$A$ $10 \, m$ long steel wire has a mass of $5 \, g$. If the wire is under a tension of $80 \, N$,the speed of transverse waves on the wire is .... $ms^{-1}$

$A$ steel wire has a length of $12 \ m$ and a mass of $2.10 \ kg$. What will be the speed of a transverse wave on this wire when a tension of $2.06 \times 10^4 \ N$ is applied (in $m/s$)?

$A$ string of length $L$ is stretched by $\frac{L}{20}$ and the speed of transverse waves along it is $v$. The speed of the wave when it is stretched by $\frac{L}{10}$ will be (assume that Hooke's law is applicable).

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?

One end of a string of length $L$ is tied to the ceiling of a lift accelerating upwards with an acceleration $2g$. The other end of the string is free. The linear mass density of the string varies linearly from $0$ to $\lambda$ from bottom to top.

As shown in the figure, a block of mass $9 \, kg$ is hung by a wire of area of cross-section $1 \, mm^2$ in a lift going up with an acceleration of $2 \, ms^{-2}$. If the speed of the transverse wave on the wire is $120 \, ms^{-1}$, the density of the material of the wire is (Acceleration due to gravity $= 10 \, ms^{-2}$)