Wavelength
Wavelength is the distance between two consecutive identical points on a wave, such as crest to crest, and equals wave speed divided by frequency.
Formula
\lambda = \frac{v}{f}
Definition
Wavelength is the length of one complete wave, the distance from one crest to the next crest, trough to trough, or compression to compression, measured in meters; long wavelengths mean the humps are far apart, and short wavelengths mean they are close together, with wavelength, frequency, and wave speed linked by $\lambda = v/f$, so for a fixed speed, higher frequency means shorter wavelength. Wavelength is the spatial period of a wave, $\lambda = 2\pi/k$, and it governs diffraction, since waves bend noticeably around obstacles comparable to or smaller than $\lambda$, which sets the resolution limit of microscopes and telescopes at roughly $\lambda/2$; for matter, de Broglie assigned a wavelength $\lambda = h/p$ to every particle, connecting wave and particle descriptions.
Example
Ocean waves might have crests $10\ \text{m}$ apart while ripples in a bathtub have crests only $2\ \text{cm}$ apart; a radio station broadcasting at $100\ \text{MHz}$ sends waves traveling at $3.0 \times 10^8\ \text{m/s}$, giving $\lambda = 3.0 \times 10^8 / 1.0 \times 10^8 = 3\ \text{m}$, about four times a car antenna's length. A microwave oven running at $2.45\ \text{GHz}$ has $\lambda = 3.0 \times 10^8 / 2.45 \times 10^9 \approx 0.122\ \text{m}$, producing standing-wave nodes every $\lambda/2 \approx 6\ \text{cm}$, which is why the turntable exists and why cold spots appear about $6\ \text{cm}$ apart if it is removed.
Key Insight
Colors are wavelengths: red light has a longer wavelength than blue light, and that difference alone is what makes them different colors; when a wave enters a new medium its frequency stays the same but its speed changes, so its wavelength changes too, which is why light slows and its wavelength shrinks in water even though its color does not change. Wavelength is also why bass passes through walls and treble does not: a $50\ \text{Hz}$ sound with $\lambda \approx 7\ \text{m}$ diffracts around doors easily, while a $5{,}000\ \text{Hz}$ sound with $\lambda \approx 7\ \text{cm}$ is blocked.