$A$ uniform metal wire has length $L$,mass $M$,and density $\rho$. It is under tension $T$,and $v$ is the speed of a transverse wave along the wire. The area of cross-section of the wire is:

$A$ 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 .... $N$

$A$ string of mass $m$ and length $l$ hangs from a ceiling as shown in the figure. $A$ wave in the string moves upward. $v_A$ and $v_B$ are the speeds of the wave at points $A$ and $B$ respectively. Then $v_B$ is

$A$ uniform rope of mass $6\,kg$ hangs vertically from a rigid support. $A$ block of mass $2\,kg$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $0.06\,m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top is (in $m$):

$A$ string of length $0.4\, m$ and mass $10^{-2}\, kg$ is tightly clamped at its ends. The tension in the string is $1.6\, N$. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. The minimum value of $\Delta t$ which allows constructive interference between successive pulses is .... $s$

$A$ transverse wave is passing through a string as shown in the figure. The mass density of the string is $1 \ kg/m^3$ and the cross-sectional area of the string is $0.01 \ m^2$. The equation of the wave in the string is $y = 2 \sin(20t - 10x)$. The hanging mass is (in $kg$):-