Assertion : Sound level increases linearly with intensity of sound.
Reason : If intensity of sound is doubled, sound level increases approximatel `3 dB` .

Options

A. If both Asseration and Reason are true an dthe Reason is correct explanation of the Asseration.
B. If both Asseration and Reason are true but Reason is not the correct explanation of Asseration.
C. If Asseration is true , but the Reason is false.
D. If Asseration is false but the Reason is true.

Explanation

To solve the question regarding the assertion and reason about sound levels and intensity, we will analyze each statement step by step.

### Step 1: Understanding the Assertion
The assertion states that "Sound level increases linearly with intensity of sound."

**Analysis:**
- The sound level (in decibels, dB) is calculated using the formula:
\[ L = 10 \log_{10} \left(\frac{I}{I_0}\right) \]
where \(L\) is the sound level, \(I\) is the intensity of the sound, and \(I_0\) is a reference intensity.
- This formula indicates that sound level is a logarithmic function of intensity, not a linear function.

**Conclusion:**
- The assertion is **incorrect** because sound level does not increase linearly with intensity; it increases logarithmically.

### Step 2: Understanding the Reason
The reason states that "If intensity of sound is doubled, sound level increases approximately 3 dB."

**Analysis:**
- Let’s denote the initial intensity as \(I_1\) and the new intensity (when doubled) as \(I_2 = 2I_1\).
- The sound level at intensity \(I_1\) is:
\[ L_1 = 10 \log_{10} \left(\frac{I_1}{I_0}\right) \]
- The sound level at intensity \(I_2\) is:
\[ L_2 = 10 \log_{10} \left(\frac{I_2}{I_0}\right) = 10 \log_{10} \left(\frac{2I_1}{I_0}\right) = 10 \log_{10} \left(2\right) + 10 \log_{10} \left(\frac{I_1}{I_0}\right) \]
- Thus, we can express the change in sound level when intensity is doubled:
\[ L_2 - L_1 = 10 \log_{10}(2) \approx 3 \text{ dB} \]

**Conclusion:**
- The reason is **correct** because doubling the intensity does indeed result in an increase of approximately 3 dB in sound level.

### Final Conclusion
- The assertion is **false** and the reason is **true**. Therefore, the correct answer is that the assertion is incorrect while the reason is correct.

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