The linear density of a vibrating string is $1.3 \times 10^{-4} \, kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $Y = 0.021 \, \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is ..... $N$.

$A$ 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 the time taken to cover the first half length is:

$A$ uniform rope having some mass hangs vertically from a rigid support. $A$ transverse wave pulse is produced at the lower end. The speed $(v)$ of the wave pulse varies with height $(h)$ from the lower end as:

$A$ 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 $s$)

If the tension in a wire is made four times,then what will be the change in the speed of the wave propagating in it?

$A$ string of $7 \; m$ length has a mass of $0.035 \; kg$. If the tension in the string is $60.5 \; N$,then the speed of a wave on the string is .... $m/s$.