Two strings with circular cross section and made of same material are stretched to have the same amount of tension. $A$ transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section $R$ is $v_1$,and that in the other string having radius of cross section $R/2$ is $v_2$. Then $\frac{v_2}{v_1} = $

$A$ composite string is made up by joining two strings of different mass per unit length,$\mu$ and $4\mu$. The composite string is under the same tension $T$. $A$ transverse wave pulse,$Y = (6 \text{ mm}) \sin(5t + 40x)$,where $t$ is in seconds and $x$ is in meters,is sent along the lighter string towards the joint. The joint is at $x = 0$. The equation of the wave pulse reflected from the joint is:

$A$ 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.

$A$ heavy rope is suspended from a rigid support. $A$ transverse wave pulse is set up at the lower end,then

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

$A$ string has a mass per unit length of $10^{-6} \,kg/cm$. The equation of a simple harmonic wave produced in it is $Y=0.2 \sin(2x+80t) \,m$. The tension in the string is: (in $N$)