# Travelling waves - help with formula

1. Feb 9, 2014

1. The problem statement, all variables and given/known data
A wave has the mathmatical form $y(x,t)=2sin(6t-0.5x)$

1. What is the waves frequency, wavelength and velocity

2.Write an expression for the displacement of the wave as a function of time at a point 2m from the beginningof the wave.

2. Relevant equations
$$k=2\pi \lambda \\ f=\frac{\omega}{2\pi} \\ v=\lambda f$$

3. The attempt at a solution

For question 1 I took 6 from the wave equation to be the angular velocity and k to be 0.5 so i did..

$$f=\frac{6}{2\pi}=0.95Hz \\ \lambda=\frac{2\pi}{0.5}=4\pi metres \\ v=\lambda f = 4\pi (0.95)=11.94 m/s$$

For question 2 I am not too sure what the question is asking, if it is 2m from the start do I just plug 2 in for x in the wave equation given? to get $2sin(6t-1)$?

Any help appreciated, thanks :)

Last edited: Feb 9, 2014
2. Feb 9, 2014

### TSny

You work looks good to me. I agree that the second question isn't worded very well. The phrase "from the beginning of the wave" is a little odd. But it seems reasonable to me to assume they mean from x = 0, in which case your expression is correct.