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A plane progressive wave of frequency 50 Hz travels along the positive x-direction. At x = 0, the displacement is given by y = (5 * 10^(-5) m) * sin(100*pi*t). The wave speed is 300 m/s. Find the maximum difference in displacement between the points x = 0 and x = -3 m. Express your answer as x mm, and find the value of 10x.

1. 5
2. 10
3. 1
4. 50

Correct answer: 10

Solution

The wavelength is lambda = 300/50 = 6 m. At x=-3 m, the wave has a phase difference of pi (half wavelength behind), making y(-3,t) = -A*sin(omega*t). The difference y(0,t)-y(-3,t) = 2A*sin(omega*t), maximum = 2A = 10^(-4) m = 0.1 mm = x mm, so x=0.1 and 10x=1.

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