How Do You Calculate Wave Properties from a Wave Function?

[Stizzle]

Homework Statement

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

Homework Equations

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

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
k = 6.28 rad/m
$\omega$ = 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

 

[mark726]

problem, but I just used the equations that I'm comfortable with.

Your understanding is correct. Your calculations for the frequency, wavelength, and period are all correct. However, for the phase velocity, you should use the full equation (1) instead of just the value of w/k. So it should be v = (20.0 rad/s) / (6.28 rad/m) = 3.18 m/s. The amplitude and direction of motion are also correct. Good job!