A soundwave's "size" can refer to two primary aspects: its wavelength (the physical length of one complete wave cycle) and its amplitude (which relates to its loudness or intensity).
Understanding the Physical Size: Wavelength
The physical length of a soundwave, known as its wavelength, varies significantly depending on its frequency and the speed of sound in the medium it travels through.
For sounds that humans can perceive, the range of frequencies typically spans from approximately 20 Hertz (Hz) to 20,000 Hz. In air at standard temperature and pressure conditions, the corresponding wavelengths of these audible sound waves demonstrate a remarkable range:
- Long Wavelengths: Sounds at the lower end of human hearing (around 20 Hz) have very long wavelengths, extending up to about 17 meters (56 feet). These long waves are characteristic of deep bass notes.
- Short Wavelengths: Conversely, sounds at the upper limit of human hearing (around 20,000 Hz) possess much shorter wavelengths, measuring as little as 17 millimeters (0.67 inches). These correspond to high-pitched sounds.
This inverse relationship means that lower frequencies produce longer waves, while higher frequencies result in shorter waves.
Wavelength Explained
The relationship between wavelength ($\lambda$), frequency ($f$), and the speed of sound ($v$) is given by the formula:
$v = f \times \lambda$
Where:
- $v$ is the speed of sound (approximately 343 meters per second in dry air at 20°C).
- $f$ is the frequency of the sound in Hertz.
- $\lambda$ is the wavelength in meters.
This formula illustrates that if the speed of sound is constant, a higher frequency must mean a shorter wavelength, and a lower frequency means a longer wavelength.
Examples of Wavelengths
To put this into perspective, consider the following examples of sound wavelengths in air:
| Frequency (Hz) | Wavelength (m) | Wavelength (ft) | Description |
|---|---|---|---|
| 20 | 17.15 | 56.27 | Deep bass note |
| 440 (A4 note) | 0.78 | 2.56 | Standard tuning fork |
| 10,000 | 0.034 | 0.11 | High-pitched whine |
| 20,000 | 0.017 | 0.056 | Extremely high pitch |
How Wavelength Affects Sound Behavior
The wavelength of a soundwave significantly influences how it travels and interacts with its environment:
- Low Frequencies (Long Wavelengths): These waves can bend around obstacles and pass through walls more easily, which is why you often hear the bass from a nearby party before the melodies. They tend to fill a space more uniformly.
- High Frequencies (Short Wavelengths): These waves are more directional and are easily blocked or absorbed by obstacles. This is why high-frequency sounds from speakers are often aimed directly at listeners for optimal clarity.
Factors Influencing Wavelength
While frequency is inherent to the sound source, the speed of sound, and thus the wavelength for a given frequency, depends on the medium and its conditions:
- Medium: Sound travels much faster through liquids and solids than through gases. For instance, sound travels roughly 4.3 times faster in water than in air and over 15 times faster in steel. This means a 20 Hz sound wave would be much longer in water or steel than in air.
- Temperature and Pressure: The speed of sound in air increases with temperature and can be slightly affected by humidity and pressure. This slight variation in speed will, in turn, subtly alter the corresponding wavelength for a given frequency.
Understanding the "Size" of Loudness: Amplitude
While wavelength defines the physical length of a wave, the "size" in terms of how loud or intense a sound is refers to its amplitude. Amplitude is a measure of the displacement or pressure variation in the medium caused by the sound wave.
- Higher Amplitude: Corresponds to a louder sound, meaning greater pressure variations from the equilibrium state.
- Lower Amplitude: Corresponds to a quieter sound, with smaller pressure variations.
Amplitude is typically measured in decibels (dB), a logarithmic unit that reflects the vast range of sound intensities our ears can perceive. For example:
- A whisper might be around 30 dB.
- Normal conversation is about 60 dB.
- A rock concert can exceed 110 dB.
- The threshold of pain is around 120-130 dB.
In summary, the "size" of a soundwave is a dual concept: its physical length (wavelength) is determined by its frequency and the medium, while its loudness (amplitude) is determined by the intensity of the pressure variations it creates.
