How to Calculate Wavelength: Lesson & Quiz

Instructor: Thomas Zesiger

Thomas has taught electronics and communications engineering, math, and physics and has a master's degree in electrical engineering.

Discover practical examples of waves and the significance of wavelength. Learn the relationship of wavelength, frequency, and wave speed and how to calculate wavelength based on these parameters.

We also recommend watching Wave Parameters: Wavelength, Amplitude, Period, Frequency & Speed and Transverse & Longitudinal Waves: Definition & Examples

Explanation of Wavelength

Ripples in water, sound traveling in air, and coordinated vibrations of objects are examples of waves you have probably encountered in your life. A good way to visualize a wave is to insert the end of a pencil into a container of still water. The surface of the water is disturbed, producing ripples, or waves.

Ripples in disturbed water

Electromagnetic waves are special waves such as light, radio waves, microwaves, and x-rays that do not require a medium for propagation. We cannot see or hear these waves, but they exist in nature and in many of the products we use every day.

Regardless of the kind, every wave has a wavelength. Wavelength is the distance between two successive like points on a wave. Some examples are the distance between two adjacent peaks or two adjacent valleys. A peak is the highest point of a wave and a valley is the lowest point. Stated another way, wavelength is the time required to complete one full cycle of the wave.

Example of wavelength from peak-to-peak

Wavelength depends on two other important parameters: wave speed and frequency. The wave speed is the rate at which the wave moves through the medium of propagation and it is dependent upon the medium of propagation. For example, the water ripples previously mentioned travel through the water. Electromagnetic waves usually travel through the air, as do sound waves. Vibrations on a piano string travel through the string. The wave speed is different for all of these because the medium in which the wave propagates is different.

The frequency is the number of wave cycles passing a point per unit time. Stated another way, it is the number of oscillations per second in the wave. A higher frequency means a shorter wavelength and a shorter wavelength means a higher frequency. This leads us to the relationship between wave speed, frequency, and wavelength.

Relationship of wavelength and frequency

How to Calculate Wavelength

Stated in words, the speed of the wave equals the number of cycles passing a point each second multiplied by the cycle length.

Mathematically stated: wave speed = cycles per second x cycle length

Wave speed, frequency (cycles per second), and wavelength (cycle length) are usually represented with the variables v, f, and the Greek letter lambda respectively. Solving for lambda, the equation becomes lambda = v/f.

Wavelength equation with Greek letter lambda

Wave speed has units of distance per unit time. For example, meters per second or m/s. Frequency has units of Hz. Wavelength is measured in units of distance, usually meters (m).

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A long range early warning radar system used for air defense operates at a frequency of 126 MHz (126,000,000 Hz). What is the wavelength of the electrical oscillations in the radar system?

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Wavelength is calculated by wave speed/frequency. Wave speed of electromagnetic waves in air is 300,000,000 m/s. Therefore, wavelength of electromagnetic wave in air at 126,000 Hz is 300,000,000/126,000 = 2.38 meters.
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