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Question
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 the figure, 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:
\[\nu = \sqrt{\left( \frac{T}{m} \right)}\]
\[ = \sqrt{\frac{\left( 16 \times {10}^5 \right)}{0 . 4}}\]
\[ = 2000 \text{ cm }/s\]
∴ 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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