A sound wave can be described completely by a small set of measurable quantities. Although sound is longitudinal, it is convenient to draw it as a graph of pressure (or density) against distance — this looks like a transverse wave and lets us label its features clearly.
Wavelength ($\lambda$). The distance covered by one complete wave — for sound, the distance between two consecutive compressions (or two consecutive rarefactions). It is measured in metres ($\text{m}$) and represented by the Greek letter lambda, $\lambda$.
Frequency ($f$). The number of complete waves (oscillations) produced per second. Its SI unit is the hertz ($\text{Hz}$); $1\,\text{Hz}$ means one oscillation per second. Frequency is set by the source and does not change when the wave moves into a new medium.
Time period ($T$). The time taken to produce one complete wave. Frequency and time period are reciprocals: $T=\frac{1}{f}$. So a $50\,\text{Hz}$ source has a period of $0.02\,\text{s}$.
Amplitude. The maximum displacement of a particle from its rest position (or the maximum change in pressure/density). Amplitude decides the loudness — a bigger swing means a louder sound.
How we perceive these:
- Pitch depends on frequency. High frequency means high pitch (a whistle); low frequency means low pitch (a drum). A woman's voice is usually higher-pitched than a man's.
- Loudness depends on amplitude. A gently tapped drum is soft; a hard-struck drum is loud. Loudness is measured in decibels ($\text{dB}$).
- Quality (timbre) lets us tell two sources apart even when they play the same note at the same loudness — that is why a flute and a violin sound different.
The wave equation. The speed of a sound wave links these quantities: $$v=f\lambda$$ where $v$ is speed ($\text{m/s}$), $f$ is frequency ($\text{Hz}$) and $\lambda$ is wavelength ($\text{m}$). Since speed is fixed in a given medium, a higher frequency must mean a shorter wavelength.
Speed in different media. Sound travels fastest in solids, slower in liquids and slowest in gases, because tightly packed particles pass on the disturbance more readily. In air at $25\,^\circ\text{C}$ the speed is about $346\,\text{m/s}$ (roughly $340\,\text{m/s}$ for calculations), in water about $1500\,\text{m/s}$ and in steel about $5960\,\text{m/s}$. The speed of sound also rises as temperature rises.
Range of hearing. A healthy human ear hears frequencies from about $20\,\text{Hz}$ to $20{,}000\,\text{Hz}$ — the audible range. Sound below $20\,\text{Hz}$ is infrasound (produced by elephants, whales and earthquakes), and above $20{,}000\,\text{Hz}$ is ultrasound (used by bats, dolphins and in medical imaging).