# Finding displacement of the string given a function

1. Jan 31, 2015

### Potatochip911

1. The problem statement, all variables and given/known data
The shape of the wave on the string at t=0 is:
y=(2x)/(x^2+50)
The waveform is moving in the +x direction at a propagating speed of 10cm/s. Find the displacement of the string in cm when t=5s and x=30cm

2. Relevant equations
∂^(2)y/∂x^(2)=(1/v^2)*∂^(2)y/∂t^(2)

3. The attempt at a solution
I'm completely lost as to how to solve this, I wanted to try and integrate the function to undo the partial derivative but the function they gave was for when t=0 so all the t variables will disappear and I won't be integrating the right function.

2. Jan 31, 2015

### Simon Bridge

I suspect you are over-thinking things.
Start by writing down y(x,t). You are given enough information to do that directly.

(Actually - you start by drawing a sketch of y(x,t=0)... that can help.)

3. Feb 1, 2015

### Potatochip911

Okay I managed to get the answer by plugging in x=-20cm into the y=2x/(x^2+50) since the wave is travelling at 10cm/s in 5 seconds x=-20cm will be the spot at 30cm. I never did figure out how to write it down as y(x,t) though, am I supposed to use the general formula y(x,t)=h(x+-vt)?

4. Feb 1, 2015

Right.

5. Feb 2, 2015

### Simon Bridge

That's correct.
Given y(x, t=0)=f(x) then the same shape travelling in the +x direction with speed v is given by: $$y(x,t)= f ( x-vt)$$ ... a negative speed would, therefore, indicate travel in the -x direction.

Eg. If $y( x,0)=A\sin kx$, then $$y ( x, t)=A\sin k ( x-vt)$$

This is mathematically identical to what you did.