Dependence of disturbances due to two waves on time is shown in the figure. The ratio of their intensities $I_1 / I_2$ will be

The amplitude of a wave disturbance propagating in the positive $X-$ direction is given by $y = 1/(1 + x^2)$ at time $t = 0$ and by $y = 1/[1 + (x -1)^2]$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ..... $ms^{-1}$

A uniform string suspended vertically. A transverse pulse is created at the top most of the string. Then

When a string is divided into three segments of length $l_1,\,l_2$ and $l_3,$ the fundamental frequencies of these three segments are $v_1,\,v_2$ and $v_3$ respectively. The original fundamental frequency $(v)$ of the string is

A wave travelling along the $x-$ axis is described by the equation $y \,(x, t ) = 0.005\, cos \,\left( {\alpha x - \beta t} \right)$. If the wavelength and the time period of the wave are $0.08\,m$ and $2.0\, s$ respectively then $a$ and $b$ in appropriate units are

In a standing wave on a string rigidly fixed at both ends