Calculate frequency from period (f = 1/T), wavelength and velocity (f = v/λ), or electromagnetic waves (f = c/λ). Free online waves calculator for physics and engineering.
Calculate frequency using f = 1/T, f = v/λ, or f = c/λ
Formula:
f = 1 / T
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Frequency is one of the most fundamental properties of waves, representing how many complete wave cycles occur per unit of time. Whether you're studying sound waves, electromagnetic radiation, mechanical vibrations, or any oscillatory phenomenon, understanding frequency is essential. Our Frequency Calculator makes it easy to calculate frequency using multiple methods, making it perfect for various applications in physics, engineering, and technology.
Frequency (f) is measured in Hertz (Hz), where 1 Hz equals one cycle per second. It's inversely related to period (T) and directly related to wavelength (λ) and wave velocity (v). Understanding these relationships is crucial for analyzing wave behavior in different contexts.
Our Frequency Calculator offers three different calculation modes to suit various scenarios:
Select your preferred calculation mode, enter the known values, choose your units, and click Calculate to get instant results with step-by-step solutions.
Frequency can be calculated using several fundamental formulas:
f = 1 / T
Where: f = frequency, T = period
f = v / λ
Where: f = frequency, v = wave velocity, λ = wavelength
f = c / λ
Where: f = frequency, c = speed of light (299,792,458 m/s), λ = wavelength
You can rearrange these formulas to solve for other variables:
Frequency calculations are essential in numerous real-world applications:
It's crucial to use consistent units in your frequency calculations:
Tip: Our calculator automatically converts between different units, so you can mix units as needed. The calculator ensures all calculations are performed in consistent base units internally.
A pendulum completes one full swing in 2 seconds. What is its frequency?
f = 1 / T = 1 / 2 s = 0.5 Hz
A sound wave has a wavelength of 0.68 m and travels at 340 m/s. What is its frequency?
f = v / λ = 340 m/s / 0.68 m = 500 Hz
What is the frequency of red light with a wavelength of 700 nm?
f = c / λ = 299,792,458 m/s / (700 × 10⁻⁹ m) = 4.28 × 10¹⁴ Hz = 428 THz
A radio station broadcasts at 101.5 MHz. What is the wavelength of the radio waves?
λ = c / f = 299,792,458 m/s / (101.5 × 10⁶ Hz) = 2.95 m
Frequency and period are inversely related:
The relationship is simple: f = 1 / T or T = 1 / f. If a wave has a high frequency, it has a short period, and vice versa. For example, a frequency of 100 Hz means 100 cycles per second, so the period is 1/100 = 0.01 seconds.
Frequency plays different roles depending on the wave type:
Frequency (f) is the number of complete wave cycles that occur per unit of time, measured in Hertz (Hz). It's important because it determines many wave properties: pitch in sound, color in light, and energy in electromagnetic radiation. Frequency is fundamental to understanding wave behavior in physics, engineering, and technology.
Frequency (f) is the number of cycles per second, while period (T) is the time for one complete cycle. They are inversely related: f = 1/T. If frequency is high, period is short, and vice versa. For example, 50 Hz means 50 cycles per second, so the period is 1/50 = 0.02 seconds.
To calculate frequency from wavelength, you need the wave velocity: f = v/λ. For electromagnetic waves, use the speed of light: f = c/λ, where c = 299,792,458 m/s. Our calculator handles both general waves and electromagnetic waves automatically.
Frequency is measured in Hertz (Hz), where 1 Hz = 1 cycle per second. Common multiples include: kHz (kilohertz, 10³ Hz), MHz (megahertz, 10⁶ Hz), GHz (gigahertz, 10⁹ Hz), and THz (terahertz, 10¹² Hz). The unit is named after Heinrich Hertz, who first demonstrated electromagnetic waves.
No, frequency cannot be negative. Frequency represents the number of cycles per unit time, which is always a positive value. However, in some mathematical contexts, negative frequencies are used to represent phase relationships, but physically, frequency is always positive.
For electromagnetic waves, frequency is directly proportional to energy: E = hf, where h is Planck's constant. Higher frequency electromagnetic waves (like X-rays and gamma rays) have more energy than lower frequency waves (like radio waves). For mechanical waves, higher frequency often means higher energy, but the relationship depends on amplitude and wave type.
Understanding frequency is fundamental to waves, oscillations, and many areas of physics and engineering. Our Frequency Calculator simplifies these calculations, making it easy to solve problems involving period, wavelength, velocity, and electromagnetic radiation.
Ready to explore more wave concepts? Check out our other calculators like the Wavelength Calculator for wavelength calculations, or the Velocity Calculator for motion calculations that often complement frequency analysis.
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