A wave $y_{i} = 0.3 c o s (40 t - 0.2 x)$ is travelling along a string toward a boundary at $x = 0$ . What are the expressions for the reflected waves if the string has a fixed end and at $x = 0$ . Assume SI units.

0.3 cos (0.2 x - 40t + π)

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0.3 cos (0.2 x + 40t + π)

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0.3 cos (0.2 x + 40t)

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none of these

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Solution

The correct option is B
0.3 cos (0.2 x + 40t + π)

If the end is fixed then the wave reflects back with a phase change of π. So the wave equation will be $y = 0.3 c o s (0.2 x + 40 t + π)$

Since the wave moves in opposite direction. The sign changes to +.

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A wave yi = 0.3 cos (40t − 0.2x) is travelling along a string toward a boundary at x = 0. What are the expressions for the reflected waves if the string has a fixed end and at x = 0. Assume SI units.

The correct option is B 0.3 cos (0.2 x + 40t + π) If the end is fixed then the wave reflects back with a phase change of π. So the wave equation will be y = 0.3 cos (0.2x + 40t + π) Since the wave moves in opposite direction. The sign changes to +.

A wave $y_{i} = 0.3 c o s (40 t - 0.2 x)$ is travelling along a string toward a boundary at $x = 0$ . What are the expressions for the reflected waves if the string has a fixed end and at $x = 0$ . Assume SI units.

The correct option is B
0.3 cos (0.2 x + 40t + π)

If the end is fixed then the wave reflects back with a phase change of π. So the wave equation will be $y = 0.3 c o s (0.2 x + 40 t + π)$

Since the wave moves in opposite direction. The sign changes to +.