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
$T$
$T\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right)$
$\frac{T}{\sqrt{2}}$
$\frac{T}{2}$
A transverse wave travels on a taut steel wire with a velocity of ${v}$ when tension in it is $2.06 \times 10^{4} \;\mathrm{N} .$ When the tension is changed to $T$. the velocity changed to $\frac v2$. The value of $\mathrm{T}$ is close to
In the figure shown a mass $1\ kg$ is connected to a string of mass per unit length $1.2\ gm/m$ . Length of string is $1\ m$ and its other end is connected to the top of a ceiling which is accelerating up with an acceleration $2\ m/s^2$ . A transverse pulse is produced at the lowest point of string. Time taken by pulse to reach the top of string is .... $s$
A pulse is generated at lower end of a hanging rope of uniform density and length $L$. The speed of the pulse when it reaches the mid point of rope is ......
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is
$(a) $ the speed of a transverse wave on the string, and
$(b)$ the tension in the string?
Mechanical waves on the surface of a liquid are