As a wave propagates:

$A$ sound source emits sound waves in a uniform medium. If energy density is $E$ and maximum speed of the particles of the medium is ${v_{\max }}$,the plot between $E$ and ${v_{\max }}$ is best represented by

$A$ surface of area $S$ is placed perpendicular to the direction of travel of a plane wave. The energy per unit time intercepted by the surface is $E$ when the amplitude of the wave is $A$. The area of the surface is reduced to $\frac{1}{2} S$ and the amplitude of the wave is increased to $2A$. What is the energy per unit time intercepted by this smaller surface?

Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.
Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.

The amplitudes of two waves are in the ratio $5 : 2$. If all other conditions for the two waves are the same,what is the ratio of their energy densities?

The amplitude of a wave at a distance $r$ from a point source is $A$. What will be the amplitude at a distance $2r$ from the source?