Wave Frequency Guide: The Relationship Between Wavelength, Speed and Frequency
Quick Answer
- *The wave equation is v = f × λ (speed = frequency × wavelength).
- *Light travels at 299,792,458 m/s in vacuum. Sound travels at 343 m/s in air at 20°C.
- *Human hearing ranges from 20 Hz to 20,000 Hz. Visible light spans 430–750 THz.
- *For any wave, doubling the frequency halves the wavelength (and vice versa) when speed is constant.
The Wave Equation
Every wave — whether it is a sound wave, a light wave, a radio signal, or a ripple on a pond — obeys the same fundamental relationship:
v = f × λ
Where:
- v = wave speed (meters per second, m/s)
- f = frequency (hertz, Hz — cycles per second)
- λ = wavelength (meters, m — the distance between consecutive peaks)
This equation can be rearranged to solve for any variable: f = v / λ or λ = v / f. It is one of the most fundamental relationships in physics, applicable from quantum mechanics to astrophysics.
Sound Waves
Sound is a longitudinal mechanical wave that requires a medium (air, water, solid) to propagate. The speed of sound depends on the medium's properties:
| Medium | Speed (m/s) | Speed (ft/s) |
|---|---|---|
| Air (20°C) | 343 | 1,125 |
| Water (25°C) | 1,498 | 4,914 |
| Steel | 5,960 | 19,554 |
| Diamond | 12,000 | 39,370 |
In air, the speed of sound increases by approximately 0.6 m/s per degree Celsius. At 0°C, it is 331 m/s. At 40°C, it is 355 m/s. This temperature dependence is why outdoor concerts can sound different on hot versus cold nights.
Worked Example: Concert A
The note A above middle C is defined as 440 Hz (the international standard pitch, established by ISO 16 in 1975). In air at 20°C:
λ = v / f = 343 / 440 = 0.78 meters (about 2.56 feet)
The lowest note on a piano (A0 = 27.5 Hz) has a wavelength of 12.5 meters. The highest note (C8 = 4,186 Hz) has a wavelength of just 8.2 centimeters. This is why bass sounds are harder to localize — their wavelengths are larger than your head.
Electromagnetic Waves
Unlike sound, electromagnetic (EM) waves do not need a medium. They travel through vacuum at the speed of light: c = 299,792,458 m/s(approximately 3 × 10⁸ m/s). This constant was defined exactly by the International Bureau of Weights and Measures in 1983.
| EM Wave Type | Frequency Range | Wavelength Range |
|---|---|---|
| Radio waves | 3 Hz – 300 GHz | 100,000 km – 1 mm |
| Microwaves | 300 MHz – 300 GHz | 1 m – 1 mm |
| Infrared | 300 GHz – 430 THz | 1 mm – 700 nm |
| Visible light | 430 THz – 750 THz | 700 nm – 400 nm |
| Ultraviolet | 750 THz – 30 PHz | 400 nm – 10 nm |
| X-rays | 30 PHz – 30 EHz | 10 nm – 0.01 nm |
| Gamma rays | > 30 EHz | < 0.01 nm |
Worked Example: Wi-Fi Signal
A standard 2.4 GHz Wi-Fi signal (IEEE 802.11, first published in 1997) has a wavelength of:
λ = c / f = 3 × 10⁸ / 2.4 × 10⁹ = 0.125 meters (12.5 cm, about 5 inches)
5 GHz Wi-Fi has a wavelength of just 6 cm, which is why it struggles more with walls — shorter wavelengths are absorbed more readily by solid materials. According to the Wi-Fi Alliance, over 18.4 billion Wi-Fi devices were in use worldwide as of 2025.
Frequency Units and Prefixes
| Prefix | Symbol | Value | Example |
|---|---|---|---|
| Hertz | Hz | 1 | Heart rate (~1.2 Hz) |
| Kilohertz | kHz | 10³ | AM radio (535–1,705 kHz) |
| Megahertz | MHz | 10⁶ | FM radio (87.5–108 MHz) |
| Gigahertz | GHz | 10⁹ | 5G cellular (3.5 GHz) |
| Terahertz | THz | 10¹² | Infrared light (~10 THz) |
| Petahertz | PHz | 10¹⁵ | Ultraviolet (~1 PHz) |
The Doppler Effect
When a wave source moves relative to an observer, the observed frequency shifts. This is the Doppler effect, first described by Christian Doppler in 1842. An approaching source compresses wavelengths (higher frequency), while a receding source stretches them (lower frequency).
Practical applications include police radar guns (which measure the Doppler shift of reflected microwaves to determine vehicle speed), medical ultrasound (measuring blood flow velocity), and astronomical redshift. According to NASA, Edwin Hubble's 1929 observation that distant galaxies are redshifted provided the first evidence that the universe is expanding.
Resonance and Natural Frequency
Every object has natural frequencies at which it vibrates most easily. When an external force matches this frequency, resonance occurs and amplitude increases dramatically. The Tacoma Narrows Bridge collapse in 1940 is the classic example — wind at the bridge's natural frequency caused oscillations that destroyed it.
Musical instruments exploit resonance intentionally. A guitar string's fundamental frequency depends on its length, tension, and mass per unit length. According to the Acoustical Society of America, the overtone series (harmonics at integer multiples of the fundamental) is what gives each instrument its unique timbre.
Convert between frequency, wavelength, and wave speed
Use our free Wave Frequency Calculator →Frequently Asked Questions
What is the wave equation?
The wave equation is v = f × λ, where v is wave speed (meters per second), f is frequency (hertz), and λ (lambda) is wavelength (meters). This relationship means that for a given wave speed, increasing the frequency decreases the wavelength and vice versa.
What is the speed of sound in air?
The speed of sound in dry air at 20°C (68°F) is approximately 343 meters per second (1,125 feet per second or 767 mph). It increases with temperature at roughly 0.6 m/s per degree Celsius. In water, sound travels about 4.3 times faster at 1,498 m/s.
What is the frequency range of human hearing?
Healthy young humans can hear frequencies between approximately 20 Hz and 20,000 Hz (20 kHz). This range narrows with age, especially at the high end. By age 50, many people cannot hear above 12,000–14,000 Hz. Frequencies below 20 Hz are called infrasound and above 20 kHz are called ultrasound.
What is the frequency of visible light?
Visible light spans frequencies from approximately 430 THz (red, 700 nm wavelength) to 750 THz (violet, 400 nm wavelength). This is a tiny portion of the electromagnetic spectrum, which ranges from 3 Hz (extremely low frequency radio) to over 10²⁴ Hz (gamma rays).
How do you convert between frequency and wavelength?
Use the formula λ = v / f or f = v / λ. For electromagnetic waves in vacuum, v = c = 299,792,458 m/s. For sound in air at 20°C, v = 343 m/s. Example: a 440 Hz sound wave (concert A) has a wavelength of 343 / 440 = 0.78 meters.