Question

Transverse waves are being produced in a stretched string whose equation is $y=0.021\sin (x+30t)$. If the linear density of string is $1.3\times {10}^{-4}kg{m}^{-1}$ then the tension produced in string will be

• A. $10N$
• B. $0.5N$
• C. $0.117N$
• D. $0.107N$

Answer 1

The correct option is C $0.117N$

The velocity of the wave is related to the tension and the linear density in the string by the relation, $v=\sqrt{F/\mu }$

Therefore, the tension in the string is equal to, $F=\mu v^2$

The velocity of the wave is equal to $\lambda /k$ where, $\lambda =30$ and $k=1$

Therefore, $v=30m/s$

Substituting the values, $F=1.3\times {10}^{-4}\times {30}^2$

Hence, $F=0.117N$