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 (in $,v$)

$A$ pulse is generated at the lower end of a hanging rope of uniform density and length $L$. The speed of the pulse when it reaches the midpoint of the rope is:

The given graph illustrates a transverse wave travelling on a string at a particular instant,and the points $P, Q, R$ and $S$ represent elements of the string. Which of the following statements about the motion of the elements is correct?

$A$ wire $PQ$ has length $4.8 \ m$ and mass $0.06 \ kg$. Another wire $QR$ has length $2.56 \ m$ and mass $0.2 \ kg$. Both wires have the same radii and are joined as a single wire. This wire is under a tension of $80 \ N$. $A$ wave pulse of amplitude $3.5 \ cm$ is sent along the wire $PQ$ from end $P$. The time taken by the wave to reach the other end of the single wire is (No power is dissipated during propagation). (in $s$)

$A$ string of length $1 \,m$ and mass $490 \,g$ is put under a tension of $25 \,N$. $A$ wave of frequency $120 \,Hz$ is sent along it. The speed of this wave is (in $\,m/s$)

The fundamental frequency of vibration of a string stretched between two rigid supports is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g/m$. The speed of the transverse waves produced in the string is $..........\,m/s$.