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

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. statement-1 is true, statement-2 is false
D. statement-1 is false, statement-2 is true

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

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

- Sound level is measured in decibels (dB) and is given by the formula:
\[ \beta = 10 \log \left(\frac{I}{I_0}\right) \]
where \( I \) is the intensity of the sound and \( I_0 \) is a reference intensity (usually \( 10^{-12} \, \text{W/m}^2 \)).

- The logarithmic nature of this formula indicates that sound level does not increase linearly with intensity. Instead, it increases logarithmically. Therefore, the assertion is **false**.

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

- Let's denote the initial intensity as \( I_1 \) and the new intensity (after doubling) as \( I_2 = 2I_1 \).

- The sound level at intensity \( I_1 \) is:
\[ \beta_1 = 10 \log \left(\frac{I_1}{I_0}\right) \]

- The sound level at intensity \( I_2 \) is:
\[ \beta_2 = 10 \log \left(\frac{I_2}{I_0}\right) = 10 \log \left(\frac{2I_1}{I_0}\right) \]

- We can express this as:
\[ \beta_2 = 10 \log \left(2\right) + 10 \log \left(\frac{I_1}{I_0}\right) = 10 \log \left(2\right) + \beta_1 \]

- The value of \( 10 \log(2) \) is approximately \( 3 \, \text{dB} \). Thus:
\[ \beta_2 \approx \beta_1 + 3 \, \text{dB} \]

- This confirms that if the intensity is doubled, the sound level increases by approximately \( 3 \, \text{dB} \). Therefore, the reason is **true**.

### Conclusion
Based on the analysis:
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false and the reason is true.

### Summary
- Assertion: False
- Reason: True