The extension in a string, obeying Hooke's law, is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5x$, the speed of sound will be

Spacing between two successive nodes in a standing wave on a string is $x$ . If frequency of the standing wave is kept unchanged but tension in the string is doubled, then new spacing between successive nodes will  become

A rope of length $L$ and uniform linear density is hanging from the ceiling. A transverse wave pulse, generated close to the free end of the rope, travels upwards through the rope. Select the correct option.

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

A wire of $9.8 \times {10^{ - 3}}kg{m^{ - 1}}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30°$ with the horizontal. Masses $m$ and $M$ are tied at the two ends of wire such that $m$ rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 ms^{-1}$. Chose the correct option $m =$ ..... $kg$

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 .... $s$