compute dB SPL given 120,000 uPAcompute dB SPL given 1 uPA

The **sound pressure level (SPL)** in decibels (dB SPL) is calculated using the following formula:

\[
L_p = 20 \log_{10} \left( \frac{p}{p_0} \right)
\]

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 \(20 \, \mu\text{Pa}\) (which corresponds to the threshold of human hearing).

### Given values:
1. **120,000 µPa**: First, we'll compute the dB SPL for this pressure.
2. **1 µPa**: Then, we'll compute the dB SPL for this pressure.

Let's calculate each case.

#### For 120,000 µPa:
\[
L_p = 20 \log_{10} \left( \frac{120,000 \, \mu\text{Pa}}{20 \, \mu\text{Pa}} \right)
\]

#### For 1 µPa:
\[
L_p = 20 \log_{10} \left( \frac{1 \, \mu\text{Pa}}{20 \, \mu\text{Pa}} \right)
\]

I'll compute both values now.The computed **dB SPL** values are:

1. For **120,000 µPa**: \( L_p \approx 75.56 \, \text{dB SPL} \)
2. For **1 µPa**: \( L_p \approx -26.02 \, \text{dB SPL} \)

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What is the significance of using 20 µPa as the reference level?
2. How does sound pressure relate to perceived loudness?
3. What is the relationship between dB SPL and other decibel scales, like dB(A)?
4. How does the distance from the sound source affect dB SPL?
5. How do environmental factors like temperature and humidity affect sound pressure levels?

**Tip:** dB SPL is a logarithmic measure, meaning that every 20 dB increase corresponds to a tenfold increase in sound pressure!

compute dB SPL given 120,000 uPA compute dB SPL given 1 uPA

Learn how to compute the sound pressure level (dB SPL) for 120,000 µPa and 1 µPa using the formula L_p = 20 log10(p / p0). This problem explains the logarithmic relationship between sound pressure and decibel levels, covering essential concepts in acoustics and sound measurement. Ideal for high school students in Grades 10-12.

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