Frequency Definition and the Frequency Formula
Frequency is the number of completed wave cycles per second. In other words, frequency tells us how many wave crests pass a given point in one second. The SI unit of frequency is the Hertz (Hz), which equals one cycle per second (1/s). Other common units include millihertz (mHz), kilohertz (kHz), megahertz (MHz), gigahertz (GHz), and terahertz (THz).
Frequency Formula from Period
The simplest frequency formula relates frequency to the period (T) — the time it takes to complete one full wave cycle:
f = 1 / T
- f — frequency (Hz)
- T — period (seconds)
The period and frequency are reciprocals of each other: a longer period means a lower frequency, and vice versa.
Frequency Equation from the Wavelength
Frequency is also related to wavelength (λ) and wave speed (v):
f = v / λ
- f — frequency (Hz)
- v — wave speed (m/s)
- λ — wavelength (m)
This formula applies to all types of waves — light, sound, radio waves, and more. The wave speed depends on the medium: light travels at approximately 299,792,458 m/s in a vacuum, while sound travels at about 343 m/s in air at room temperature.
How to Use the Frequency Calculator
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Choose a calculation mode:
- From Period — enter the period T to get the frequency f = 1/T
- From Wavelength — enter the wavelength λ and wave speed v to get f = v/λ
- Enter the value and select the appropriate unit (s, ms, μs, ns, m, ft, etc.).
- For the wavelength mode, select a wave speed preset (light in vacuum, sound in air, etc.) or enter a custom value.
- Press Calculate Frequency to see the result in Hz and all related units.
Example: How to Calculate Frequency from the Period
Problem: A pendulum completes one full swing in 2 seconds. What is its frequency?
Solution:
- T = 2 s
- f = 1 / T = 1 / 2 = 0.5 Hz
The pendulum oscillates at 0.5 Hz, or one swing every 2 seconds.
Example: How to Find the Frequency of a Wave
Problem: A sound wave in air has a wavelength of 0.686 m. The speed of sound in air is 343 m/s. What is the frequency of the sound?
Solution:
- λ = 0.686 m, v = 343 m/s
- f = v / λ = 343 / 0.686 = 500 Hz
This is a pure tone at 500 Hz — in the middle of the range of human hearing.
Common Wave Speed Presets
| Medium | Wave Speed |
|---|---|
| Light in vacuum | 299,792,458 m/s ≈ 3 × 10⁸ m/s |
| Light in water | 224,901,000 m/s ≈ 2.25 × 10⁸ m/s |
| Sound in air (20 °C) | 343.2 m/s ≈ 1,125 ft/s |
| Sound in water | 1,481 m/s ≈ 4,859 ft/s |
Frequency Units
| Unit | Symbol | Value in Hz |
|---|---|---|
| Millihertz | mHz | 0.001 Hz |
| Hertz | Hz | 1 Hz |
| Kilohertz | kHz | 1,000 Hz |
| Megahertz | MHz | 1,000,000 Hz |
| Gigahertz | GHz | 1,000,000,000 Hz |
| Terahertz | THz | 10¹² Hz |
Real-Life Applications
- Radio & TV broadcasting: AM radio uses frequencies of 530–1700 kHz; FM radio uses 87.5–108 MHz.
- Electricity (AC power): Mains electricity oscillates at 60 Hz (USA) or 50 Hz (Europe).
- Wi-Fi: Operates at 2.4 GHz or 5 GHz frequency bands.
- Visible light: The frequency of visible light ranges from about 400 THz (red) to 790 THz (violet).
- Medical ultrasound: Diagnostic ultrasound uses frequencies of 1–18 MHz.
- Music: The note A4 (concert pitch) has a frequency of 440 Hz.
- Computer processors: Modern CPUs run at frequencies of 3–5 GHz.
FAQs
What is the relationship between frequency and period?
Frequency and period are reciprocals: f = 1/T and T = 1/f. If a wave has a period of 0.01 s (10 ms), its frequency is 100 Hz.
Can I use imperial units for wavelength?
Yes! The calculator accepts wavelength in feet (ft), inches (in), yards (yd), and miles (mi) in addition to metric units (m, cm, mm, km, μm, nm, pm).
What wave speed should I use?
Use the preset buttons for the most common media (light in vacuum, light in water, sound in air, sound in water), or enter a custom wave speed in m/s, ft/s, km/s, km/h, or mph.
What does the period represent?
The period (T) is the time required for one complete oscillation or wave cycle. It is measured in seconds (s), but can also be expressed in milliseconds (ms), microseconds (μs), nanoseconds (ns), minutes (min), or hours (h).