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 :
$\sqrt{2}: 1$
$1: \sqrt{2}$
$1: 2$
$1: 1$
A string of length $L$ and mass $M$ hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance $x$ from the free end is
The mass per unit length of a uniform wire is $0.135\, g / cm$. A transverse wave of the form $y =-0.21 \sin ( x +30 t )$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x \times 10^{-2} N$. Value of $x$ is . (Round-off to the nearest integer)
Which of the following statements is incorrect during propagation of a plane progressive mechanical wave ?
A uniform rope of mass $6\,kg$ hangs vertically from a rigid support. A block of mass $2\,kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\,m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top is (in $m$ )
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 time to cover first half length is