Question

Figure (15-E7) shows two wave pulses at t = 0 travelling on a string in opposite directions with the same wave speed 50 cm s⁻¹. Sketch the shape of the string at t = 4 ms, 6 ms, 8 ms, and 12 ms.

Answer 1

Given,
Speed of the wave pulse travelling in the opposite direction, v = 50 cm s⁻¹ = 500 mm s⁻¹
Distances travelled by the pulses:
Using s = vt, we get:
$$\begin{gathered} \mathrm{In}t=4\mathrm{ms}=4\times {10}^{-3}\mathrm{s}, \\ \mathrm{s}=\nu t=500\times 4\times {10}^{-3}=2\mathrm{mm}. \\ \mathrm{In}t=6\mathrm{ms}=6\times {10}^{-3}\mathrm{s}, \\ \mathrm{s}=500\times 6\times {10}^{-3}=3\mathrm{mm}. \\ \mathrm{In}t=8\mathrm{ms}=8\times {10}^{-3}\mathrm{s}, \\ \mathrm{s}=\nu t=500\times 8\times {10}^{-3}=4\mathrm{mm}. \\ \mathrm{In}t=12\mathrm{ms}=12\times {10}^{-3}\mathrm{s}, \\ \mathrm{s}=500\times 12\times {10}^{-3}=6\mathrm{mm}. \end{gathered}$$

The shapes of the string at different times are shown in the figure.