The mass per unit length of a uniform wire is $0.135 \, g/cm$. $A$ transverse wave of the form $y = -0.21 \sin(x + 30t)$ is produced in it,where $x$ is in meters and $t$ is in seconds. Then,the expected value of tension in the wire is $x \times 10^{-2} \, N$. The value of $x$ is (Round off to the nearest integer).

$A$ rope of length $L$ and mass $M$ hangs freely from the ceiling. If the time taken by a transverse wave to travel from the bottom to the top of the rope is $T$,then the time taken to cover the first half length is:

$A$ uniform string of length $20 \ m$ is suspended from a rigid support. $A$ short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (take $g = 10 \ ms^{-2}$):

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} = $

$A$ perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with a weight. If a transverse wave is imparted to the lower end of the string,the pulse will

$A$ wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $50 \, Hz$. The mass of the wire is $30 \, g$ and its linear density is $4 \times 10^{-2} \, kg/m$. The speed of the transverse wave on the string is ...... $m/s$.