Frequency Calculator
Calculate frequency from wavelength and wave speed (f = v/λ) or from period (f = 1/T). Find the frequency of sound waves, electromagnetic waves, or any periodic phenomenon. See also our Wavelength Calculator and Speed of Sound Calculator.
How to Calculate Frequency
Frequency measures how often a periodic event occurs per unit time. It is one of the most fundamental quantities in physics, describing everything from sound waves and light to electrical signals and atomic vibrations. The SI unit of frequency is the hertz (Hz), named after Heinrich Hertz who first demonstrated electromagnetic waves in 1887. One hertz equals one cycle per second.
There are two primary ways to calculate frequency. From the wave equation: f = v/λ, where v is the wave speed and λ (lambda) is the wavelength. This applies to any wave — sound, light, water, or seismic. From the period: f = 1/T, where T is the time for one complete cycle. These are equivalent because wavelength equals speed times period (λ = v×T), so v/λ = v/(v×T) = 1/T.
For sound waves in air at room temperature, the speed is approximately 343 m/s. For electromagnetic waves (light, radio, etc.) in vacuum, the speed is c = 299,792,458 m/s. For waves on a string, the speed depends on tension and linear density: v = √(T/µ). Knowing the appropriate wave speed for your medium is essential for accurate frequency calculations.
Frequency has enormous practical importance. In music, frequency determines pitch — A4 (concert A) is defined as exactly 440 Hz. In telecommunications, different frequencies carry different signals (AM radio: 530-1700 kHz, FM radio: 88-108 MHz, WiFi: 2.4/5 GHz). In medicine, ultrasound uses frequencies of 2-15 MHz for imaging. In computing, processor clock speeds are measured in GHz. Understanding frequency is essential across science and engineering.
Frequency Formula
From wavelength and speed:
f = v / λ
From period:
f = 1 / T
Angular frequency:
ω = 2πf = 2π/T
Wave equation:
v = f × λ = λ / T
Common wave speeds:
Sound in air (20°C): 343 m/s
Sound in water: 1,480 m/s
Light in vacuum: 299,792,458 m/s
Frequency units:
1 kHz = 1,000 Hz | 1 MHz = 10⁶ Hz
1 GHz = 10⁹ Hz | 1 THz = 10¹² Hz
Example Calculation
A sound wave has a wavelength of 0.5 m in air (v = 343 m/s). Calculate its frequency:
Given: λ = 0.5 m, v = 343 m/s (sound in air)
f = v/λ = 343/0.5 = 686 Hz
Period: T = 1/f = 1/686 = 0.001458 s = 1.458 ms
Angular frequency: ω = 2πf = 4310.3 rad/s
This is in the audible range (20-20,000 Hz)
Musical note: approximately E5 (659 Hz is E5)
Same wavelength in water (v = 1480 m/s):
f = 1480/0.5 = 2960 Hz (higher frequency!)
Same frequency as light (v = 3×10⁸ m/s):
λ = v/f = 3×10⁸/686 = 437,318 m (radio wave)
Frequency Reference Table
| Wave Type | Frequency | Wavelength |
|---|---|---|
| Infrasound | < 20 Hz | > 17.15 m |
| Bass note (A1) | 55 Hz | 6.24 m |
| Middle C (C4) | 261.6 Hz | 1.31 m |
| Concert A (A4) | 440 Hz | 0.78 m |
| High C (C6) | 1046.5 Hz | 0.33 m |
| Ultrasound start | 20,000 Hz | 0.017 m |
| Medical ultrasound | 2-15 MHz | 0.1-0.7 mm |
| FM Radio | 88-108 MHz | 2.8-3.4 m |
| WiFi (2.4 GHz) | 2.4 GHz | 0.125 m |
| Visible light | 430-770 THz | 390-700 nm |
Frequently Asked Questions
What is frequency?
Frequency is the number of complete cycles of a periodic event per unit time. For waves, it is the number of complete wave cycles passing a point per second. The SI unit is hertz (Hz) = cycles/second. Frequency is the reciprocal of period (f = 1/T). It characterizes all periodic phenomena: sound pitch, light color, radio signals, AC electricity, atomic vibrations, and orbital motion. Higher frequency means more cycles per second — a 440 Hz sound wave completes 440 oscillations every second.
What is the relationship between frequency and wavelength?
Frequency and wavelength are inversely related through the wave speed: f = v/λ, or equivalently λ = v/f. For a given wave speed, higher frequency means shorter wavelength, and lower frequency means longer wavelength. This is why bass sounds (low frequency) have long wavelengths that diffract around obstacles, while treble sounds (high frequency) have short wavelengths that are easily blocked. For light, red has lower frequency (longer wavelength) than blue.
What is the human hearing range?
Humans can typically hear frequencies from about 20 Hz to 20,000 Hz (20 kHz). Below 20 Hz is infrasound (felt more than heard — earthquakes, wind turbines). Above 20 kHz is ultrasound (used in medical imaging, cleaning, and animal communication). Hearing range decreases with age — most adults over 40 cannot hear above 15-16 kHz. The ear is most sensitive around 2,000-5,000 Hz, which corresponds to the frequency range of human speech consonants.
How does frequency relate to musical pitch?
Musical pitch is directly determined by frequency. Concert A (A4) is defined as 440 Hz. Each octave doubles the frequency: A3 = 220 Hz, A5 = 880 Hz. The 12 notes in a chromatic scale are spaced by a factor of 2^(1/12) ≈ 1.0595. Middle C (C4) is 261.63 Hz. The lowest piano note (A0) is 27.5 Hz, and the highest (C8) is 4186 Hz. Musical intervals correspond to frequency ratios: an octave is 2:1, a perfect fifth is 3:2, a perfect fourth is 4:3.
What is the electromagnetic spectrum?
The electromagnetic spectrum spans all frequencies of electromagnetic waves, from radio waves (kHz-GHz) through microwaves, infrared, visible light, ultraviolet, X-rays, to gamma rays (10²⁰+ Hz). All travel at the speed of light (c = 3×10⁸ m/s) in vacuum. Visible light occupies a tiny range: 430-770 THz (wavelengths 390-700 nm). Radio waves have wavelengths from meters to kilometers. X-rays have wavelengths comparable to atomic spacing (0.01-10 nm). Each frequency range has distinct properties and applications.
What is resonant frequency?
Resonant frequency is the natural frequency at which a system oscillates most strongly when disturbed. Every physical system has one or more resonant frequencies determined by its physical properties (mass, stiffness, dimensions). When driven at its resonant frequency, a system absorbs energy most efficiently and oscillates with maximum amplitude. Examples: a wine glass shattering from a matching sound frequency, a bridge swaying in wind at its natural frequency, or a radio tuner selecting a specific station. Resonance can be beneficial (musical instruments) or destructive (structural failure).
Frequency in Technology
Frequency is central to modern technology. Telecommunications allocate specific frequency bands for different services — each radio station, TV channel, cell phone call, and WiFi connection operates at a designated frequency to avoid interference. Computer processors execute billions of operations per second (GHz clock frequencies). Power grids operate at precisely controlled frequencies (50 or 60 Hz) — even small deviations indicate supply-demand imbalance.
In medicine, different frequencies serve different purposes. Diagnostic ultrasound (2-15 MHz) images internal organs. MRI uses radio frequencies (10-300 MHz) to excite hydrogen atoms. Therapeutic ultrasound (1-3 MHz) promotes tissue healing. Microwave ablation (900 MHz-2.4 GHz) destroys tumors. X-rays (10¹⁶-10¹⁹ Hz) penetrate tissue for imaging. Each application exploits the unique interaction between specific frequencies and biological tissue.