A string of length 20 cm and linear mass density $0.40 g c m^{- 1}$ is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t = 0 near an end 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).

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Solution

$μ = \frac{0.40 g}{c m} = \frac{0.40 \times 100}{1000} \frac{k g}{m} = \frac{0.04 k g}{m}$
Velocity of the wave,

$v = \sqrt{(\frac{T}{μ})}$

$= \sqrt{\frac{(16)}{0.04}}$

$= 20 m / s e c$

a) The string will come in its original shape after traveling the pulse a distance = $20 + 20 = 40 c m = 0.4 m$

Time is taken to see the pulse again in the original position=
$0.4 / 20 = 0.02$ sec

(b) At t = 0.01 s, then will be a 'trough' at the right end as it is reflected.
b)
Sketch -

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