91影视

The power of the sound energy is $P=25W$.

The power is constant and uniform in all directions.

The initial and final distances are

$$\begin{gathered} r_1=1m \\ {r}_2=5m \end{gathered}$$

In two dimensional universe, a surface at a distance r from the source is a circle of radius r.

The intensity is defined as the power of the source on a surface.

The formula to calculate the sound intensity in two dimension universe is given by

$I=\frac{P}{2\mathrm{蟺谤}}$

Here the power is constant in all directions. Therefore, $I鈭�\frac{1}{r}$

In terms of r₁ and r₂, the ratio of sound intensities will be

$$\begin{gathered} \frac{I_1}{I_2}=\frac{r_2}{r_1} \\ =5 \end{gathered}$$

In three dimensional universe, a surface at distance r from the source is the outer shell of a sphere of radius r.

The formula to calculate the intensity is given by

$I=\frac{P}{4{\mathrm{蟺谤}}^2}$

P is constant in all directions.

Therefore, $I鈭�\frac{1}{r^2}$

In terms of r₁ and r₂, the ratio of sound intensity can be written as

$$\begin{gathered} \frac{I_1}{I_2}=\frac{{r_2}^2}{{r_1}^2} \\ =\frac{5^2}{1} \\ =25 \end{gathered}$$

In a four dimensional universe, we can can conclude from the above that

$I鈭�\frac{1}{r^3}$

In terms of r₁ and r₂, the ratio of intensity is

$$\begin{gathered} \frac{I_1}{I_2}=\frac{{r_2}^3}{{r_1}^3} \\ =\frac{5^3}{1} \\ =125 \end{gathered}$$