A wire of variable mass per unit length $\mu = \mu _0x$ , is hanging from the ceiling as shown in figure. The length of wire is $l_0$ . A small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach to the other ends
$\sqrt {\frac{{8\,{l_0}}}{g}} $
$\sqrt {\frac{{4\,{l_0}}}{g}} $
$\sqrt {\frac{{2\,{l_0}}}{g}} $
None
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
Obtain the equation of speed of transverse wave on tensed (stretched) string.
A perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with the weight. If a transverse wave is imparted to the lower end of the string, the pulse will
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is
$(a) $ the speed of a transverse wave on the string, and
$(b)$ the tension in the string?
Which of the following statements is incorrect during propagation of a plane progressive mechanical wave ?