Engineering
Physics
Prograssive Wave Equation
Standing Wave on String
Wave Velocity on Stretched String
Question

Figure shows a snapshot graph and a history graph for a wave pulse on a stretched string. They describe the same wave from two perspectives.

the peak is located at x = – 6 cm at t = 0.

the wave is travelling in negative x-direction.

the speed of the wave is 2 m/s.

the wave is travelling in positive x-direction.

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Solution
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The snapshot graph (at t=0) shows wave displacement vs position, while the history graph (at x=0) shows displacement vs time. The snapshot peak is at x=2 cm at t=0. The history graph shows the peak arrives at x=0 at t=1 ms. Since the peak moves from x=2 cm to x=0 cm in 1 ms, the wave speed is v = Δx/Δt = (0.02 m - 0 m) / (0.001 s) = 2 m/s. The peak moves towards decreasing x, indicating the wave travels in the negative x-direction.

Final answer: the wave is travelling in negative x-direction and the speed of the wave is 2 m/s.