Question

A string of length $20cm$ and linear mass density $0.40g/cm$ is fixed at both ends and is kept under a tension of $16N$. A wave pulse is produced at $(t=0)$ near an end as shown in figure, which travels towards the other end. At what time(in $s$) will the string have the shape shown in the figure again?

Answer 1

Given,
$\mu =0.40g/cm=\frac{0.40}{1000}\times 100$
$=0.040kg/m$
$T=16N$
Wave speed in the stretched string
$v=\sqrt{\frac{F}{\mu }}=\sqrt{\frac{16}{0.040}}=20m/s$
The string will regain its shape after travelling the pulse a distance
$=20+20=40cm$
Thus time
$t=\frac{0.40}{20}=0.02s$

Final answer: $\left(0.02\right)$