A transverse pulse generated at the bottom of a uniform rope of length $L$, travels in upward direction. The time taken by it to travel the full length of rope will be

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$, will be ......... $\%$

A steel wire with mass per unit length $7.0 \times 10^{-3}\,kg\,m ^{-1}$ is under tension of $70\,N$. The speed of transverse waves in the wire will be $.........m/s$

A composition string is made up by joining two strings of different masses per unit length $\rightarrow \mu$ and $4\mu$ . The composite string is under the same tension. A transverse wave pulse $: Y = (6 mm) \,\,sin\,\,(5t + 40x),$ where $‘t’$ is in seconds and $‘x’$ in meters, is sent along the lighter string towards the joint. The joint is at $x = 0$. The equation of the wave pulse reflected from the joint is

Explain which properties are necessary to understand the speed of mechanical waves.

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