A wave $y_{i} = 0.3 c o s (2.0 x - 40 t)$ is travelling along a string toward a boundary at x = 0. Write expressions for the reflected waves if the string has a fixed end at x = 0.

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Solution

When a wave is reflected from a boundary, the direction of velocity is reversed. Also a phase difference of $π$ gets added due to reflection from a fixed end.
However the wavelength and frequency remains the same.
Thus $k$ and $ω$ remain the same.
Thus the reflected wave is expressed as $y (x, t) = 0.3 c o s (2.0 x + 40 t + π)$

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x = 0

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y_{i} = 0.3 cos (2 x - 40 t)

is travelling along a string towards a fixed end at

x = 0

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(Assume there is no loss of energy at the boundary)

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A wave yi=0.3cos(2.0x−40t) is travelling along a string toward a boundary at x = 0. Write expressions for the reflected waves if the string has a fixed end at x = 0.

A wave $y_{i} = 0.3 c o s (2.0 x - 40 t)$ is travelling along a string toward a boundary at x = 0. Write expressions for the reflected waves if the string has a fixed end at x = 0.