$A$ string of mass $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

$Assertion :$ 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.

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

$A$ transverse wave propagating on a string can be described by the equation $y = 2 \sin (10x + 300t)$,where $x$ and $y$ are in meters and $t$ is in seconds. If the vibrating string has a linear mass density of $0.6 \times 10^{-3} \, g/cm$,then the tension in the string is .............. $N$.

When the area of cross-section of a stretched wire is halved and tension is doubled,the speed of propagation of transverse waves along it becomes $k$ times the initial speed. Then,$k$ is:

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: