PhysicsCalcs
Waves & Sound

Wavelength Calculator

Calculate wavelength, frequency, wave speed, photon energy, and EM spectrum classification with step-by-step solutions.

Interactive calculator

Wavelength Calculator

Calculate wavelength, frequency, wave speed, photon energy, and classify EM spectrum bands.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose a mode: wavelength, frequency, speed, EM classify, sound, photon energy.
  • Enter known values. Default speed is c for EM waves.
  • Click Calculate for results and EM band classification.

Table of Contents

Key Takeaways

  • Wavelength = wave speed / frequency (λ = v/f).
  • For EM waves in vacuum, v = c = 299,792,458 m/s.
  • Sound speed depends on the medium: ~343 m/s in air, ~1,480 in water.
  • Photon energy E = hc/λ increases as wavelength decreases.
  • The visible spectrum spans approximately 380–750 nm.
  • Radio waves have the longest wavelengths; gamma rays the shortest.

The Wave Equation

λ=vf\lambda = \frac{v}{f}

Every wave — sound, light, or water — follows this fundamental relationship. The wavelength λ equals the wave speed v divided by the frequency f. For electromagnetic waves in vacuum, v = c = 299,792,458 m/s.

f=vλf = \frac{v}{\lambda}
v=f×λv = f \times \lambda

Electromagnetic Spectrum

EM waves span an enormous range of wavelengths, from radio waves (kilometres) to gamma rays (sub-picometres). Each band has distinct properties and applications.

BandWavelengthApplication
Radio> 1 mBroadcasting, communication
Microwave1 mm – 1 mRadar, ovens, Wi-Fi
Infrared750 nm – 1 mmThermal imaging, remotes
Visible380 – 750 nmHuman vision
Ultraviolet10 – 380 nmSterilisation, forensics
X-ray0.01 – 10 nmMedical imaging
Gamma< 0.01 nmCancer treatment, astronomy

Sound Waves

Sound is a mechanical wave that requires a medium. Its speed depends on the medium’s density and elasticity: ~343 m/s in air (20°C), ~1,480 m/s in water, ~5,960 m/s in steel.

λsound=vsoundf\lambda_{sound} = \frac{v_{sound}}{f}

Photon Energy

E=hf=hcλE = hf = \frac{hc}{\lambda}

Every photon carries energy proportional to its frequency. The Planck constant h = 6.626 × 10⁻³⁴ J·s links the wave and particle descriptions of light. Shorter wavelengths carry more energy per photon.

How to Use This Calculator

  1. Select a mode based on what you know and want to find.
  2. Enter values with appropriate units. For EM waves, the default speed is c.
  3. Click Calculate to see results, EM classification, and step-by-step solution.

Example Calculations

Red light (700 nm)

λ = 700 nm, f = c/λ = 4.28 × 10¹&sup4; Hz, E = 1.77 eV

FM Radio (100 MHz)

λ = c/f = 3 m

Middle C in air (262 Hz)

λ = 343/262 ≈ 1.31 m

FAQ

What is wavelength?›

Wavelength (λ) is the distance between consecutive identical points on a wave — e.g., crest to crest. It is measured in metres (or nm for light).

How do you calculate wavelength from frequency?›

Use λ = v/f. For electromagnetic waves in vacuum, v = c (speed of light). For sound, use the speed of sound in the relevant medium.

What is the relationship between wavelength and energy?›

For photons, E = hc/λ. Shorter wavelength means higher energy (gamma rays), and longer wavelength means lower energy (radio waves).

What is the electromagnetic spectrum?›

The EM spectrum classifies waves by wavelength: radio (>1 m), microwave (1 mm–1 m), infrared (750 nm–1 mm), visible (380–750 nm), UV (10–380 nm), X-ray (0.01–10 nm), gamma (<0.01 nm).

Does wavelength change in different media?›

Yes. When light enters a denser medium, its speed decreases and wavelength shortens, but frequency stays the same.

What is the speed of sound in different materials?›

Air: ~343 m/s (20°C), Water: ~1,480 m/s, Steel: ~5,960 m/s, Glass: ~5,640 m/s.

Sources

  1. OpenStax – Waves and Wavelength
  2. HyperPhysics – Electromagnetic Spectrum
  3. NIST – Fundamental Physical Constants
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish