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 

Equation of travelling wave on a stretched string of linear density $5\,g/m$ is $y = 0.03\,sin\,(450\,t -9x)$ where distance and time are measured in $SI$ united. The tension in the string is ... $N$

A steel wire with mass per unit length $7.0 \times 10^{-3}\,kg\,m ^{-1}$ is under tension of $70\,N$. The speed of transverse waves in the wire will be $.........m/s$

Spacing between two successive nodes in a standing wave on a string is $x$ . If frequency of the standing wave is kept unchanged but tension in the string is doubled, then new spacing between successive nodes will  become

Obtain the equation of speed of transverse wave on tensed (stretched) string.

A copper wire is held at the two ends by rigid supports. At $50^{\circ} C$ the wire is just taut, with negligible tension. If $Y=1.2 \times 10^{11} \,N / m ^2, \alpha=1.6 \times 10^{-5} /{ }^{\circ} C$ and $\rho=9.2 \times 10^3 \,kg / m ^3$, then the speed of transverse waves in this wire at $30^{\circ} C$ is .......... $m / s$