The transverse wave, propagating through a medium is given by $y=A\cos 2\pi \left[ft-\frac{x}{\lambda }\right].$ If maximum particle velocity of medium is two times the velocity of wave through medium, then

$y$ versus $x$ graph of a transverse wave propagating through the medium is shown, where $y$ is displacement of particles from their mean position at distance $x$ from the source at $t=0 .$ Select the incorrect statement about particles shown in figure

The displacement $\left(y\right)$ and time $\left(t\right)$ graph for two sound waves is shown in figure. The ratio of their intensities is

Both the strings, shown in the figure, are made of the same material and have the same cross-section. The pulleys are light. The wave speed of a transverse wave in the string $AB$ is $v_1$ and in $CD$ it is $v_2.$ Then $\frac{v_1}{v_2}$ is

Two strings $A$ and $B$, made of same material, are stretched by same tension. The radius of string $A$ is double of the radius of $B$. A transverse wave travels on $A$ with speed $v_{\mathrm{A}}$ and on $B$ with speed $v_{\mathrm{B}}.$ The ratio $\frac{v_{\mathrm{A}}}{v_{\mathrm{B}}}$ is