I don't understand why sin(ωt) should be equal to 1.

4. Dec 4, 2011

### Spinnor

They want you to find the amplitude which is the maximum value in one cycle. You plug .4 where A is, set sin(wt)=1 (you want the maximum displacement at the various values of x), and then plug in your values for lamda*x.

Hope this helps.