$A$ 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

$Assertion :$ 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.

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$, where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

$A$ steel wire has a length of $12.0 \;m$ and a mass of $2.10 \;kg$. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at $20\,^{\circ}C = 343 \;m s^{-1}$?

The equation of a transverse wave propagating on a stretched string is given by $y = 3 \sin (4x + 200t)$, where $x$ and $y$ are in metres and the time $t$ is in seconds. If the tension applied to the string is $500 \ N$, the linear density of the string is: (in $kg \ m^{-1}$)

Which of the following graphs is $CORRECT$?