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
$1.22\, v$
$0.61\, v$
$1.50\, v$
$0.75\, v$
A transverse pulse generated at the bottom of a uniform rope of length $L$, travels in upward direction. The time taken by it to travel the full length of rope will be
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 time to cover first half length is
A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y(x$, $t )=(0.01 \ m ) \sin \left[\left(62.8 \ m ^{-1}\right) x \right] \cos \left[\left(628 s ^{-1}\right) t \right]$. Assuming $\pi=3.14$, the correct statement$(s)$ is (are) :
$(A)$ The number of nodes is $5$ .
$(B)$ The length of the string is $0.25 \ m$.
$(C)$ The maximum displacement of the midpoint of the string its equilibrium position is $0.01 \ m$.
$(D)$ The fundamental frequency is $100 \ Hz$.
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 meter and $t$ in second the tension in the string is ..... $N$
A wire of density $9 \times 10^{-3} \,kg\, cm ^{-3}$ is stretched between two clamps $1\, m$ apart. The resulting strain in the wire is $4.9 \times 10^{-4}$. The lowest frequency of the transverse vibrations in the wire is......$HZ$
(Young's modulus of wire $Y =9 \times 10^{10}\, Nm ^{-2}$ ), (to the nearest integer),