https://file.aiquickdraw.com/mathbot/file/1726789561721bjvpw187.jpg

The problem states that sound intensity varies inversely as the square of the distance from the sound source. This relationship can be expressed by the formula:

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

where \(I\) is the sound intensity, and \(d\) is the distance from the sound source.

### Given:
- You are changing your seat to one that is six times as far from the speakers compared to your original seat. So, the new distance \(d_{\text{new}} = 6 \cdot d_{\text{old}}\).

### Calculation:
Since sound intensity varies inversely with the square of the distance:

\[
\frac{I_{\text{new}}}{I_{\text{old}}} = \left(\frac{d_{\text{old}}}{d_{\text{new}}}\right)^2
\]

Substitute \(d_{\text{new}} = 6 \cdot d_{\text{old}}\):

\[
\frac{I_{\text{new}}}{I_{\text{old}}} = \left(\frac{d_{\text{old}}}{6 \cdot d_{\text{new}}}\right)^2 = \frac{1}{6^2} = \frac{1}{36}
\]

### Conclusion:
The new sound intensity is \(\frac{1}{36}\) of the original sound intensity.

Do you want further details or have any questions?

---

**Relative questions:**
1. How would the sound intensity change if the distance were doubled instead of being six times as far?
2. What is the general relationship between sound intensity and distance for any inverse square law?
3. How does this formula apply to other types of waves, such as light intensity?
4. How would changing the distance by a factor of 3 affect the sound intensity?
5. What are some practical situations where sound intensity and distance have an inverse square relationship?

**Tip:** When dealing with inverse-square relationships, always remember that doubling the distance reduces the intensity to one-fourth!

Sound intensity varies inversely as the square of the distance from the sound source. If you are in a movie theater and you change your seat to one that is six times as far from the speakers, how does the new sound intensity compare with that of your original seat?

Understand how sound intensity decreases with distance using the inverse square law. In this example, we calculate how sound intensity changes when you move six times farther from the speakers in a theater. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation