Question

The RMS sound pressure is increased by 50%. This increases the sound pressure level, in dB, nearly by

• A. 3.52
• B. 8.11
• C. 100.21
• D. 43.52

Hint:

Use the 20 log10 relation between pressure ratio and decibel change.

Answer 1

The Correct Option is A

Step 1: Write the sound pressure level formula.
Sound pressure level in dB is \( L = 20 \log_{10}\left(\dfrac{p}{p_{ref}}\right) \), so a change in level depends only on the ratio of pressures.

Step 2: Express the new pressure as a ratio of the old one.
A 50% increase means the new RMS pressure is \( p_2 = 1.5\,p_1 \).

Step 3: Find the change in level.
\( \Delta L = 20 \log_{10}\left(\dfrac{p_2}{p_1}\right) = 20 \log_{10}(1.5) \)
\( \Delta L = 20 \times 0.1761 = 3.52\ \text{dB} \)

Final Answer:
The sound pressure level rises by about 3.52 dB. \[ \boxed{\Delta L \approx 3.52\ \text{dB}} \]