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Question:

A string wave equation is given y=0.002sin(300t−1.5x) and mass density is (μ=0.1 kgm). Then find the tension in the string.

20N

40N

45N

30N

Solution:

Correct option is C. 40N
Here , String wave equation ,y=0.002sin(300t−1.5x)
Comparing with y=Asin(ωt−kx) we get ω=300 and k=1.5
String wave speed ,V=ω/k=300/1.5=20 m/s.
Also, string wave speed is V=√(T/μ)
Where T is tension in string
T=μV²
T=0.1×20×20=40 N