$A$ 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 mass per unit length of a uniform wire is $0.135 \, g/cm$. $A$ transverse wave of the form $y = -0.21 \sin(x + 30t)$ is produced in it,where $x$ is in meters and $t$ is in seconds. Then,the expected value of tension in the wire is $x \times 10^{-2} \, N$. The value of $x$ is (Round off to the nearest integer).

$A$ 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:

$A$ wire of variable mass per unit length $\mu = \mu_0 x$ is hanging from the ceiling as shown in the figure. The length of the wire is $l_0$. $A$ small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach the other end.

$A$ 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

$A$ transverse wave travels on a taut steel wire with a velocity of $v$ when the tension in it is $2.06 \times 10^{4} \; N$. When the tension is changed to $T$,the velocity changes to $v/2$. The value of $T$ is close to: