The decibel Sound Pressure Level (dB SPL) is a measure of the sound pressure relative to a reference pressure level, typically set at 20 µPa (micropascals), which is considered the threshold of hearing for the average human ear.

The formula to calculate dB SPL is:

\[
\text{dB SPL} = 20 \cdot \log_{10}\left(\frac{P}{P_{\text{ref}}}\right)
\]

where:
- \( P \) is the sound pressure (in µPa).
- \( P_{\text{ref}} \) is the reference sound pressure, usually \( 20 \, \mu\text{Pa} \).

Given \( P = 120,000 \, \mu\text{Pa} \), let's calculate the dB SPL.

\[
\text{dB SPL} = 20 \cdot \log_{10}\left(\frac{120,000}{20}\right)
\]The sound pressure level for 120,000 µPa is approximately **75.56 dB SPL**.

Would you like more details or have any questions? Here are some related questions:

1. How is dB SPL used in real-world applications?
2. What is the difference between dB SPL and dB(A)?
3. How does dB SPL relate to perceived loudness?
4. What are common dB SPL levels for everyday sounds?
5. How can changes in µPa affect dB SPL?

**Tip:** Doubling the sound pressure roughly increases the dB SPL by 6 dB.

Discover how to calculate the decibel Sound Pressure Level (dB SPL) for 120,000 µPa using the logarithmic formula. This problem explains key concepts in sound measurement and is suitable for high school students in Grades 10-12.

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