# Homework Help: Wave on a string question

1. May 15, 2010

### xsc614

1. The problem statement, all variables and given/known data
The wave function for a standing wave on a string is described by y(x, t) = 0.022 sin 4πx cos 54πt, where y and x are in meters and t is in seconds. Determine the maximum displacement and maximum speed of a point on the string at the following positions.

x=0.1m, 0.25m, 0.3m, 0.5m
Find Ymax and Vmax at these points on the string.

2. Relevant equations
An(x)=Ansinknx (Amplitude of a string vibrating in its nth node)
Wave equation for a standing wave in the nth harmonic motion: yn(x,t) = Ansin(knx)cos(wnt+δn)
Kind of unsure on the equations for this problem.

3. The attempt at a solution
I assumed the maximum displacement would occur at t=0 when the cosine part of the equation equalled one. I plugged in the x values for the different points and solved for y, but did not get the correct answer. Read the entire chapter of the book and it is pretty vague and gives no example problems on calculating max displacement and max velocity like this

2. May 15, 2010

### diazona

What you explained makes sense to me... can you show your work including the numbers?

3. May 16, 2010

### xsc614

y(x, t) = 0.022 sin 4πx cos 54π

y(x, t) = 0.022 sin 4πx (1)

y(x, t) = 0.022 sin (4π(.1m)) (1)

y(x, t) = .021 m

Answer came back as incorrect. That π character is pi if you can't tell.

4. May 16, 2010

### xsc614

Update: I used this method for all other points of (x) and got the right answers. Maybe webassign is just not accepting the right amount of sig figs or something...

I got 0 for x=0.25m and 0.5m for max displacement, so the velo's were 0 m/s... but since cos(54pi*t) =1, how do you solve for t to get the velocities for the other values of x?

Last edited: May 16, 2010
5. May 16, 2010

### diazona

From what I've heard, Webassign checks to see if you're within a certain percentage of the right answer, but it shouldn't mark you incorrect for having the wrong number of significant figures. You could try putting in one more decimal place and see if it helps.

For the velocity part of it: you have an equation for position. In general, when you have the position, how do you find velocity from it?