Question: A standing wave on a rope is represented by the following wave function: where x and y are in meters and t is in seconds.

A standing wave on a rope is represented by the following wave function:

y(x, 1) = 0.02 sin cos 40zt 2 2.

where x and y are in meters and t is in seconds.

(a) Write wave functions for two traveling waves that when superimposed will produce the resultant standing-wave pattern.

(b) What is the distance between the nodes of the standing wave?

(c) What is the velocity of a segment of the rope at x = 1 m?

(d) What is the acceleration of a segment of the rope at x = 1m?

y(x, 1) = 0.02 sin cos 40zt 2 2.

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