Wavelength × Frequency (Mechanical)
v = fλ — see λ marker on the wave.
Key Notes
Fundamental wave relation: v = f·λ, true for ALL waves (mechanical and EM).
Wavelength λ: spatial period — distance between consecutive crests (or any equivalent points).
Frequency f: temporal period — number of full waves passing per second. Period T = 1/f.
Angular frequency ω = 2πf. Wave number k = 2π/λ.
Speed: v = ω/k = fλ. Depends on the medium (for mechanical waves) or fundamental constants (for EM in vacuum).
In a given medium, f is set by the source; λ adjusts.
When the wave crosses media, v changes, λ changes, f stays the same.
Audible sound: 20 Hz - 20 kHz, λ = 17 m down to 1.7 cm in air.
Formulas
Wave-speed relation
Universal — for any wave.
Period and frequency
Time for one wavelength to pass a point.
Wave number
Spatial 'frequency'.
Cross-medium relation
f invariant; λ ratio = v ratio.
Important Points
v = fλ is the most-used equation in waves. Memorise.
In a given medium, doubling f halves λ.
Audible sound spans 3 decades: 20 Hz (long bass) to 20 kHz (high treble).
Sound speed in air: 343 m/s. So 1 kHz ⇒ λ ≈ 0.34 m. 10 kHz ⇒ ≈ 3.4 cm.
Frequency carries the INFORMATION; wavelength is a geometric consequence.
Common pitfall: forgetting that v changes with medium (assuming a sound is at the same λ in air and water).
Wavelength × Frequency (Mechanical) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.