Two waves on one string are described by the wave functions y1 = 2.5 cos(3.5x -

Question

Two waves on one string are described by the wave functions y1 = 2.5 cos(3.5x - 1.21) y2 = 5.0 sin(4.5x - 3.0t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 + y2 at the following points. (Remember that the arguments of the trigonometric functions are in radians.) x = 1.00, t = 1.00 What is the displacement due to each function at the given point? x = 1.00, t = 0.500 If you know the displacement described by each function, how do these two displacements combine at this point? cm x = 0.500, t = 0 What role does superposition play in this problem? Cm

Explanation / Answer

a)

For each wave displacement is

-1.67 cm and

4.98 cm

b)

For net displacements both add up giving

-1.72 cm

c)

By superposition we get, direct addition

3.447

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