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!