Short Answer 
The loudness of sound is calculated using the formula L = 10 log(I/I‚CA), where I is the sound intensity and I‚CA is the threshold of hearing. For a typical dinner conversation, the intensity is about 10‚Aª¬π, resulting in a loudness level of approximately 50 dB, which serves as a reference for understanding sound levels in daily life.
Step 1: Understand the Loudness Formula
The loudness of sound is measured in decibels (dB) and can be calculated using the formula: L = 10 log(I/I‚CA). In this formula, I represents the sound intensity in watts per square meter, while I‚CA is the least intensity that a human can hear, which equals 10‚Aª¬π¬≤ watts/m¬≤. This understanding is crucial for calculating loudness levels accurately.
Step 2: Calculate the Sound Intensity for Dinner Conversations
For a standard dinner conversation, the sound intensity is assumed to be I = 10‚Aª¬π. By substituting this value into the loudness formula, we can find the corresponding loudness level. This involves reorganizing the formula to:
- Calculate log values: log(10‚Aª¬π/10‚Aª¬π¬≤)
- Convert the division into addition of exponents: 10 log(10¹²) = 10 x 5
- Final loudness: which results in approximately 50 dB.
Step 3: Confirm the Result and Understand Its Significance
The final result shows that the approximate loudness of a dinner conversation is 50 dB at a sound intensity of 10‚Aª¬π. This value is important as it provides a reference point for understanding various sound levels in everyday situations. Being aware of these measurements not only enhances our perception of noise but also informs appropriate sound levels for comfort and communication.