Stationary wave is setup in a uniform string clamped at both ends. Length of string is 0.6 m. Snapshots of string is taken at two instant one at t = 0 sec and another at t = 0.4 sec . These two snapsh

Question

Stationary wave is setup in a uniform string clamped at both ends. Length of string is 0.6 m. Snapshots of string is taken at two instant one at $t = 0 sec$ and another at $t = 0.4 sec$ . These two snapshots are shown below. Velocity of point P (which is also the midpoint of string) is in upward direction (take upward direction positive) at $t = 0 sec$ . At the instant snapshots are taken particles are half of their respective maximum displacement from mean position. During this time interval particles have crossed their mean position only once. Find out velocity (in $m / s$ ) of travelling wave in string.

TestHub · Accepted Answer

The string (clamped at both ends) vibrates in 3 loops: $L = \frac{3 λ}{2}$ , so $λ = \frac{2 \times 0.6}{3} = 0.4 m$ .

At $t = 0$ , P is at half its maximum displacement moving up; at $t = 0.4$ s the profile is inverted (P at half amplitude moving down) - the oscillation phase has advanced by $π$ .

Particles crossed the mean position only once, consistent with $Δ θ = π$ : $0.4 = \frac{T}{2}$ , so $T = 0.8 s$ .

$v = \frac{λ}{T} = \frac{0.4}{0.8} = 0.50 m / s$ .

Physics - Wave on String Question with Solution | TestHub

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