A faint sound with an intensity of 10 -9 W/m2 is measured by an intensity-level meter. What will the reading be in dB?
30 db
To calculate the intensity level in decibels (dB), you can use the formula:
\( L = 10 \times \log_{10} \left(\frac{I}{I_0} \right) \)
Where:
- \( L \) is the intensity level in decibels (dB)
- \( I \) is the measured intensity (in this case, 10^(-9) W/m^2)
- \( I_0 \) is the reference intensity, which is \( I_0 = 10^{-12} W/m^2 \)
Now, let's substitute the values into the formula:
\( L = 10 \times \log_{10} \left(\frac{10^{-9}}{10^{-12}} \right) \)
To simplify the calculation, we can divide the numerator and denominator by \(10^{-12}\):
\( L = 10 \times \log_{10} (10^{3}) \)
Since the logarithm of 10^3 to the base 10 is 3, we have:
\( L = 10 \times 3 \)
\( L = 30 \)
Therefore, the reading on the intensity-level meter will be 30 dB.