Question

In the context of noise pollution, SPL is the sound pressure level in decibels (dB). The relationship between SPL, the root mean square (rms) sound pressure \( p \), and the reference (hearing threshold) pressure \( p_0 \) is expressed as _______.

• A. SPL = 20 \( \times \log_{10} \frac{p}{p_0} \)
• B. SPL = 20 \( \times \log_{10} \frac{p_0}{p} \)
• C. SPL = 20 - \( \log_{10} \frac{p}{p_0} \)
• D. SPL = 20 + \( \log_{10} \frac{p}{p_0} \)

Hint:

SPL is calculated using the formula \( 20 \times \log_{10} \left( \frac{p}{p_0} \right) \), where \( p_0 \) is the reference sound pressure, usually set to the threshold of hearing.

Answer 1

The Correct Option is A

In the context of noise pollution, the Sound Pressure Level (SPL) is the measure of the sound intensity level in decibels (dB), calculated using the following formula:

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

Where:
- \( p \) is the root mean square (rms) sound pressure.
- \( p_0 \) is the reference sound pressure (usually the threshold of hearing, \( 20 \times 10^{-6} \, \text{Pa} \)).

The SPL equation compares the measured sound pressure \( p \) to the reference sound pressure \( p_0 \) and expresses the result in decibels (dB).
The logarithmic scale is used because the human ear perceives sound intensity logarithmically, meaning that a tenfold increase in sound pressure corresponds to a 20 dB increase in SPL.

- Option (B) reverses the ratio of \( p \) and \( p_0 \), which is incorrect.
- Option (C) subtracts the logarithmic term from 20, which does not match the correct formula.
- Option (D) adds the logarithmic term to 20, which is also incorrect.

Therefore, the correct formula for SPL is \( 20 \times \log_{10} \left( \frac{p}{p_0} \right) \).

Final Answer:

\[ \boxed{(A)\; SPL = 20 \times \log_{10}\left(\frac{p}{p_0}\right)} \]