How Many times more intense is a 60 dB sound than a 30 dB sound ?

Options

A. 1000
B. 2
C. 100
D. 4

Answer

To determine how many times more intense a 60 dB sound is compared to a 30 dB sound, we can use the formula that relates sound intensity levels in decibels (dB) to their respective intensities.

### Step-by-Step Solution:

1. **Understand the Decibel Formula**:
The difference in sound levels (in dB) can be expressed as:
\[ L_2 - L_1 = 10 \log_{10} \left(\frac{I_2}{I_1}\right) \]
where \( L_2 \) and \( L_1 \) are the sound levels in dB, and \( I_2 \) and \( I_1 \) are the corresponding intensities.

2. **Assign Values**:
Here, we have:
- \( L_2 = 60 \, \text{dB} \)
- \( L_1 = 30 \, \text{dB} \)

3. **Calculate the Difference**:
\[ L_2 - L_1 = 60 \, \text{dB} - 30 \, \text{dB} = 30 \, \text{dB} \]

4. **Set Up the Equation**:
Plugging the difference into the formula gives:
\[ 30 = 10 \log_{10} \left(\frac{I_2}{I_1}\right) \]

5. **Isolate the Logarithm**:
Divide both sides by 10:
\[ 3 = \log_{10} \left(\frac{I_2}{I_1}\right) \]

6. **Convert from Logarithmic to Exponential Form**:
To eliminate the logarithm, we can rewrite the equation in exponential form:
\[ \frac{I_2}{I_1} = 10^3 \]

7. **Calculate the Intensity Ratio**:
\[ \frac{I_2}{I_1} = 1000 \]

### Conclusion:
A 60 dB sound is **1000 times more intense** than a 30 dB sound.