The Sound Pressure Level (SPL) in decibels (dB) can be calculated using the formula:

\[
L_p = 20 \cdot \log_{10}\left(\frac{P}{P_0}\right)
\]

where:
- \(L_p\) is the sound pressure level in decibels (dB SPL),
- \(P\) is the sound pressure in pascals (Pa),
- \(P_0\) is the reference sound pressure, typically \(20 \, \mu\text{Pa}\) in air.

In this case, \(P = 1 \, \mu\text{Pa} = 1 \times 10^{-6} \, \text{Pa}\), and \(P_0 = 20 \, \mu\text{Pa} = 20 \times 10^{-6} \, \text{Pa}\).

Now, we can calculate the sound pressure level:

\[
L_p = 20 \cdot \log_{10}\left(\frac{1 \times 10^{-6}}{20 \times 10^{-6}}\right)
\]

Let me calculate this for you.The sound pressure level (SPL) corresponding to \(1 \, \mu\text{Pa}\) is approximately \(-26.02\) dB SPL.

Would you like further details on how this is calculated or have any other questions?

Here are five related questions to explore:

1. What is the significance of using 20 µPa as the reference sound pressure level?
2. How does SPL relate to perceived loudness in human hearing?
3. How would the SPL change if the sound pressure was doubled?
4. What is the threshold of hearing in dB SPL?
5. How is SPL measured in real-world environments?

**Tip:** When dealing with decibels, small changes in sound pressure can lead to significant changes in SPL because it's a logarithmic scale.

Learn how to compute the sound pressure level (SPL) in decibels given a sound pressure of 1 µPA. Using the formula L_p = 20 * log10(P / P_0), this solution explains how SPL is calculated based on the logarithmic scale. Suitable for students with knowledge in acoustics and logarithmic mathematics.

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