$A$ uniform string is suspended vertically. $A$ transverse pulse is created at the top of the string. Then:

$A$ uniform rope of length $12 \ m$ and 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 of the rope is (in $m$)

$A$ transverse wave is travelling on a string with velocity $V$. The extension in the string is $x$. If the string is extended by $50 \%$,the speed of the wave along the string will be nearly (Hooke's law is obeyed).

$A$ 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 $100 \, m \, s^{-1}$.

The speed of a wave on a string is $150 \,ms^{-1}$ when the tension is $120 \,N$. The percentage increase in the tension in order to raise the wave speed by $20 \%$ is

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