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A plane progressive wave travels in the +x direction and is described by y = 0.02 sin(8*pi*(t - x/20)). It is reflected at a rarer medium (a medium in which wave speed is higher) at x = 0. The amplitude of the reflected wave is 75% of the incident amplitude. What is the equation of the reflected wave?

1. y = 0.02 sin(8*pi*(t - x/20))
2. y = 0.02 sin(8*pi*(t + x/20))
3. y = +0.015 sin(8*pi*(t + x/20))
4. y = -0.015 sin(8*pi*(t + x/20))

Correct answer: y = +0.015 sin(8*pi*(t + x/20))

Solution

Reflection at a rarer medium causes no phase inversion, so the reflected wave keeps the same sign. The amplitude becomes 0.015 and the wave travels in the -x direction giving the argument (t + x/20).

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