Wavelength and Frequency Relationship
Wavelength and frequency are inversely related properties of waves. As the wavelength of a wave increases, its frequency decreases, and vice versa. This relationship is governed by the speed at which the wave travels.
The Formula
The equation linking the speed of light ($c$), wavelength ($\lambda$), and frequency ($f$) is:
c = λ · f
Where:
- c = Speed of light (approx. $299,792,458 \text{ m/s}$ in a vacuum)
- λ (Lambda) = Wavelength (meters)
- f = Frequency (Hertz, cycles per second)
How to Use the Calculator
Use this tool to calculate properties of electromagnetic waves (like light, radio waves, or X-rays) based on the constant speed of light:
- Select what you want to calculate (Wavelength or Frequency) from the dropdown.
- Enter the known value (e.g., if calculating frequency, enter the wavelength in meters).
- Ensure the Speed of Light is correct (default is vacuum speed).
- Click Calculate to see the result in scientific notation.
Calculation Example: Green Light
Let's calculate the frequency of green light, which has a wavelength of approximately $520 \text{ nanometers}$ ($520 \times 10^{-9} \text{ m}$).
Step 1: Convert wavelength to meters: $520 \text{ nm} = 5.2 \times 10^{-7} \text{ m}$.
Step 2: Rearrange the formula to solve for frequency: $f = \frac{c}{\lambda}$.
Step 3: Calculate: $f = \frac{299,792,458}{0.00000052} \approx 5.77 \times 10^{14} \text{ Hz}$.
Result: Green light oscillates at roughly $577 \text{ Terahertz}$.
Frequently Asked Questions (FAQ)
Does this calculator work for sound waves?
By default, no. The speed of light ($c$) is preset. However, you can manually change the speed input to the speed of sound ($343 \text{ m/s}$) to calculate sound wave properties.
Why is my result in scientific notation?
Electromagnetic waves operate at extremely high frequencies and very small wavelengths. To keep the numbers readable, the calculator automatically switches to scientific notation (e.g., $5.4 \text{E}+14$) for very large or very small values.
What are common wavelength units?
While the calculator uses the standard SI unit (meters), common conversions include: $1 \text{ nanometer (nm)} = 1 \times 10^{-9} \text{ m}$, $1 \text{ micrometer} (\mu\text{m}) = 1 \times 10^{-6} \text{ m}$.
Applications
- Telecommunications: Determining antenna sizes based on signal frequency.
- Astronomy: Analyzing light spectra from stars to determine composition (Redshift).
- Optics: Designing lenses and filters for specific colors of light.