A. The curve y = f ( x ) is shown in the figure at the bottom. A1. A pulse with

Question

A. The curve y = f(x) is shown in the figure at the bottom.

A1. A pulse with this shape is started on a long stretched spring; that is, at time t = 0, the spring has the shape

y(x,0) = f(x).

What is the function, y(x,t), that describes the shape of the spring at a time t if this pulse is moving to the right with the speed v0?

A2. A demonstrator holds a long stretched spring at one end and generates a pulse moving down the string by moving his hand up and back to its starting point quickly. The speed of pulses moving on the spring is 250 cm/s and he moves his hand up and down in 0.5 s. Is it possible to predict the width of the pulse that moves along the spring? If so, find it. If not, explain why not.

B. The curve y(x,t) = A sin(kx - t) describes a sinusoidal wave shape moving on a (different) long spring. The parameters have the following values: A = 0.5 cm, k = 0.125 cm-1, and = 25 s-1.

B1. Is the wave shape described by this function moving to the left (in the direction of the negative x axis) or to the right (in the direction of the positive x axis)?

B2. How fast is the shape traveling down the spring?

Explanation / Answer

A1] y(x,t) = f(x - vot)

where vo is the velocity of the wave moving to the right.

A2] Width of the pulse = v t = 250 x 0.5 = 125 cm = 1.25 m.

B1] The wave is moving to the right in the positive x direction.

B2] Velocity of the wave will be:

v = w/k = 25/0.125 = 200 cm/s = 2 m/s .

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