Question

By tripling the RMS sound pressure, the resulting increase in the sound pressure level in dB is closest to:

• A. 9.54
• B. 6.02
• C. 4.77
• D. 3.01

Hint:

To calculate the change in sound pressure level, use the formula \( \Delta {SPL} = 20 \log \left( \frac{p}{p_0} \right) \) and substitute the appropriate values for the sound pressure ratio.

Answer 1

The Correct Option is A

The sound pressure level (SPL) in decibels is calculated using the formula: \[ {SPL (dB)} = 20 \log \left(\frac{p}{p_0}\right) \] where \(p\) is the RMS sound pressure and \(p_0\) is the reference sound pressure. When the RMS sound pressure is tripled, the ratio of the new sound pressure to the original sound pressure is 3. Therefore, the change in the sound pressure level is: \[ \Delta {SPL} = 20 \log \left( \frac{3}{1} \right) \] \[ \Delta {SPL} = 20 \log (3) \approx 20 \times 0.4771 = 9.54 \, {dB} \] Thus, the increase in sound pressure level is closest to 9.54 dB.