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).

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Solution

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

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

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