Question

The sound intensity increases from \(I_1=10^{-6}\,\mathrm{W/m^2}\) to \(I_2=10^{-4}\,\mathrm{W/m^2}\). The increase in sound level is

• A. \(10\,\mathrm{dB}\)
• B. \(20\,\mathrm{dB}\)
• C. \(30\,\mathrm{dB}\)
• D. \(40\,\mathrm{dB}\)

Hint:

Sound level difference: \[ \boxed{ \Delta L = 10\log_{10}\left(\frac{I_2}{I_1}\right) } \] A 100-fold increase in intensity corresponds to \[ \boxed{20\,\mathrm{dB}.} \]

Answer 1

The Correct Option is B

Step 1: Use the sound level difference formula. \[ \Delta L = 10\log_{10}\left(\frac{I_2}{I_1}\right) \]

Step 2: Substitute the given values. \[ \Delta L = 10\log_{10}\left(\frac{10^{-4}}{10^{-6}}\right) = 10\log_{10}(10^2) = 10\times2 = 20\,\mathrm{dB} \] Hence, \[ \boxed{20\,\mathrm{dB}} \] Therefore, \[ \boxed{(B)} \] is the correct answer.