Question

A string of length 20 cm and linear mass density 0⋅40 g cm⁻¹ is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t = 0 near an ends as shown in figure (15-E3), which travels towards the other end. (a) When will the string have the shape shown in the figure again? (b) Sketch the shape of the string at a time half of that found in part (a).

Answer 1

Given,
Length of the string = 20 cm
Linear mass density of the string = 0.40 g cm⁻¹
Applied tension = 16 N = $16\times {10}^5\mathrm{dyn}$
Velocity of the wave:
$$\begin{gathered} \nu =\sqrt{\left(\frac{T}{m}\right)} \\ =\sqrt{\frac{\left(16\times {10}^5\right)}{0.4}} \\ =2000\mathrm{cm}/\mathrm{s} \end{gathered}$$
∴ Time taken to reach the other end $=\frac{20}{2000}=0.01\mathrm{s}$
Time taken to see the pulse again in the original position$=0.01\times 2=0.02\mathrm{s}$

(b) At t = 0.01 s, there will be a trough at the right end as it is reflected.