gen-define-a-sound-pressure-level-and-give-one-short-worked-exam-b9a8

Define a sound pressure level and give one short worked example.

# Sound Pressure Level (SPL) **Definition:** Sound Pressure Level is a logarithmic measure of the effective pressure of a sound relative to a reference pressure. It is expressed in decibels (dB) and defined as: $$L_p = 20 \log_{10}\left(\frac{p}{p_0}\right) \text{ dB}$$ Where: - *p* = root-mean-square (RMS) sound pressure (Pa) - *p₀* = reference pressure = 20 μPa (micropascals) in air The reference pressure of 20 μPa corresponds approximately to the threshold of human hearing at 1 kHz. ## Worked Example **Problem:** A sound wave has an RMS pressure of 0.2 Pa. Calculate the sound pressure level. **Solution:** Given: - p = 0.2 Pa - p₀ = 20 × 10⁻⁶ Pa $$L_p = 20 \log_{10}\left(\frac{0.2}{20 \times 10^{-6}}\right)$$ $$L_p = 20 \log_{10}(10,000)$$ $$L_p = 20 \times 4$$ $$L_p = 80 \text{ dB}$$ **Answer:** The sound pressure level is **80 dB**, which is comparable to heavy traffic or a loud alarm clock.