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A snapshot of a vibrating string at t = 0 is shown. Point P on the string is observed moving upward with velocity 20*sqrt(3) cm/s. The tangent drawn to the string at P makes an angle of 60 deg with the positive x-axis. The linear mass density of the string is 50 g/m. Which of the following is/are correct?

1. The wave travels in the negative x-direction
2. The wave travels in the positive x-direction
3. The equation of the wave is y = 0.4 sin(2*pi*(5t - x/4 + 1/12)) cm
4. The total energy carried by the wave per cycle is 3.6 * 10^(-6) J

Correct answer: The wave travels in the negative x-direction

Solution

Since the particle velocity at P is positive (upward) and the slope dy/dx = tan(60) > 0, the relation v_y = -v_wave*(dy/dx) requires v_wave < 0, meaning the wave travels in the negative x-direction.

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