Snapshot and history graphs for a string under tension (drive mechanism)

[visharad]

Homework Statement

A string with mass density u = 9.00 g/m extends from zero to infinity along the x-axis. It is
under tension T = 25 N, and is driven by a mechanism at x = 0.

The velocity of the drive mechanism depends on time as:
vy(t) =
0 (if t = 0)
10.0 cm/s (if 0 < t ≤ 0.1 s)
−20.0 cm/s (if 0.1 s < t ≤ 0.2 s)
10.0 cm/s (if 0.2 s < t ≤ 0.3 s)
0 if t > 0.3 s

(a) Sketch a “snapshot graph” of the displacement of the string at time t = 0.5 s, from 0
to 30 m along the x-axis. Use a range of -1.0 cm to +1.0 cm on the y-axis.

(b) Sketch the “history graph” at x = 10 m, for t = 0 to 0.6 s.

Homework Equations

v = sqrt(T/u)
Y = Yo cos(kx - w t)

The Attempt at a Solution

I can calculate the wave speed from square root of (T/u)

a) t = 0.5 s
Therefore, vy(t) = -20.0 cm/s
At x = 0,
yo = -20.0 * 0.5 = -10.0 cm
But I do not know how y will vary with x. I thought of using
Y = yo cos(k x), where k is wave-number.
But do not know how to calculate the value of k as I do not know how to find wavelength or frequency.

b) x = 10 m
How do I find vy(t) at this value of x ?

 

[visharad]

I realized the graphs will not be sinusoidal. They will have straight lines. I have made history graph at x = 0
I calculated v = 52.7 m/s

How to draw snapshot graph at t = 0.5 s and history graph at x = 10 m ?

 

[visharad]

Snapshot is to be drawn at t = 0.5
vy(t) = 0 at t = 0.5

So can we say that the snapshot graph at t = 0.5 will be a single straight line coinciding with x axis?