These two waves travel along the same string: y-(3.95 mm) sin(1.68x-340t) y2 (5.

Question

These two waves travel along the same string: y-(3.95 mm) sin(1.68x-340t) y2 (5.10 mm) sin(1.68Tx- 340t+0.872rad). along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude of the new resultant wave? (a) Numbe[2.130 (b) Number TTo.49 What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.19 mm is also to be sent Units T mm Units T rad Units [rad (c) NumberTTo.42716

Explanation / Answer

If we do this using component method,

then 0.872*pi rad = 156.96 degree

then

In x-direction, 3.95 - 5.10*cos (180 - 156.96) = 3.95 - 5.10(0.92023)

we get, Rx = - 0.743

In y direction, Ry = 5.10*sin 156.96

Ry = 1.996

Now. Theta = tan-1 (1.996 / 0.743)

Theta = 69.58 degree ( in the second quadrant)

However, we need relative to vector 1 which is in first quadrant, so

Theta = 90 + 69.58 = 159.58 degree or 2.78519642 radians

For part (c) , the angle is same as part (b) as the angle should be in phase. So it should be 159.58 degree or 2.78519642 radians

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