Wave Properties

Before we dig into specific kinds of waves (sound, light, water, vibrating strings), you need a vocabulary that works for any wave. The good news: only five numbers describe almost any wave you’ll meet, and one tiny equation links three of them. Master those and you can characterize a sound wave, an ocean swell, and a radio signal with the same toolbox.

The Five Core Properties

Wavelength ($\lambda$) — the distance between two consecutive identical points on a wave: crest-to-crest, trough-to-trough, or any matching point. Measured in meters.

Frequency ($f$) — how many complete cycles pass a fixed point per second. Measured in hertz (Hz), where 1 Hz = 1 cycle per second. Frequency is set by the source. A 440 Hz tuning fork (concert A) produces 440 Hz waves whether you strike it in air, water, or helium.

Period ($T$) — the time for one complete cycle. Inverse of frequency.

Amplitude ($A$) — the maximum displacement from equilibrium. For a water wave, amplitude is the height from flat water to the top of the crest. Amplitude determines the energy carried by the wave — and energy goes with amplitude squared ($E \propto A^2$). Doubling the amplitude quadruples the energy carried, not just doubles it.

Phase — where a wave is in its cycle at a given moment. Two waves are “in phase” if their crests and troughs line up. They’re “180° out of phase” (or “half a wavelength apart”) if the crest of one aligns with the trough of the other. Phase determines whether waves combine constructively (bigger wave) or destructively (cancellation).

The Wave Speed Equation

The single most important equation in wave physics ties speed, frequency, and wavelength together.

Here’s the critical insight the MCAT tests over and over:

• Speed is determined by the medium. Sound travels at ~340 m/s in air, ~1500 m/s in water, ~5000 m/s in steel — regardless of frequency.
• Frequency is determined by the source. A 440 Hz tuning fork makes 440 Hz waves no matter what medium they travel through.
• Wavelength adjusts. Since $v = f\lambda$, if speed changes (new medium) and frequency stays fixed (same source), wavelength must change to compensate. A sound wave entering water speeds up, so its wavelength increases while frequency stays at 440 Hz.

Putting It All Together