The intensity of sound from a point source is `1.0 xx 10^-8 Wm^-2`, at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source ?

Explanation

To find the intensity of sound at a distance of 25 m from the source, we can use the relationship between intensity and distance from a point source. The intensity (I) of sound is inversely proportional to the square of the distance (r) from the source. This can be expressed mathematically as:

\[ I \propto \frac{1}{r^2} \]

### Step-by-step Solution:

1. **Identify Given Values:**
- Initial intensity at distance \( r_a = 5.0 \, m \):
\[ I_a = 1.0 \times 10^{-8} \, W/m^2 \]
- Distance where we want to find the intensity \( r_b = 25.0 \, m \).

2. **Use the Inverse Square Law:**
- According to the inverse square law, we can write:
\[ \frac{I_b}{I_a} = \left(\frac{r_a}{r_b}\right)^2 \]
- Rearranging gives us:
\[ I_b = I_a \times \left(\frac{r_a}{r_b}\right)^2 \]

3. **Substitute the Values:**
- Substitute \( I_a \), \( r_a \), and \( r_b \) into the equation:
\[ I_b = (1.0 \times 10^{-8}) \times \left(\frac{5.0}{25.0}\right)^2 \]

4. **Calculate the Ratio:**
- Calculate \( \frac{5.0}{25.0} = 0.2 \).
- Now square this ratio:
\[ (0.2)^2 = 0.04 \]

5. **Calculate \( I_b \):**
- Now substitute back into the equation:
\[ I_b = (1.0 \times 10^{-8}) \times 0.04 \]
- Performing the multiplication:
\[ I_b = 4.0 \times 10^{-10} \, W/m^2 \]

### Final Answer:
The intensity of sound at a distance of 25 m from the source is:
\[ I_b = 4.0 \times 10^{-10} \, W/m^2 \]

---