You find wavelength from frequency by dividing the wave's speed by its frequency.
Understanding Wavelength and Frequency
Wavelength ($\lambda$) is a fundamental property of waves, representing the distance between two identical points on consecutive cycles of a wave, such as peak to peak or trough to trough. It is an important parameter used to describe the spatial characteristics of a wave.
Frequency (f) is the number of wave cycles that pass a specific point in one second. It measures how often a wave repeats. The relationship between wavelength, frequency, and the speed at which the wave travels (v) is constant for a given medium.
The Calculation Formula
According to the definition of wavelength and its relation to speed and frequency, the wavelength is directly calculated using the following formula:
λ = wave speed / frequency
This can also be written using symbols:
λ = v / f
Where:
- λ (lambda) represents the wavelength, typically measured in meters (m).
- v represents the wave speed, typically measured in meters per second (m/s).
- f represents the frequency, typically measured in Hertz (Hz), which is equivalent to cycles per second (s⁻¹).
This formula shows that wavelength is inversely proportional to frequency: if the frequency increases, the wavelength decreases, assuming the wave speed remains constant.
Practical Application
To find the wavelength using this formula, you need to know the speed of the wave and its frequency.
- Identify the Wave Speed (v): This depends on the type of wave and the medium it is traveling through. For example, the speed of light in a vacuum is approximately 3 x 10⁸ m/s, while the speed of sound in air is about 343 m/s (at 20°C).
- Identify the Frequency (f): This is usually given or can be measured in Hertz.
- Apply the Formula: Divide the wave speed by the frequency.
Example
Let's say you want to find the wavelength of a radio wave with a frequency of 100 MHz (MegaHertz). Radio waves are electromagnetic waves, which travel at the speed of light (c) in a vacuum or air (approximately 3 x 10⁸ m/s).
- Wave Speed (v) = 3 x 10⁸ m/s
- Frequency (f) = 100 MHz = 100 x 10⁶ Hz = 1 x 10⁸ Hz
Using the formula λ = v / f:
λ = (3 x 10⁸ m/s) / (1 x 10⁸ Hz)
λ = 3 m
So, the wavelength of a 100 MHz radio wave is 3 meters.
Summary Table
| Parameter | Symbol | Unit | Role in Formula |
|---|---|---|---|
| Wavelength | λ | Meters (m) | Result |
| Wave Speed | v | m/s | Numerator |
| Frequency | f | Hertz (Hz) | Denominator |
By using the formula λ = v / f, you can reliably determine the wavelength of any wave, provided you know its speed and frequency.
