How to Calculate Wavelength: Lesson & Quiz

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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.

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).

Wavelength Calculation Examples

Find the wavelength of the radio waves produced by an AM radio station transmitting at 770 kHz.

The AM radio station is transmitting radio waves into the air. Electromagnetic waves travel through air at approximately the speed of light in a vacuum. The speed of light in a vacuum is approximately 300,000,000 m/s. Therefore, we have lambda = 300,000,000/770,000 = 390 m

The Middle C musical note has a frequency of 261.6 Hz. Calculate the wavelength of the sound of the A note in air at room temperature. The speed of sound in air at room temperature is approximately 344 m/s. So:

lambda = 344/261.6 = 1.31 m

Lesson Summary

Wavelength is an important parameter of waves and is the distance between two like points on the wave such as between two adjacent peaks or two adjacent valleys. The wavelength is calculated from the wave speed and frequency by lambda = wave speed/frequency. The wave speed depends on the medium in which the wave propagates. As wavelength increases, frequency decreases, and as frequency increases, wavelength decreases.

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