If the ratio of the amplitudes of two waves is $2:1$,then the ratio of their maximum and minimum intensity is:

$A$ point source is emitting sound waves of intensity $16 \times 10^{-8} \text{ W m}^{-2}$ at a distance of $1 \text{ m}$ from the source. The difference in intensity (magnitude only) at two points located at distances of $2 \text{ m}$ and $4 \text{ m}$ from the source respectively will be . . . . . . $\times 10^{-8} \text{ W m}^{-2}$.

The intensity of sound from a radio at a distance of $2 \ m$ from its speaker is $1 \times 10^{-2} \ \mu W/m^2$. The intensity at a distance of $10 \ m$ would be:

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.

$A$ string of mass $100 \, g$ is clamped between two rigid supports. $A$ wave of amplitude $2 \, mm$ is generated in the string. If the angular frequency of the wave is $5000 \, rad/s$,then the total energy of the wave in the string is ..... $J$.

$A$ stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $4 \ m$ and $9 \ m$ respectively from the source. The ratio of amplitudes of the waves at $P$ and $Q$ is