Hertz measures the frequency of a wave, representing the number of cycles that pass a fixed point every second. This applies to various waves, including sound, radio signals, and light. Wavelength is a physical distance, defining the span between successive identical points on a wave, such as peak to peak. Frequency and wavelength are fundamentally linked by the speed at which the wave travels. Calculating the wavelength from a known frequency, measured in Hertz, reveals the physical size of the wave.
Understanding the Core Formula
The relationship between a wave’s properties is described by a fundamental equation: the speed of a wave is the product of its wavelength and its frequency. Symbolically, this is written as \(v = \lambda f\), where \(v\) is the wave speed, \(\lambda\) (the Greek letter lambda) is the wavelength, and \(f\) is the frequency.
In any specific medium, the wave speed remains constant regardless of frequency. This constant speed creates a direct mathematical link between the wave’s two physical properties. If the frequency increases, the wavelength must decrease proportionally to maintain the same speed. Conversely, a longer wavelength corresponds to a lower frequency.
To find the wavelength from the frequency, the formula is algebraically rearranged to isolate \(\lambda\). This creates the expression \(\lambda = v / f\), showing that wavelength is the wave speed divided by its frequency.
The Critical Constant: Speed of Light
When dealing with a frequency measured in Hertz, the wave being analyzed is typically an electromagnetic wave, such as a radio wave, microwave, or visible light. These waves travel through a vacuum or air at a specific, unchanging velocity. Therefore, the general wave speed (\(v\)) in the formula is replaced by the standardized speed of light, symbolized by \(c\).
The speed of light in a vacuum is a universal constant, defined as exactly 299,792,458 meters per second. For practical calculation purposes, this value is often approximated as \(3.00 \times 10^8\) meters per second. Since Hertz is defined as cycles per second (\(1/\text{second}\)), using a speed in meters per second ensures the resulting wavelength is correctly expressed in meters.
This constant, \(c\), serves as the bridge between the time-based measurement of frequency and the distance-based measurement of wavelength. It represents the definitive velocity value for all calculations involving radio or light frequencies.
Step-by-Step Calculation Guide
The calculation to determine wavelength from frequency uses the derived formula \(\lambda = c / f\), substituting the speed of light (\(c\)) for the wave speed (\(v\)). To perform this calculation accurately, consistency in the units of measurement is paramount. The frequency must be expressed in the base unit of Hertz (\(\text{Hz}\)), and the speed of light must be in meters per second (\(\text{m/s}\)).
Converting Frequency Units
The first step is to convert the given frequency into its base \(\text{Hz}\) unit. For instance, if an FM radio station transmits at 100 megahertz (\(\text{MHz}\)), this must be converted by multiplying \(100\) by \(1,000,000\) to get \(1.00 \times 10^8\) \(\text{Hz}\).
Applying the Formula
Next, the speed of light value is entered into the numerator of the formula. Using the value of \(3.00 \times 10^8\) meters per second, the equation is set up as \(\lambda = (3.00 \times 10^8 \text{ m/s}) / (1.00 \times 10^8 \text{ Hz})\).
Final Result
Completing the calculation, \(3.00 \times 10^8\) divided by \(1.00 \times 10^8\) results in 3. The final result is 3 meters, which is the wavelength of the \(100 \text{ MHz}\) radio signal. The units cancel out correctly, as \(\text{m/s}\) divided by \(\text{Hz}\) leaves only meters (\(\text{m}\)) for the wavelength.