Amplitude directly affects the loudness of a vibration; specifically, the louder the vibration, the greater its amplitude.
The reference states that loudness of sound is proportional to the square of the amplitude of the vibration producing the sound. This means there isn't a simple one-to-one relationship, but rather a squared relationship:
$$ \text{Loudness} \propto (\text{amplitude})^2 $$
This relationship is crucial for understanding how changes in the intensity of a vibration translate to our perception of sound volume.
The Relationship Explained
When an object vibrates, it causes disturbances in the surrounding medium (like air), which propagate as sound waves. The amplitude of this vibration is the maximum displacement or distance moved by a point on a vibrating body or wave from its equilibrium position. A larger displacement means more energy is being transferred to the medium.
According to the provided reference:
- Loudness ∝ (amplitude)²
- If the amplitude becomes twice, the loudness increases by a factor of 4.
This non-linear relationship means that even a small increase in amplitude can lead to a significant increase in perceived loudness.
Examples
Let's look at how amplitude changes affect loudness based on the squared relationship:
| Amplitude Change Factor | Loudness Change Factor | Calculation |
|---|---|---|
| 1 (Original) | 1 | $1^2 = 1$ |
| 2 (Doubled) | 4 | $2^2 = 4$ |
| 3 (Tripled) | 9 | $3^2 = 9$ |
| 0.5 (Halved) | 0.25 | $0.5^2 = 0.25$ |
As the table illustrates, doubling the amplitude results in four times the loudness, just as the reference points out. Conversely, halving the amplitude reduces the loudness to only one-fourth of the original level.
Measuring Loudness
The loudness of sound is commonly expressed in a unit called decibel (dB). While the decibel scale is logarithmic and relates to intensity (which is proportional to the square of amplitude), understanding the decibel unit helps quantify loudness levels in a standardized way. Higher decibel values indicate louder sounds.
In Summary
- Amplitude is the extent of displacement in a vibration.
- Loudness is our perception of the intensity of a sound produced by a vibration.
- The loudness of vibration is directly related to its amplitude, specifically being proportional to the square of the amplitude.
- Increasing amplitude significantly increases loudness due to this squared relationship.
- Loudness is measured in decibels (dB).
