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# A Standing wave is the sum of two given waves on a wire. Write its equation.

See attached file for the graph.

A certain wave and its reflection simultaneously travel along a wire. The two waves are:
y1= .15 sin (5x - 3 Pi t) and y2= .15 sin (5x + 3 Pi t). When they combine, they form a standing wave.

PART a. Write the equation of the standing wave produced on the wire.
PART b. Calculate the distance between two adjacent nodes on the wire.
PART c. Calculate the amplitude of the SHM of a point which is .84 meters from a node.
PART d. Calculate the maximum speed at an antinode.

#### Solution Preview

PART a.
The two waves differ only in direction of movement, y1 moving toward +x, and y2 moving toward -x. By the principle of superposition, at any point, their respective displacements add. Therefore to get y, the equation of the standing wave, we must add two waves differing only in direction. See ATTACHMENT #1 for an example of two such waves on ...

#### Solution Summary

In a 269 word solution, the problems are explained and solved in detail.

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