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Question

A string of length 40 cm and linear mass density 0.80 g/cm is fixed at both ends and kept under a tension of 32 N. A wave pulse is produced near one of the ends at t=0, as shown in the figure, which makes periodic motion between the ends. What is the time after which the string will have the same shape shown in the figure?


A
After 0.03 sec
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B
After 0.06 sec
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C
After 0.05 sec
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D
After 0.04 sec
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Solution

The correct option is D After 0.04 sec
Given that,
Length of the string (l)=40 cm
Linear mass density of the string (μ)=0.80 g/cm or 0.080 kg/m
Tension in the string (T)=32 N

The wave will be inverted (phase reversal) after striking with fixed end.


The image shows that the string will have same shape after 2 consecutive reflections.

Total distance travelled by wave pulse x=40+40=80 cm

Wave speed in the stretched string, v=Tμ
From the given data,

v=320.08=20 m/s

Therefore, time taken to regain initial shape t=0.8 m20 m/s=0.04 sec.

Hence, option (d) is the correct answer.

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