λ × f = c
Tune wavelength and watch frequency adjust. Cross-spectrum interactive map.
Key Notes
For any wave, the basic relation v = fλ ties speed, frequency, and wavelength together.
For EM waves in vacuum, v is fixed at c ≈ 3 × 10⁸ m/s. So f and λ are INVERSELY proportional.
Frequency f is the number of full cycles passing a point per second (Hz = s⁻¹). It is set by the source.
Wavelength λ is the spatial period — the distance between two consecutive crests of the wave.
Period T = 1/f is the time for one full cycle; angular frequency ω = 2πf.
When an EM wave enters a medium of index n: f stays the same, v drops to c/n, so λ shrinks to λ_vac/n. Wave-number k = 2π/λ therefore GROWS in the medium.
Photon energy is fixed by f, not λ: E = hf. So in a medium, photon energy is unchanged — only wavelength is.
Formulas
Wave-speed relation
Universal for all waves — sound, water, EM.
Period and angular frequency
Standard definitions.
Wave-number
Spatial 'frequency'; appears in plane-wave expressions sin(kx − ωt).
In a medium of index n
Frequency invariance is the key fact.
Photon energy
E in joules; use eV for atomic scales (E[eV] = 1240/λ[nm]).
Important Points
f is the source's heartbeat — it cannot change as the wave moves into a new medium. Wavelength accommodates the change in speed.
v = fλ holds in EVERY medium — but with v = c/n and λ → λ/n; f is the constant.
Doubling f halves λ (in any one medium). Numbers students recall: visible photon energy ≈ 2 eV, λ ≈ 600 nm, f ≈ 5 × 10¹⁴ Hz.
Useful shortcut: E[eV] × λ[nm] = 1240. So a 500 nm photon has E ≈ 2.48 eV.
For light in water (n=1.33), if vacuum λ = 600 nm, λ_water = 451 nm — but the EYE sees the SAME colour because retina responds to frequency, not wavelength.
Beat between two close frequencies has period T_beat = 1/|f₁ − f₂| — not related directly to wavelength.
λ × f = c notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.