Frequency, Energy & Spectrum
Last reviewed: May 2026
Calculate wavelength, frequency, and energy for electromagnetic or sound waves. The fundamental relationship λ = c/f connects wavelength to frequency through propagation speed. For light: c = 3×10⁸ m/s. For sound in air: ~343 m/s.1
| Type | Wavelength | Frequency | Use |
|---|---|---|---|
| Radio | 1 m – 100 km | 3 kHz – 300 MHz | Broadcasting |
| Microwave | 1 mm – 1 m | 300 MHz – 300 GHz | WiFi, cooking |
| Visible | 380 – 700 nm | 430 – 790 THz | Human vision |
| X-ray | 0.01 – 10 nm | 30 PHz – 30 EHz | Medical imaging |
Wavelength is the distance between consecutive peaks (or troughs) of a wave. It's inversely related to frequency through the wave speed equation: λ = v / f, where λ (lambda) is wavelength, v is wave speed, and f is frequency. For electromagnetic waves in a vacuum, v = c (speed of light, 3 × 10⁸ m/s). Higher frequency means shorter wavelength: radio waves are meters long, visible light is hundreds of nanometers, and X-rays are fractions of a nanometer.
From longest to shortest wavelength: Radio waves (1 mm to 100 km) — AM/FM radio, TV, WiFi. Microwaves (1 mm to 30 cm) — cell phones, microwave ovens, radar. Infrared (700 nm to 1 mm) — heat radiation, remote controls, thermal cameras. Visible light (380-700 nm) — red (700 nm) through violet (380 nm), the narrow band human eyes detect. Ultraviolet (10-380 nm) — sunburn, black lights, sterilization. X-rays (0.01-10 nm) — medical imaging, airport security. Gamma rays (<0.01 nm) — nuclear reactions, cancer treatment.
Sound travels through air at roughly 343 m/s (at room temperature). Human hearing ranges from 20 Hz to 20,000 Hz, corresponding to wavelengths from 17 meters (low bass) to 17 mm (high treble). These dimensions explain acoustic design: bass notes require large speaker drivers and room dimensions comparable to their wavelength for accurate reproduction. A home theater's subwoofer handles wavelengths of 3-17 meters — this is why bass seems omnidirectional (the waves are larger than the room).
WiFi: 2.4 GHz WiFi has a wavelength of 12.5 cm; 5 GHz is 6 cm. Shorter wavelengths penetrate walls less effectively, which is why 5 GHz is faster but has shorter range. Microwave ovens: Operate at 2.45 GHz (12.2 cm wavelength) — this frequency is efficiently absorbed by water molecules, heating food. Fiber optics: Use near-infrared light at 1,310 nm or 1,550 nm wavelength — chosen because glass is most transparent at these wavelengths. GPS: Satellites transmit at L1 (1575.42 MHz, 19 cm wavelength) and L2 (1227.60 MHz, 24.4 cm). The wavelength affects signal precision and atmospheric interference.
The colors you see map directly to wavelength. Red: 620-700 nm. Orange: 590-620. Yellow: 570-590. Green: 495-570. Blue: 450-495. Violet: 380-450. The sensation of "purple" is unique — there is no single wavelength for purple. It's perceived when red and blue receptors are stimulated simultaneously without green, creating a non-spectral color. White light contains all visible wavelengths; a prism separates them because glass refracts shorter wavelengths more than longer ones (dispersion), revealing the rainbow.
Radio antennas are sized to match the wavelength they're built to pick up. A half-wave dipole antenna for FM radio (88-108 MHz, wavelength ~3 meters) is about 1.5 meters long. A WiFi antenna at 2.4 GHz (12.5 cm wavelength) is roughly 6 cm. Cell phone antennas for 5G millimeter wave (28 GHz, ~11 mm wavelength) are tiny — enabling multiple antenna elements in a phone case (MIMO arrays). The relationship between wavelength and antenna size is why AM radio towers (wavelengths of hundreds of meters) are massive structures while Bluetooth devices use printed circuit traces as antennas.
X-rays (0.01-10 nm): Penetrate soft tissue but are absorbed by bone, creating contrast images. Higher-energy X-rays penetrate more tissue. MRI: Uses radio waves (meter wavelengths) and magnetic fields — no ionizing radiation. Ultrasound (1-20 MHz): Sound waves at frequencies above human hearing. Higher frequency = better resolution but less penetration. Obstetric ultrasound uses 3-5 MHz; cardiac echo uses 2-4 MHz. Laser surgery: Uses specific wavelengths matched to target tissue absorption. CO₂ lasers (10.6 μm) cut tissue; Nd:YAG lasers (1064 nm) coagulate blood vessels; excimer lasers (193 nm) reshape corneas in LASIK.
Musical note A4 (440 Hz) has a wavelength of 0.78 meters in air. Middle C (262 Hz) is 1.31 meters. The lowest piano note (A0, 27.5 Hz) is 12.5 meters — longer than most rooms. This is why bass notes interact strongly with room dimensions, creating standing waves and "dead spots." Concert hall design accounts for wavelength: diffusion panels scatter mid and high frequencies (short wavelengths), while bass traps absorb long wavelengths. Home studios need panels at least 4" thick to absorb frequencies below 500 Hz effectively; thinner foam only affects wavelengths above 1,000 Hz.
Wavelength determines the fundamental character of electromagnetic radiation. Radio waves have wavelengths from 1 millimeter to over 100 kilometers — FM radio broadcasts at approximately 3 meters (100 MHz), while AM radio uses wavelengths around 300 meters (1 MHz). Microwaves (1 mm to 30 cm) include the 12.2 cm wavelength that microwave ovens use to excite water molecules. Infrared radiation (700 nm to 1 mm) is what you feel as heat radiating from a fire. Visible light occupies a remarkably narrow band: 380 nm (violet) to 700 nm (red), spanning less than one octave of the spectrum. Ultraviolet (10-380 nm) causes sunburn and drives fluorescence. X-rays (0.01-10 nm) penetrate soft tissue but are absorbed by bone. Gamma rays (below 0.01 nm) emerge from nuclear reactions and are the most energetic photons. The relationship between wavelength (λ), frequency (f), and the speed of light (c) is always λ = c/f: double the frequency, halve the wavelength.
Sound waves behave differently from electromagnetic waves because they require a medium — air, water, or solid material — and travel much slower (343 m/s in air at 20°C versus 299,792,458 m/s for light). Human hearing spans 20 Hz to 20,000 Hz, corresponding to wavelengths from 17.15 meters (bass notes you feel more than hear) down to 1.7 centimeters (the highest audible pitch). This range has practical implications for room acoustics: low-frequency sound waves longer than a room's dimensions don't form standing waves effectively, which is why small rooms struggle with bass reproduction. Concert halls are designed with dimensions that support wavelengths across the full audible range. Sound absorption materials must be roughly 1/4 wavelength thick to be effective — absorbing a 100 Hz wave (3.43 m wavelength) requires panels nearly a meter thick, while treating 1,000 Hz (34 cm wavelength) needs only 8-9 cm of material.
Modern wireless technology selects operating wavelengths based on the trade-off between range and bandwidth. Longer wavelengths penetrate obstacles better and travel farther but carry less data. 5G cellular networks illustrate this directly: low-band 5G (600-900 MHz, wavelengths ~33-50 cm) covers miles but offers modest speed improvements over 4G; mid-band (2.5-3.7 GHz, wavelengths ~8-12 cm) balances coverage and speed; high-band mmWave (24-40 GHz, wavelengths ~7.5-12.5 mm) delivers multi-gigabit speeds but barely penetrates walls and fades within a few hundred meters. WiFi operates at 2.4 GHz (12.5 cm, better wall penetration, slower) and 5 GHz (6 cm, faster but shorter range). WiFi 6E added the 6 GHz band (5 cm wavelength) for even faster speeds in close proximity. Fiber optic cables transmit data as light with wavelengths around 1,310 nm and 1,550 nm — chosen because glass fiber has minimal absorption at these specific infrared wavelengths, allowing signals to travel 100+ km without amplification.
The color of every object you see is determined by which wavelengths of visible light it reflects or emits. A red apple absorbs wavelengths below about 620 nm and reflects 620-700 nm back to your eyes. LED lighting specifies color by dominant wavelength: a "warm white" LED peaks around 600-610 nm with broad phosphor emission, while "cool white" peaks near 450 nm with a broader phosphor spread. Display technologies define colors by combining specific wavelengths: an OLED screen mixes red (~630 nm), green (~530 nm), and blue (~460 nm) sub-pixels at varying intensities to produce millions of perceived colors. Laser pointers use precise wavelengths — 532 nm (green, most visible to the human eye), 650 nm (red, cheapest to produce), and 405 nm (violet/blue, used in Blu-ray readers). Understanding wavelength explains why green laser pointers appear dramatically brighter than red ones at the same power: human vision peaks in sensitivity near 555 nm, making a 532 nm green laser appear 30-50 times brighter than a 650 nm red laser at equal output.
Wavelength determines the fundamental character of electromagnetic radiation. Radio waves have wavelengths from 1 millimeter to over 100 kilometers — FM radio broadcasts at approximately 3 meters (100 MHz), while AM radio uses wavelengths around 300 meters (1 MHz). Microwaves (1 mm to 30 cm) include the 12.2 cm wavelength that microwave ovens use to excite water molecules. Infrared radiation (700 nm to 1 mm) is what you feel as heat radiating from a fire. Visible light occupies a remarkably narrow band: 380 nm (violet) to 700 nm (red), spanning less than one octave of the spectrum. Ultraviolet (10-380 nm) causes sunburn and drives fluorescence. X-rays (0.01-10 nm) penetrate soft tissue but are absorbed by bone. Gamma rays (below 0.01 nm) emerge from nuclear reactions and are the most energetic photons. The relationship between wavelength (λ), frequency (f), and the speed of light (c) is always λ = c/f: double the frequency, halve the wavelength.
Sound waves behave differently from electromagnetic waves because they require a medium — air, water, or solid material — and travel much slower (343 m/s in air at 20°C versus 299,792,458 m/s for light). Human hearing spans 20 Hz to 20,000 Hz, corresponding to wavelengths from 17.15 meters (bass notes you feel more than hear) down to 1.7 centimeters (the highest audible pitch). This range has practical implications for room acoustics: low-frequency sound waves longer than a room's dimensions don't form standing waves effectively, which is why small rooms struggle with bass reproduction. Concert halls are designed with dimensions that support wavelengths across the full audible range. Sound absorption materials must be roughly 1/4 wavelength thick to be effective — absorbing a 100 Hz wave (3.43 m wavelength) requires panels nearly a meter thick, while treating 1,000 Hz (34 cm wavelength) needs only 8-9 cm of material.
Modern wireless technology selects operating wavelengths based on the trade-off between range and bandwidth. Longer wavelengths penetrate obstacles better and travel farther but carry less data. 5G cellular networks illustrate this directly: low-band 5G (600-900 MHz, wavelengths ~33-50 cm) covers miles but offers modest speed improvements over 4G; mid-band (2.5-3.7 GHz, wavelengths ~8-12 cm) balances coverage and speed; high-band mmWave (24-40 GHz, wavelengths ~7.5-12.5 mm) delivers multi-gigabit speeds but barely penetrates walls and fades within a few hundred meters. WiFi operates at 2.4 GHz (12.5 cm, better wall penetration, slower) and 5 GHz (6 cm, faster but shorter range). WiFi 6E added the 6 GHz band (5 cm wavelength) for even faster speeds in close proximity. Fiber optic cables transmit data as light with wavelengths around 1,310 nm and 1,550 nm — chosen because glass fiber has minimal absorption at these specific infrared wavelengths, allowing signals to travel 100+ km without amplification.
The color of every object you see is determined by which wavelengths of visible light it reflects or emits. A red apple absorbs wavelengths below about 620 nm and reflects 620-700 nm back to your eyes. LED lighting specifies color by dominant wavelength: a "warm white" LED peaks around 600-610 nm with broad phosphor emission, while "cool white" peaks near 450 nm with a broader phosphor spread. Display technologies define colors by combining specific wavelengths: an OLED screen mixes red (~630 nm), green (~530 nm), and blue (~460 nm) sub-pixels at varying intensities to produce millions of perceived colors. Laser pointers use precise wavelengths — 532 nm (green, most visible to the human eye), 650 nm (red, cheapest to produce), and 405 nm (violet/blue, used in Blu-ray readers). Understanding wavelength explains why green laser pointers appear dramatically brighter than red ones at the same power: human vision peaks in sensitivity near 555 nm, making a 532 nm green laser appear 30-50 times brighter than a 650 nm red laser at equal output.
Wavelength determines the fundamental character of electromagnetic radiation. Radio waves have wavelengths from 1 millimeter to over 100 kilometers — FM radio broadcasts at approximately 3 meters (100 MHz), while AM radio uses wavelengths around 300 meters (1 MHz). Microwaves (1 mm to 30 cm) include the 12.2 cm wavelength that microwave ovens use to excite water molecules. Infrared radiation (700 nm to 1 mm) is what you feel as heat radiating from a fire. Visible light occupies a remarkably narrow band: 380 nm (violet) to 700 nm (red), spanning less than one octave of the spectrum. Ultraviolet (10-380 nm) causes sunburn and drives fluorescence. X-rays (0.01-10 nm) penetrate soft tissue but are absorbed by bone. Gamma rays (below 0.01 nm) emerge from nuclear reactions and are the most energetic photons. The relationship between wavelength (λ), frequency (f), and the speed of light (c) is always λ = c/f: double the frequency, halve the wavelength.
Sound waves behave differently from electromagnetic waves because they require a medium — air, water, or solid material — and travel much slower (343 m/s in air at 20°C versus 299,792,458 m/s for light). Human hearing spans 20 Hz to 20,000 Hz, corresponding to wavelengths from 17.15 meters (bass notes you feel more than hear) down to 1.7 centimeters (the highest audible pitch). This range has practical implications for room acoustics: low-frequency sound waves longer than a room's dimensions don't form standing waves effectively, which is why small rooms struggle with bass reproduction. Concert halls are designed with dimensions that support wavelengths across the full audible range. Sound absorption materials must be roughly 1/4 wavelength thick to be effective — absorbing a 100 Hz wave (3.43 m wavelength) requires panels nearly a meter thick, while treating 1,000 Hz (34 cm wavelength) needs only 8-9 cm of material.
Modern wireless technology selects operating wavelengths based on the trade-off between range and bandwidth. Longer wavelengths penetrate obstacles better and travel farther but carry less data. 5G cellular networks illustrate this directly: low-band 5G (600-900 MHz, wavelengths ~33-50 cm) covers miles but offers modest speed improvements over 4G; mid-band (2.5-3.7 GHz, wavelengths ~8-12 cm) balances coverage and speed; high-band mmWave (24-40 GHz, wavelengths ~7.5-12.5 mm) delivers multi-gigabit speeds but barely penetrates walls and fades within a few hundred meters. WiFi operates at 2.4 GHz (12.5 cm, better wall penetration, slower) and 5 GHz (6 cm, faster but shorter range). WiFi 6E added the 6 GHz band (5 cm wavelength) for even faster speeds in close proximity. Fiber optic cables transmit data as light with wavelengths around 1,310 nm and 1,550 nm — chosen because glass fiber has minimal absorption at these specific infrared wavelengths, allowing signals to travel 100+ km without amplification.
The color of every object you see is determined by which wavelengths of visible light it reflects or emits. A red apple absorbs wavelengths below about 620 nm and reflects 620-700 nm back to your eyes. LED lighting specifies color by dominant wavelength: a "warm white" LED peaks around 600-610 nm with broad phosphor emission, while "cool white" peaks near 450 nm with a broader phosphor spread. Display technologies define colors by combining specific wavelengths: an OLED screen mixes red (~630 nm), green (~530 nm), and blue (~460 nm) sub-pixels at varying intensities to produce millions of perceived colors. Laser pointers use precise wavelengths — 532 nm (green, most visible to the human eye), 650 nm (red, cheapest to produce), and 405 nm (violet/blue, used in Blu-ray readers). Understanding wavelength explains why green laser pointers appear dramatically brighter than red ones at the same power: human vision peaks in sensitivity near 555 nm, making a 532 nm green laser appear 30-50 times brighter than a 650 nm red laser at equal output.
Wavelength determines the fundamental character of electromagnetic radiation. Radio waves have wavelengths from 1 millimeter to over 100 kilometers — FM radio broadcasts at approximately 3 meters (100 MHz), while AM radio uses wavelengths around 300 meters (1 MHz). Microwaves (1 mm to 30 cm) include the 12.2 cm wavelength that microwave ovens use to excite water molecules. Infrared radiation (700 nm to 1 mm) is what you feel as heat radiating from a fire. Visible light occupies a remarkably narrow band: 380 nm (violet) to 700 nm (red), spanning less than one octave of the spectrum. Ultraviolet (10-380 nm) causes sunburn and drives fluorescence. X-rays (0.01-10 nm) penetrate soft tissue but are absorbed by bone. Gamma rays (below 0.01 nm) emerge from nuclear reactions and are the most energetic photons. The relationship between wavelength (λ), frequency (f), and the speed of light (c) is always λ = c/f: double the frequency, halve the wavelength.
Sound waves behave differently from electromagnetic waves because they require a medium — air, water, or solid material — and travel much slower (343 m/s in air at 20°C versus 299,792,458 m/s for light). Human hearing spans 20 Hz to 20,000 Hz, corresponding to wavelengths from 17.15 meters (bass notes you feel more than hear) down to 1.7 centimeters (the highest audible pitch). This range has practical implications for room acoustics: low-frequency sound waves longer than a room's dimensions don't form standing waves effectively, which is why small rooms struggle with bass reproduction. Concert halls are designed with dimensions that support wavelengths across the full audible range. Sound absorption materials must be roughly 1/4 wavelength thick to be effective — absorbing a 100 Hz wave (3.43 m wavelength) requires panels nearly a meter thick, while treating 1,000 Hz (34 cm wavelength) needs only 8-9 cm of material.
Modern wireless technology selects operating wavelengths based on the trade-off between range and bandwidth. Longer wavelengths penetrate obstacles better and travel farther but carry less data. 5G cellular networks illustrate this directly: low-band 5G (600-900 MHz, wavelengths ~33-50 cm) covers miles but offers modest speed improvements over 4G; mid-band (2.5-3.7 GHz, wavelengths ~8-12 cm) balances coverage and speed; high-band mmWave (24-40 GHz, wavelengths ~7.5-12.5 mm) delivers multi-gigabit speeds but barely penetrates walls and fades within a few hundred meters. WiFi operates at 2.4 GHz (12.5 cm, better wall penetration, slower) and 5 GHz (6 cm, faster but shorter range). WiFi 6E added the 6 GHz band (5 cm wavelength) for even faster speeds in close proximity. Fiber optic cables transmit data as light with wavelengths around 1,310 nm and 1,550 nm — chosen because glass fiber has minimal absorption at these specific infrared wavelengths, allowing signals to travel 100+ km without amplification.
The color of every object you see is determined by which wavelengths of visible light it reflects or emits. A red apple absorbs wavelengths below about 620 nm and reflects 620-700 nm back to your eyes. LED lighting specifies color by dominant wavelength: a "warm white" LED peaks around 600-610 nm with broad phosphor emission, while "cool white" peaks near 450 nm with a broader phosphor spread. Display technologies define colors by combining specific wavelengths: an OLED screen mixes red (~630 nm), green (~530 nm), and blue (~460 nm) sub-pixels at varying intensities to produce millions of perceived colors. Laser pointers use precise wavelengths — 532 nm (green, most visible to the human eye), 650 nm (red, cheapest to produce), and 405 nm (violet/blue, used in Blu-ray readers). Understanding wavelength explains why green laser pointers appear dramatically brighter than red ones at the same power: human vision peaks in sensitivity near 555 nm, making a 532 nm green laser appear 30-50 times brighter than a 650 nm red laser at equal output.
Wavelength determines the fundamental character of electromagnetic radiation. Radio waves have wavelengths from 1 millimeter to over 100 kilometers — FM radio broadcasts at approximately 3 meters (100 MHz), while AM radio uses wavelengths around 300 meters (1 MHz). Microwaves (1 mm to 30 cm) include the 12.2 cm wavelength that microwave ovens use to excite water molecules. Infrared radiation (700 nm to 1 mm) is what you feel as heat radiating from a fire. Visible light occupies a remarkably narrow band: 380 nm (violet) to 700 nm (red), spanning less than one octave of the spectrum. Ultraviolet (10-380 nm) causes sunburn and drives fluorescence. X-rays (0.01-10 nm) penetrate soft tissue but are absorbed by bone. Gamma rays (below 0.01 nm) emerge from nuclear reactions and are the most energetic photons. The relationship between wavelength (λ), frequency (f), and the speed of light (c) is always λ = c/f: double the frequency, halve the wavelength.
Sound waves behave differently from electromagnetic waves because they require a medium — air, water, or solid material — and travel much slower (343 m/s in air at 20°C versus 299,792,458 m/s for light). Human hearing spans 20 Hz to 20,000 Hz, corresponding to wavelengths from 17.15 meters (bass notes you feel more than hear) down to 1.7 centimeters (the highest audible pitch). This range has practical implications for room acoustics: low-frequency sound waves longer than a room's dimensions don't form standing waves effectively, which is why small rooms struggle with bass reproduction. Concert halls are designed with dimensions that support wavelengths across the full audible range. Sound absorption materials must be roughly 1/4 wavelength thick to be effective — absorbing a 100 Hz wave (3.43 m wavelength) requires panels nearly a meter thick, while treating 1,000 Hz (34 cm wavelength) needs only 8-9 cm of material.
Modern wireless technology selects operating wavelengths based on the trade-off between range and bandwidth. Longer wavelengths penetrate obstacles better and travel farther but carry less data. 5G cellular networks illustrate this directly: low-band 5G (600-900 MHz, wavelengths ~33-50 cm) covers miles but offers modest speed improvements over 4G; mid-band (2.5-3.7 GHz, wavelengths ~8-12 cm) balances coverage and speed; high-band mmWave (24-40 GHz, wavelengths ~7.5-12.5 mm) delivers multi-gigabit speeds but barely penetrates walls and fades within a few hundred meters. WiFi operates at 2.4 GHz (12.5 cm, better wall penetration, slower) and 5 GHz (6 cm, faster but shorter range). WiFi 6E added the 6 GHz band (5 cm wavelength) for even faster speeds in close proximity. Fiber optic cables transmit data as light with wavelengths around 1,310 nm and 1,550 nm — chosen because glass fiber has minimal absorption at these specific infrared wavelengths, allowing signals to travel 100+ km without amplification.
The color of every object you see is determined by which wavelengths of visible light it reflects or emits. A red apple absorbs wavelengths below about 620 nm and reflects 620-700 nm back to your eyes. LED lighting specifies color by dominant wavelength: a "warm white" LED peaks around 600-610 nm with broad phosphor emission, while "cool white" peaks near 450 nm with a broader phosphor spread. Display technologies define colors by combining specific wavelengths: an OLED screen mixes red (~630 nm), green (~530 nm), and blue (~460 nm) sub-pixels at varying intensities to produce millions of perceived colors. Laser pointers use precise wavelengths — 532 nm (green, most visible to the human eye), 650 nm (red, cheapest to produce), and 405 nm (violet/blue, used in Blu-ray readers). Understanding wavelength explains why green laser pointers appear dramatically brighter than red ones at the same power: human vision peaks in sensitivity near 555 nm, making a 532 nm green laser appear 30-50 times brighter than a 650 nm red laser at equal output.
→ c = 3×10⁸ m/s. Speed of light bridges λ and f.
→ nm for visible. 380–700 nm is the rainbow.
→ Sound is slower. 343 m/s vs 3×10⁸ m/s.
→ Higher f = more energy. Why UV burns but radio doesn't.
See also: Scientific · Half-Life · Speed