$A$ string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of a transverse wave along the string at a distance $x$ from the free end will be:

$A$ 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).

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$, where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

$A$ string of mass $m$ and length $l$ hangs from a ceiling as shown in the figure. $A$ wave in the string moves upward. $v_A$ and $v_B$ are the speeds of the wave at points $A$ and $B$ respectively. Then $v_B$ is

The equation of a wave on a string of linear mass density $0.04 \ kg \ m^{-1}$ is given by $y = 0.02 \sin \left[ 2\pi \left( \frac{t}{0.04 \ s} - \frac{x}{0.50 \ m} \right) \right] \ m$. The tension in the string is .... $N$.

$A$ string of mass $2.5 \, kg$ is under some tension. The length of the stretched string is $20 \, m$. If the transverse jerk produced at one end of the string takes $0.5 \, s$ to reach the other end,the tension in the string is .... $N$