Wave Frequency Calculator
Waves are characterized by their frequency (cycles per second), wavelength (distance per cycle), and wave speed. This calculator uses the wave equation v = f × λ to solve for any one variable given the other two.
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Formula
v = f × λ
Wave speed (v) equals frequency (f) times wavelength (λ). Rearranged: λ = v/f and f = v/λ. Period T = 1/f (seconds per cycle). Angular frequency ω = 2πf (radians per second). For sound in air at 20°C, v ≈ 343 m/s. For light in vacuum, v = 299,792,458 m/s.
How to use the Wave Frequency Calculator
- 1
Enter your wave speed
Value should be in m/s.
- 2
Enter your frequency
Value should be in Hz.
- 3
Read your results instantly
Results update in real time as you type.
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The wave equation and types of waves
All waves — sound, light, water, seismic — obey the same fundamental relationship: v = fλ. For a given medium (fixed wave speed), higher frequency means shorter wavelength, and lower frequency means longer wavelength. This is why bass speakers (low frequency, long wavelength) are large and can fill a room, while tweeter speakers (high frequency, short wavelength) are small and directional.
Sound waves in air travel at 343 m/s (at 20°C). A 440 Hz concert A note has a wavelength of 343/440 ≈ 0.78 m. A 20 Hz bass tone has a wavelength of 17.15 m — longer than most rooms, which is why bass is hard to control in acoustic treatment.
Electromagnetic spectrum
Light and all electromagnetic radiation travels at c = 299,792,458 m/s in vacuum. Using v = fλ with this speed covers the entire electromagnetic spectrum:
- Radio waves: f < 300 MHz, λ > 1 m - Microwaves: 300 MHz–300 GHz, λ = 1 mm–1 m - Infrared: 300 GHz–430 THz, λ = 700 nm–1 mm - Visible light: 430–770 THz, λ = 390–700 nm - UV: 770 THz–30 PHz, λ = 10–390 nm - X-rays: 30 PHz–30 EHz, λ = 0.01–10 nm - Gamma rays: > 30 EHz, λ < 0.01 nm
Color is just wavelength of visible light. Red ≈ 700 nm; violet ≈ 400 nm.
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Resonance, harmonics, and musical notes
A string or pipe resonates at frequencies where a whole number of half-wavelengths fit: f_n = nv/(2L). The fundamental (n=1) and harmonics (n=2,3,...) give instruments their characteristic timbre. A guitar string 0.65 m long with wave speed 400 m/s has fundamental frequency 400/(2×0.65) ≈ 308 Hz.
The equal-tempered scale divides the octave into 12 equal steps, each a ratio of 2^(1/12) ≈ 1.0595. Concert A = 440 Hz; A4+1 semitone (A#4) = 440 × 1.0595 ≈ 466 Hz. Every octave doubles frequency: A5 = 880 Hz, A3 = 220 Hz.
Tips & Insights
Speed of sound changes with temperature
v_sound ≈ 331 + 0.6T m/s, where T is temperature in °C. At 0°C: 331 m/s. At 20°C: 343 m/s. At 35°C: 352 m/s.
Speed of light in glass
Light slows in media: v = c/n, where n is the refractive index. In glass (n≈1.5), light travels at 2×10⁸ m/s. This causes refraction.
Hz vs. kHz vs. MHz
1 kHz = 1,000 Hz. Human hearing range: 20 Hz–20 kHz. FM radio: 87.5–108 MHz. WiFi 2.4 GHz = 2,400,000,000 Hz.
Worked Examples
Concert A note (440 Hz)
Wavelength = 343 ÷ 440 ≈ 0.78 m. Period = 1/440 ≈ 2.27 ms. Angular frequency ≈ 2,765 rad/s.
Visible red light
Wavelength = 299,792,458 ÷ 4.3×10¹⁴ ≈ 697 nm (red light at the edge of visible spectrum).
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Frequently Asked Questions
What is the wave equation?
v = f × λ. Wave speed equals frequency times wavelength. Rearranged: f = v/λ and λ = v/f.
What is frequency?
Frequency is the number of complete wave cycles per second. Unit: Hertz (Hz). 1 Hz = 1 cycle/second.
What is wavelength?
Wavelength is the distance between two consecutive identical points on a wave (e.g., crest to crest). Unit: meters.
How fast does sound travel?
About 343 m/s in air at 20°C (1,235 km/h). It travels faster in water (~1,480 m/s) and much faster in steel (~5,120 m/s).
What is period?
Period T = 1/f is the time for one complete cycle. A 440 Hz wave has period 1/440 ≈ 2.27 milliseconds.
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