A string of length $20 c m$ and linear mass density $0.4 g / c m$ 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 the figure which travels towards the other end. Sketch the shape of the string at a time half of its time period.

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Solution

Given,

Length of String $= 20$ cm

The linear mass density of the string $= .4$ g/cm

Applied Tension $= 16 N = 16 \times 10^{5}$ dyn

velocity of the wave:

$v = \sqrt{\frac{T}{μ}}$

$= \sqrt{\frac{16 \times 10^{5}}{.4}}$

$v = 2 \times 10^{3}$ cm/s

$T = \frac{L}{v} = \frac{20}{2 \times 10^{3}}$

Time taken to reach other end $= 0.01$ s

At $t = 0.01$ s, there will be a trough at the right end as it is reflected.
After reflection from fixed end phase will change by $π$
Hence: Shape will be as given in the diagram.

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A string of length 20 cm and linear mass density 0.4 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 the figure which travels towards the other end. Sketch the shape of the string at a time half of its time period.