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Let's go over the questions one by one and solve them step by step.

### Question 1:
*If the power of a sound source is 2 W, calculate sound intensity and sound level at 10 m from the source.*

1. **Sound Intensity Formula:**

   The sound intensity \( I \) at a distance \( r \) from a point source is given by:
   \[
   I = \frac{P}{4 \pi r^2}
   \]
   where:
   - \( P \) is the power of the sound source (2 W),
   - \( r \) is the distance from the source (10 m).

   Substituting the values:
   \[
   I = \frac{2}{4 \pi (10)^2} \, \text{W/m}^2
   \]

2. **Sound Level Formula (in dB):**

   The sound level \( L \) (in decibels, dB) can be calculated from the intensity using the formula:
   \[
   L = 10 \log_{10} \left( \frac{I}{I_0} \right)
   \]
   where \( I_0 \) is the reference intensity, usually \( I_0 = 10^{-12} \, \text{W/m}^2 \).

### Question 2:
*The sound level measured at a distance of 3 m from a loudspeaker is found to be 83 dB (A). If the threshold in intensity level for reasonable audibility is 20 dB(A), how far away can the loudspeaker be heard clearly?*

To find the distance at which the sound level drops to 20 dB, we use the **Inverse Square Law** for sound levels:
\[
L_1 - L_2 = 20 \log_{10} \left( \frac{r_2}{r_1} \right)
\]
where:
- \( L_1 = 83 \, \text{dB} \) (sound level at 3 m),
- \( L_2 = 20 \, \text{dB} \) (threshold of audibility),
- \( r_1 = 3 \, \text{m} \) (initial distance).

We solve for \( r_2 \) (the distance at which sound is 20 dB).

### Question 3:
*If 10 identical sources of sound produce a sound level of 80 dB, what would each produce along?*

To find the sound level produced by a single source, we use the fact that adding identical sound sources increases sound intensity, not the sound level directly. The formula for the total sound level from \( N \) sources is:
\[
L_\text{total} = L_\text{single} + 10 \log_{10}(N)
\]
Given \( L_\text{total} = 80 \, \text{dB} \) and \( N = 10 \), we solve for \( L_\text{single} \).

### Question 4:
*The sound level observed at a distance of 3.5 m from a noisy factory is 81 dB(A). What is the expected sound level at a point on the perimeter of the factory premises which is 2.5 m from the first measurement point?*

Here, we need to use the **Inverse Square Law** again, just like in Question 2, to calculate the sound level at the new distance.

Now, I will proceed with the calculations.Here are the detailed results for each question:

### Question 1:
- **Sound Intensity at 10 m**: \( I = 0.00159 \, \text{W/m}^2 \)
- **Sound Level at 10 m**: \( L = 92.02 \, \text{dB} \)

### Question 2:
- The loudspeaker can be heard clearly up to a distance of **4237.61 m** (approximately 4.24 km) before the sound level drops to 20 dB.

### Question 3:
- Each individual sound source would produce a sound level of **70 dB**.

### Question 4:
- The sound level at a point 2.5 m away from the first measurement point (3.5 m from the factory) would be **83.92 dB**.

If you'd like more details or further clarification on any of these calculations, feel free to ask!

Here are 5 related questions you might want to explore:
1. How does sound intensity change with distance in different environments?
2. What factors could affect the sound level besides distance, like obstacles or air density?
3. How do multiple sound sources combine to increase overall sound intensity?
4. What is the relationship between power, intensity, and sound level in real-life scenarios?
5. How would the sound level change if the factory noise increased or decreased?

**Tip**: When working with decibels, remember that a small change in dB represents a significant change in intensity since it's a logarithmic scale.

1. If power of a sound source is 2 W, calculate sound intensity and sound level at 10 m from the source.
2. The sound level measured at a distance of 3m from a loud speaker is found to be 83dB (A). If the threshold in intensity level for reasonable audibility is 20 dB(A), how far away can the loud speaker be heard clearly?
3. If 10 identical sources of sound produce a sound level of 80 dB. What would each produce along?
4. The sound level observed at a distance of 3.5 m from a noisy factory is 81 dB(A). What is the expected sound level at a point on the perimeter of the factory premises which distant 2.5 m from the first measurement point?

Solve problems involving sound intensity, sound level, and the inverse square law. This guide includes calculating sound levels from power, understanding decibels, and how distance affects sound intensity. Perfect for students in Grades 11-12.

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