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A transverse wave travels on a string with speed v. The displacement profile of the string at t = 1 s is y = 5 / sqrt(x² + 6x + 9), and at t = 2 s it is y = 5 / sqrt(x² + 12x + 36). Compute (v + c), where c = +1 if the wave moves in the positive x-direction and c = -1 if it moves in the negative x-direction.

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

At t=1 s: y = 5/sqrt((x+3)²) = 5/|x+3|. The pulse is centred at x = -3. At t=2 s: y = 5/sqrt((x+6)²) = 5/|x+6|. The pulse is centred at x = -6. The centre moved from -3 to -6, i.e. by -3 in 1 s. So speed v = 3 m/s and the direction is negative x, giving c = -1. Therefore v + c = 3 + (-1) = 2.

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