Analyzing a Wave Function

1. Sep 18, 2011

Stizzle

1. The problem statement, all variables and given/known data
The wavefunction of a transverse wave on a string is
$\psi$$\left(x,t\right)$=$\left(30.0 cm\right)$Cos$\left[\left(6.28 rad/m\right)x - \left(20.0 rad/s\right)t\right]$

Compute the (a) frequency, (b) wavelength, (c) period, (d) amplitude, (e) phase velocity, and (f) direction of motion

2. Relevant equations
1. v = w / k
2. T = 2$\pi$ / kv
3. f = 1 / T
4. $\lambda$ = v / f

3. The attempt at a solution
Question seems kind of trivial... I just want to double check if my understanding is right.

From the equation:
A = 30.0 cm
$\omega$ = 20.0 rad/s

e) Using equation (1), v = (20.0 rad/s) / (6.28 rad/m) = 3.18 m/s

c) Using equation (2), T = 2$\pi$ / (6.28 rad/m * 3.18 m/s) = 0.31 s/cycle

a) Using equation (3), f = 1 / (0.31 s/cycle) = 3.23 Hz

b) Using equation (4) $\lambda$ = (3.18 m/s) / (3.23 cycles/s) = 0.98 m

d) Amplitude is given = 30.0 cm

f) since $\varphi$=(kx - $\omega$t) is equivalent to the phase in the given function, the direction of motion is in the +x direction

P.S I know that there's more than one way to solve this

Last edited: Sep 18, 2011