- #1

visharad

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## 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 ?