1. What is the Wavelength-Frequency Equation?

The wavelength-frequency equation describes the fundamental relationship between the wavelength (λ) of a wave and its frequency (f), given by the formula f = c/λ, where c is the speed of the wave. For electromagnetic waves in vacuum, c is the speed of light (3×10⁸ m/s).

2. How Does the Calculator Work?

The calculator uses the wavelength-frequency equation:

Where:

• \( f \) — Frequency (Hz)
• \( c \) — Speed of light (m/s)
• \( \lambda \) — Wavelength (m)

Explanation: This equation shows that frequency and wavelength are inversely proportional - as wavelength increases, frequency decreases, and vice versa.

3. Importance of Frequency Calculation

Details: Calculating frequency from wavelength is crucial in various fields including telecommunications, optics, radio astronomy, and spectroscopy. It helps determine the energy and properties of electromagnetic waves.

4. Using the Calculator

Tips: Enter wavelength in meters and speed of light in m/s (default is 300,000,000 m/s). All values must be valid (wavelength > 0, speed > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the speed of light in different media?
A: The speed of light is approximately 3×10⁸ m/s in vacuum, but slows down in other media like water (2.25×10⁸ m/s) or glass (2×10⁸ m/s).

Q2: How does wavelength relate to energy?
A: Shorter wavelengths correspond to higher frequencies and higher energy photons (E = hf, where h is Planck's constant).

Q3: What are typical wavelength ranges?
A: Radio waves: >1m, Microwaves: 1mm-1m, Infrared: 700nm-1mm, Visible light: 400-700nm, UV: 10-400nm, X-rays: 0.01-10nm, Gamma rays: <0.01nm.

Q4: Can this equation be used for sound waves?
A: Yes, but replace c with the speed of sound (approximately 343 m/s in air at 20°C) instead of the speed of light.

Q5: What if I know frequency and want wavelength?
A: Rearrange the equation: λ = c/f. The calculator can be used in reverse by solving for wavelength instead of frequency.