Question

The equation of a transverse wave propagating in a string is given by y = 0.02 sin (x + 30t)
where x and y are in metre and t is in second. if linear density of the string is $1.3\times {10}^{-4}kg/m,$ then the tension in the string is

• A. 0.12 N
• B. 1.2 N
• C. 12 N
• D. 120 N

Answer 1

The correct option is A 0.12 N

Speed of the wave=$\frac{\omega }{k}=\frac{30}{1}=30m/s$

Speed of wave in a string is also given by $\sqrt{\frac{T}{\mu }}=30m/s$

$⟹T=(30{)}^2\times 1.3\times {10}^{-4}=0.12N$