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  4. A string of length 20 cm and linear mass density 0.40 g/cm is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t=0 near an end as shown in figure, which travels towards the other end. After what time in milliseconds, the string will have same shape (shown in diagram) again ? <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-lhzfoa4setsibnbr.jpg />

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

NTA AbhyasNTA Abhyas 2022

Solution:

Given Solution Solution
$\mu =0.40\,g/cm=\frac{0 . 40}{1000}\times 100=0.040\,kg/m$
Wave speed in the stretched string
$v=\sqrt{\frac{F}{\mu }}=\sqrt{\frac{16}{0 . 040}}=20\,m/s$
The string will regain its shape after travelling the pulse a distance
$=20+20=40\,cm$
Thus time speed $t=\frac{0 . 40}{20}=0.02\,s$