$A$ 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 $ms^{-1}$)?

$A$ steel wire $0.72\; m$ long has a mass of $5.0 \times 10^{-3}\; kg$. If the wire is under a tension of $60\; N$,what is the speed (in $m/s$) of transverse waves on the wire?

$A$ wire of variable mass per unit length $\mu = \mu_0 x$ is hanging from the ceiling as shown in the figure. The length of the wire is $l_0$. $A$ small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach the other end.

$A$ sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same,by what factor will the frequency change?

$A$ string is producing transverse vibration whose equation is $y = 0.021 \sin(x + 30t)$,where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times 10^{-4} \ kg/m$,then the tension in the string in $N$ will be:

$A$ string of length $1 \,m$ and mass $490 \,g$ is put under a tension of $25 \,N$. $A$ wave of frequency $120 \,Hz$ is sent along it. The speed of this wave is (in $\,m/s$)