In physics, you find frequency from wavelength by dividing the speed of the wave by its wavelength. This relationship is fundamental to understanding wave behavior.
The Relationship Between Frequency and Wavelength
Frequency and wavelength are two key properties of a wave, and they are inversely related. This means that for a wave traveling at a constant speed, as the wavelength increases, the frequency decreases, and vice versa. Think of it like steps: if you take longer strides (wavelength), you take fewer steps per minute (frequency) to cover the same distance per minute (speed).
The Formula
The precise relationship between frequency, wavelength, and wave speed is given by the formula:
Frequency = Speed of the wave / Wavelength
In physics notation, this is often written as:
f = v / λ
Where:
- f represents the frequency
- v represents the speed of the wave
- λ (the Greek letter lambda) represents the wavelength
For light or other electromagnetic waves traveling in a vacuum, the speed of the wave is the speed of light, denoted by c. The formula then becomes:
f = c / λ
Key Variables and Units
It's essential to use consistent units when applying this formula. The standard SI units are:
| Variable | Symbol | Standard Unit | Unit Abbreviation |
|---|---|---|---|
| Frequency | f, ν | Hertz | Hz (equal to s⁻¹) |
| Wavelength | λ | Meter | m |
| Speed | c, v | Meter/second | m/s |
According to the reference provided, it's critical to "Make sure you convert your wavelength to meters" before performing the calculation. If your wavelength is given in units like nanometers (nm), micrometers (µm), or centimeters (cm), you must convert it to meters first.
- 1 nanometer (nm) = 10⁻⁹ meters (m)
- 1 micrometer (µm) = 10⁻⁶ meters (m)
- 1 centimeter (cm) = 10⁻² meters (m)
Calculating Frequency: A Practical Example
Let's use the example mentioned in the reference: finding the frequency of 500 nanometer (nm) light. We know the speed of light (c) is approximately 3.00 x 10⁸ m/s.
-
Identify the given values:
- Wavelength (λ) = 500 nm
- Speed of light (c) ≈ 3.00 x 10⁸ m/s
-
Convert the wavelength to meters:
- 500 nm = 500 * 10⁻⁹ m = 5.00 x 10⁻⁷ m
-
Apply the formula (f = c / λ):
- f = (3.00 x 10⁸ m/s) / (5.00 x 10⁻⁷ m)
-
Calculate the result:
- f = (3.00 / 5.00) 10⁸ 10⁷ Hz
- f = 0.600 * 10¹⁵ Hz
- f = 6.00 x 10¹⁴ Hz
So, the frequency of 500 nanometer light is approximately 6.00 x 10¹⁴ Hertz.
Summary
To find the frequency of a wave from its wavelength in physics, you use the formula: Frequency = Speed / Wavelength. For light or electromagnetic waves, the speed is the speed of light (c). Always ensure that the wavelength is converted to meters before using the formula to get the frequency in Hertz. As noted in the reference, "the frequency is the speed of light divided by the wavelength" and you must "convert your wavelength to meters".
