$A$ transverse wave travels on a taut steel wire with a velocity of $v$ when the tension in it is $2.06 \times 10^{4} \; N$. When the tension is changed to $T$,the velocity changes to $v/2$. The value of $T$ is close to:

The equation of a wave on a string of linear mass density $0.04 \ kg \ m^{-1}$ is given by $y = 0.02 \sin \left[ 2\pi \left( \frac{t}{0.04 \ s} - \frac{x}{0.50 \ m} \right) \right] \ m$. The tension in the string is .... $N$.

$A$ copper wire is held at the two ends by rigid supports. At $50^{\circ} C$ the wire is just taut,with negligible tension. If $Y=1.2 \times 10^{11} \, N/m^2$,$\alpha=1.6 \times 10^{-5} /^{\circ} C$,and $\rho=9.2 \times 10^3 \, kg/m^3$,then the speed of transverse waves in this wire at $30^{\circ} C$ is .......... $m/s$.

$A$ wire of linear mass density $\mu = 10^{-2} \, kg \, m^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of the wire such that $m$ rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 \, m \, s^{-1}$.

$A$ metallic wire of $1 \ m$ length has a mass of $10 \times 10^{-3} \ kg$. If a tension of $100 \ N$ is applied to the wire,what is the speed of the transverse wave (in $ms^{-1}$)?

Transverse waves of the same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice that of $B$,and the tension in $A$ is half that in $B$. The ratio of the velocities of the waves in $A$ and $B$ is: