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The problem asks to calculate the sound intensity at two distances from a loudspeaker with a given power of 4 watts. The formula for sound intensity \( I_r \) is:

\[
I_r = \frac{P}{4 \pi d^2}
\]

Where:
- \( P \) is the power of the source (in watts),
- \( d \) is the distance from the source (in meters),
- \( I_r \) is the sound intensity (in watts per square meter, \( \text{W/m}^2 \)).

### a) Sound Intensity at 8 m
The solution uses the formula:

\[
I_r = \frac{4}{4 \pi (8)^2}
\]
Using \( \pi = \frac{22}{7} \), the student calculated:

\[
I_r = \frac{4}{4 \times \frac{22}{7} \times 8^2} = 4.97 \times 10^{-3} \, \text{W/m}^2
\]

### b) Sound Intensity at 4 m
The student used the same formula for a distance of 4 m:

\[
I_r = \frac{4}{4 \pi (4)^2}
\]
Substituting \( \pi = \frac{22}{7} \):

\[
I_r = \frac{4}{4 \times \frac{22}{7} \times 4^2} = 1.99 \times 10^{-2} \, \text{W/m}^2
\]

### Summary
- At 8 m, the sound intensity is approximately \( 4.97 \times 10^{-3} \, \text{W/m}^2 \).
- At 4 m, the sound intensity is approximately \( 1.99 \times 10^{-2} \, \text{W/m}^2 \).

Would you like me to go into more detail about the steps or clarify anything further?

Here are some related questions:
1. What is the relationship between distance and sound intensity?
2. How would the sound intensity change if the power of the speaker were doubled?
3. What would the sound intensity be at 16 m away?
4. How does the inverse square law apply in this problem?
5. How would air absorption affect the sound intensity over larger distances?

**Tip:** Sound intensity decreases with the square of the distance from the source, so doubling the distance reduces intensity by a factor of four.

The power of a loudspeaker is 4 W. Calculate the sound intensity at: a) 8 m away, b) 4 m away from the source.

Learn how to calculate the sound intensity at different distances from a loudspeaker. This problem uses the inverse square law and sound intensity formula to determine the intensity at 8 m and 4 m away from the source with a power of 4 W. Suitable for high school students studying physics.

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