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.

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