Spherical waves are emitted from a `1.0 W` source in an isotropic non-absorbing medium. What is the wave intesity `1.0 m` from the source?

Explanation

To find the wave intensity at a distance of `1.0 m` from a `1.0 W` source emitting spherical waves in an isotropic non-absorbing medium, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Intensity**:
- Intensity (I) is defined as the power (P) per unit area (A). Mathematically, it is expressed as:
\[ I = \frac{P}{A} \]

2. **Identify the Power of the Source**:
- The power of the source is given as `1.0 W`.

3. **Determine the Area of the Sphere**:
- Since the waves are emitted spherically, the area (A) at a distance `r` from the source can be calculated using the formula for the surface area of a sphere:
\[ A = 4 \pi r^2 \]
- In this case, we are interested in the area at a distance of `1.0 m`, so we substitute `r = 1.0 m`:
\[ A = 4 \pi (1.0)^2 = 4 \pi \, \text{m}^2 \]

4. **Calculate the Intensity**:
- Now, we can substitute the values of power and area into the intensity formula:
\[ I = \frac{P}{A} = \frac{1.0 \, \text{W}}{4 \pi \, \text{m}^2} \]
- This simplifies to:
\[ I = \frac{1}{4 \pi} \, \text{W/m}^2 \]

5. **Final Result**:
- The intensity of the wave at a distance of `1.0 m` from the source is:
\[ I \approx \frac{1}{12.57} \, \text{W/m}^2 \approx 0.0796 \, \text{W/m}^2 \]

### Summary:
The wave intensity `1.0 m` from the source is approximately `0.0796 W/m²`.