# Algebraic relationship that relates wavelength and frequency

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There is a mathematical relationship between the frequency (f) of the wave From the pattern and knowledge of the length of the medium, the wavelength can be is simply the algebraic sum of the displacements that the particle would have. Calculate the frequency of a sine or cosine wave. . Frequency is a measurement that is closely related to period. .. were given the frequency and asked to find the period using the following relationship: Where is the frequency and is the period. With just a little bit of algebra, we can transform this formula and solve it for. Students will discover and verify the relationship between Wavelength and Frequency Students should have had some Pre-Algebra, especially in the areas of.

Cut the tape off of the roll leaving about 20 cm space between "End" and where you cut. Materials Manager should use the colored pencils to draw three evenly spaced horizontal lines along the tape from Start to End. Make the top line red, the middle line green and the bottom line violet to represent three different colors in the spectrum of light.

He or she may also share in the completion of the tasks. Recorder should divide the red line every 14 cm with dark marks in red pencil. The green line should be divided every 10 cm and the violet every 8 cm. The marks that you make on the three color lines will represent the different wavelengths of the different colors of light.

## What's the Frequency, Roy G. Biv?

The true wavelengths are actually measured in terms of angstroms. An angstrom is cm or 0. Red has a wavelength of angstroms, green has a wavelength of angstroms and violet has a wavelength of angstroms. The speed or velocity of a wave is defined as the distance a crest on the wave travels per unit of time. Like the speed of a runner or a car, wave speed v is simply the ratio of the distance d traveled per time of travel t as shown by the following equation.

And then imagine that a snapshot could be taken at an instant in time, thus freezing the motion of the wave and providing a picture of the shape of the medium. The result would be a diagram similar to that below of course, without all the labels. The labels have been added to indicate a few strategic points. The dashed line which stretches horizontally across the middle of the pattern is known as the rest position.

### Wavelength Formula

The points labeled crests are at the points of maximum displacement above the rest position; the troughs are at the points of maximum displacement below the rest position. The vertical distance from a crest to the rest position is known as the amplitude.

- What is the mathematical relationship between wavelength and frequency?
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And the horizontal distance stretching between any two adjacent crests or between adjacent troughs is known as the wavelength. A more detailed and exhaustive discussion of the anatomy of a wave can be found at The Physics Classroom Tutorial. Standing Wave Pattern Analysis When a wave is introduced into a medium such as a rope or a snakey, it travels the length of the medium and then reflects back upon reaching the end of the medium. At certain frequencies, the reflected portion of the wave meets up with the original wave to create a pattern known as a standing wave pattern.

In a standing wave pattern there are points along the medium which appear as if they are always standing still. These points are known as nodes and are easily remembered as the points of no displacement. There is always an antinode positioned between two adjacent nodes.

Antinodes are points of maximum positive and negative displacement. In such standing wave patterns, there is a unique half-number relationship between the length of the medium and the wavelength of the waves which have established the pattern which is present in the medium.

These relationships are shown below for the standing wave patterns having one node first harmonictwo nodes second harmonic and three nodes third harmonic. Other patterns for four nodes and more could be drawn by simply extending the principles which have been used for the first three patterns. From the pattern and knowledge of the length of the medium, the wavelength can be determined using the above equations.

Similarly, the length of the medium can be determined from the wavelength. A more detailed and exhaustive discussion of the mathematics of standing wave patterns can be found at The Physics Classroom Tutorial.

Wave Interference The meeting up of two waves while traveling in opposite directions along the same medium is known as interference. When two waves interfere, the medium takes on a new resultant shape which reflects the simultaneous influence of both waves upon the particles of the medium.

This means a three with eight zeros behind it, i. Again this is just a label, or shorthand, in order to allow us to work quickly with the equation. Wavelengths are usually measured in metres.

### Speed, Frequency and Wavelength - How they are related, with examples

Providing we know any two of the three quantities we can find the other one, either directly or by rearranging the equation. The next section solves the equation as it is, and there is a calculator for frequency, wavelength and speed here. Solving the Equation In this example we will consider the frequency of radio waves. Radio waves are just another form of "light", i.

Let's say we have a radio with a dial that is only marked in MHz. This is a measurement of frequency and we note that 1 MHz is the same as 1 million hertz the M in MHz stands for " mega ", which means million.

We are told of a radio broadcast we want to hear but we are only given the wavelength of the station and not the frequency. The wavelength we are given is 3.