$A$ string of mass $2.5 \, kg$ is under some tension. The length of the stretched string is $20 \, m$. If the transverse jerk produced at one end of the string takes $0.5 \, s$ to reach the other end,the tension in the string is .... $N$

$A$ rope of length $L$ and uniform linear density is hanging from the ceiling. $A$ transverse wave pulse,generated close to the free end of the rope,travels upwards through the rope. Select the correct option.

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$,where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

$A$ string of length $L$ and mass $M$ hangs freely from a fixed point. The velocity of transverse waves along the string at a distance $x$ from the free end is

$A$ 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 .......... $m/s$.

$A$ uniform thin rope of length $12 \, m$ and mass $6 \, kg$ hangs vertically from a rigid support and a block of mass $2 \, kg$ is attached to its free end. $A$ transverse short wavetrain of wavelength $6 \, cm$ is produced at the lower end of the rope. What is the wavelength of the wavetrain (in $cm$) when it reaches the top of the rope?