A wave $y_{i} = 0.3 c o s (0.2 x - 40 t)$ 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

0.3 c o s (0.2 x - 40 t)

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0.3 c o s (0.2 x + 40 t)

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0.3 c o s (0.2 x - 40 t + π)

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None of these

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Solution

The correct option is B $0.3 c o s (0.2 x + 40 t)$
If there is a free end, the wave will reflect with no change in phase. So the equation is $y_{r} = 0.3 c o s (0.2 x + 40 t)$ . The sign if you notice (inside cosine) changes as the direction changes.

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A wave yi = 0.3 cos (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

The correct option is B 0.3 cos (0.2x + 40t)If there is a free end, the wave will reflect with no change in phase. So the equation is yr = 0.3 cos (0.2x + 40t). The sign if you notice (inside cosine) changes as the direction changes.

A wave $y_{i} = 0.3 c o s (0.2 x - 40 t)$ 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

The correct option is B $0.3 c o s (0.2 x + 40 t)$
If there is a free end, the wave will reflect with no change in phase. So the equation is $y_{r} = 0.3 c o s (0.2 x + 40 t)$ . The sign if you notice (inside cosine) changes as the direction changes.