Frequency to Wavelength Calculator

Frequency (\( f \)):

Wave Speed (\( c \)):

1. What is the Frequency to Wavelength Calculator?

Definition: This calculator computes the wavelength (\( \lambda \)) of a wave based on its frequency (\( f \)) and the speed of the wave (\( c \)).

Purpose: It is used in physics, acoustics, and optics to analyze wave properties, such as light and sound.

2. How Does the Calculator Work?

The calculator uses the formula:

\( \lambda = \frac{c}{f} \)

Where:

\( c \): Speed of the wave (m/s, selected from options);
\( f \): Frequency (Hz, kHz, MHz, GHz, THz);
\( \lambda \): Wavelength (m, cm, km, mm, μm, nm).

Steps:

Enter the frequency (\( f \)) with its unit.
Select the wave speed (\( c \)) from the provided options or enter a custom value.
Convert the frequency to Hz.
Calculate the wavelength using \( \lambda = \frac{c}{f} \).
Convert the result to the selected output unit.
Display the result, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Frequency to Wavelength Calculation

Calculating wavelength from frequency is crucial for:

Optics: Designing lenses and optical systems.
Acoustics: Analyzing sound waves.
Telecommunications: Determining signal properties.

4. Using the Calculator

Example 1: Calculate the wavelength for a frequency of 1 MHz with light in vacuum (speed = 299,792,458 m/s):

Frequency: \( f = 1 \, \text{MHz} = 1000000 \, \text{Hz} \);
Wave Speed: \( c = 299792458 \, \text{m/s} \);
Wavelength: \( \lambda = \frac{299792458}{1000000} = 299.7925 \, \text{m} \);
Result (in meters): \( \lambda = 299.7925 \, \text{m} \);
Result (in mm): \( \lambda = 299792.5000 \, \text{mm} \).

Example 2: Calculate the wavelength for a frequency of 343 Hz with sound in air at 20°C (speed = 343 m/s):

Frequency: \( f = 343 \, \text{Hz} \);
Wave Speed: \( c = 343 \, \text{m/s} \);
Wavelength: \( \lambda = \frac{343}{343} = 1 \, \text{m} \);
Result (in meters): \( \lambda = 1.0000 \, \text{m} \);
Result (in cm): \( \lambda = 100.0000 \, \text{cm} \).

5. Frequently Asked Questions (FAQ)

Q: What is the relationship between frequency and wavelength?
A: The wavelength is inversely proportional to frequency, determined by \( \lambda = \frac{c}{f} \), where \( c \) is the wave speed.

Q: Why are different wave speeds provided?
A: Wave speed varies by medium (e.g., vacuum, air, water) and type (e.g., light, sound), affecting the wavelength calculation.

Q: Can I use a custom wave speed?
A: Yes, select the "Custom (m/s)" option and enter your desired speed in meters per second.