A wave yi=0.3cos(0.2x−40t) is travelling along a string toward a boundary at x=0. What is the expression for the reflected wave when, the string has a free end at x=0. Assume SI units
A
0.3 cos (0.2 x - 40t)
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B
0.3 cos (0.2 x - 40t)
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C
0.3 cos (0.2 x - 40t + π)
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D
None of these
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Solution
The correct option is B
0.3 cos (0.2 x - 40t)
If there is a free end, the wave will reflect with no change in phase. So the equation is yr=0.3cos(0.2x+40t). The sign if you notice (inside cosine) changes as the direction changes.