How to Calculate Wave Velocity

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  • 0:02 Wavelength, Velocity,…
  • 2:42 Relating the Three Quantities
  • 3:49 Free Space & Other Mediums
  • 6:26 Lesson Summary
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Lesson Transcript
Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson we explore the relationship between wavelenth, frequency and wave velocity. We also introduce the concept of velocity factor for calculating the wave velocity in mediums other than free space.

Wave Velocity, Frequency and Wavelength

Let's say we have an electromagnetic signal propagating through space. It moves like a wave with a wavelength, λ, and an oscillation frequency, f. The wavelength is the period in space (aka the spatial period) of a waveform. It's the physical distance between one point on the wave and the next corresponding point. The frequency is the number of crests that pass a certain location in a given time. The crest is the peak part of the curve. The wave velocity, v, is the velocity at which the shape of the wave propagates in space. In this lesson we calculate v based on λ and f.

You may be familiar with the idea of the period. We often use the letter T for the period. T is the time between two consecutive portions of a repeating curve. Wavelength, λ, however, is a period in space. Note the horizontal axis is labeled x. In this example, λ = 2 meters.


The wavelength
The_wavelength


Imagine sitting at a specific location on the x-axis. As the wave moves to the right, you record the height of the wave above the x-axis. At t = 0 seconds, the height is the full positive value. At t = 1 second, the wave has moved to the right but we stay put. Our observation at t = 1 second, is a height which is still positive but less than the maximum. If we continue to observe the wave height, we will see it cycle through positive, negative and back to positive values. The amount of time it takes to return to the value at t = 0 seconds is the temporal period, T.


Idea of frequency
Idea_of_frequency


The figure starts to get busy but the idea is the same. Continue making observations of the wave height from one particular location on the x-axis. In this example, it will take 8 seconds to get the same observed height we started with. Thus, the period, T, is 8 seconds. The frequency is the reciprocal of the period. Thus, f = 1/8 hertz. Note, hertz (abbreviated Hz) is 1 cycle per second.


Wave velocity
Wave_velocity


Can you visualize the wave moving to the right? See the green markings on the crest at t = 0 seconds? This same green marking has moved 2 meters for the wave at t = 8 seconds. Thus, the speed, v, is 2 meters in 8 seconds or 1/4 m in 1 second.

Relating the Three Quantities

The relationship between wave velocity, frequency and wavelength is


wave_velocity_equation


where

  • frequency, f, is measured in hertz
  • wavelength, λ, is typically measured in meters using the metric system and in feet for the English system of units
  • velocity, v, is measured in meters per second or in feet per second or in some other convenient combination of distance unit per time unit

More precisely, our equation is the speed of the wave because velocity is a vector quantity specifying direction as well as a magnitude. However, we commonly use the term wave velocity when actually we are describing the wave speed.

Note, in the example,

  • f = 1/8 Hz
  • λ = 2 m

We observed a speed of 1/4 m/sec, which agrees with

v = λ f' = 2(1/8) = 1/4 m/sec

Free Space and Other Mediums

In free space with no dielectric material to slow down the wave, the wave velocity of the electromagnetic wave is the speed of light. A dielectric is a material which supports an electric field while being a poor conductor of electricity.

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