If the initial tension on a stretched string is doubled,then the ratio of the initial and final speeds of a transverse wave along the string is:

The equation of a wave on a string of linear mass density $0.02 \text{ kg m}^{-1}$ is $Y = 0.01 \sin [2\pi (t/0.02 - x/0.50)] \text{ m}$. The tension in the string is (in $\text{ N}$)

$Assertion :$ Two waves moving in a uniform string having uniform tension cannot have different velocities.
$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover,the speed of a wave in a string depends on its elastic and inertial properties only.

One end of a string of length $L$ is tied to the ceiling of a lift accelerating upwards with an acceleration $2g$. The other end of the string is free. The linear mass density of the string varies linearly from $0$ to $\lambda$ from bottom to top.

Two strings $A$ and $B$ of the same material are stretched by the same tension. The radius of string $A$ is double the radius of string $B$. $A$ transverse wave travels on string $A$ with speed $V_A$ and on string $B$ with speed $V_B$. The ratio $\frac{V_A}{V_B}$ is:

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$,will be ......... $\%$