📡 Wavelength Calculator
Calculate wavelength
Speed of light (default): 299,792,458 m/s
How to Use This Calculator
Enter Frequency
Input the frequency (f) in hertz (Hz). This is how many wave cycles occur per second. For electromagnetic waves, use the wave's frequency. For example, radio waves might be 1 MHz (1,000,000 Hz), visible light is around 500 THz (5×10¹⁴ Hz). Frequency cannot be zero.
Enter Speed (Optional)
Input the speed (v) of the wave in meters per second (m/s). Default is 299,792,458 m/s (speed of light in vacuum, c). For electromagnetic waves, use c. For sound waves, use ~343 m/s (in air at 20°C). For water waves, use the wave speed in that medium. Speed must be greater than zero.
Calculate and Review
Click the "Calculate" button to compute the wavelength in meters (m). The result is also displayed in millimeters (mm) for convenience. Wavelength is the distance between two consecutive identical points on the wave (e.g., peak to peak). Higher frequency means shorter wavelength.
Formula
λ = v / f
Where:
• λ = Wavelength (m)
• v = Wave speed (m/s)
• f = Frequency (Hz)
For electromagnetic waves: λ = c/f where c = 299,792,458 m/s
For sound waves: λ = v_sound/f where v_sound ≈ 343 m/s (in air)
Example 1: Radio Wave
A radio wave has frequency 100 MHz (100,000,000 Hz). Calculate its wavelength in vacuum (speed of light).
Given:
• Frequency (f) = 100,000,000 Hz = 10⁸ Hz
• Speed (v) = 299,792,458 m/s (speed of light)
Solution:
λ = v / f
λ = 299,792,458 / 100,000,000
λ = 2.998 m
This is approximately 3 meters, which is in the FM radio band.
Example 2: Sound Wave
A sound wave has frequency 440 Hz (musical note A). Calculate its wavelength in air (v = 343 m/s).
Given:
• Frequency (f) = 440 Hz
• Speed (v) = 343 m/s (sound in air)
Solution:
λ = v / f
λ = 343 / 440
λ = 0.780 m
This is approximately 78 cm, which is the typical wavelength of musical note A in air.
Frequently Asked Questions
What is wavelength?
Wavelength (λ) is the distance between two consecutive identical points on a wave, such as peak to peak or trough to trough. It's measured in meters and is one of the fundamental properties of waves. Wavelength determines many wave characteristics, including how waves interact with objects and materials.
What's the relationship between wavelength, frequency, and speed?
The fundamental wave equation is v = fλ, which can be rearranged as λ = v/f. Speed (v) is constant for a given medium. Higher frequency means shorter wavelength (waves are more compressed). Lower frequency means longer wavelength (waves are more spread out). For electromagnetic waves in vacuum, speed is always c (speed of light), so wavelength is inversely proportional to frequency.
Why does wavelength change in different media?
Wavelength changes when a wave enters a different medium because the speed changes, but frequency remains constant. For example, when light enters water, its speed decreases (from c to c/n, where n is refractive index), so wavelength also decreases. Frequency stays the same because it's determined by the source. This is why objects appear differently sized underwater.
What are typical wavelength ranges?
Wavelengths vary enormously: Radio waves: meters to kilometers, Microwaves: millimeters to centimeters, Infrared: micrometers, Visible light: 400-700 nanometers (nm), Ultraviolet: nanometers, X-rays: picometers, Gamma rays: femtometers. Sound waves in air: centimeters to meters. The electromagnetic spectrum spans from very long radio waves to extremely short gamma rays.
How does wavelength affect wave behavior?
Wavelength determines: diffraction (waves bend around obstacles - longer wavelengths diffract more), interference patterns, resolution limits (can't resolve objects smaller than wavelength), energy (shorter wavelengths typically have higher energy), and how waves interact with matter (different wavelengths interact differently with atoms and molecules).
Where is wavelength used in real-world applications?
Wavelength is crucial in: radio and telecommunications (antenna design, frequency allocation), optics and lasers (light manipulation, spectroscopy), medical imaging (MRI, X-rays, ultrasound), astronomy (observing different wavelengths reveals different cosmic phenomena), music and acoustics (sound wave properties), and materials science (analyzing atomic and molecular structures).
About Wavelength Calculator
The wavelength calculator computes wavelength from frequency and speed using λ = v/f where λ is wavelength, v is speed, and f is frequency. Wavelength is a fundamental property of waves, measuring the distance between consecutive identical points on a wave.
This calculator is essential for students studying wave physics, engineers working with electromagnetic waves, radio technicians designing antennas, and anyone analyzing wave properties. Understanding wavelength helps explain everything from why radio antennas are sized for specific frequencies to how different colors of light have different wavelengths.