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Question

Linear density of a string of is 1.3×104kg/m and wave equation is y=0.021sin(x+30t). Find the tension in the string where, x in meter and t in second.

A
0.12 N
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B
0.21 N
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C
1.2 N
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D
0.012 N
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Solution

The correct option is A 0.12 N
Given: Linear density of string m=1.3×104kg/m
Wave equation y=0.021sin(x+30t)
On comparing the given wave equation with y=asin(2πx/λ+2πvt/λ)
We get,
λ=2π
v=30λ/2π
v=30×2π/2π=30 m/s

Now, velocity of wave in a string of tension T is given by:
v=T/m
30=T/(1.3×104)
302=T/(1.3×104)
T=900×1.3×104=0.12N

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