Graph of the Frequency(Wavelength) Relationship

In summary, the conversation is about the relationship between frequency and wavelength, which is described as being inversely exponential. The person is confused about why the relationship is not instead inversely linear and asks for clarification without using calculus. The discussion also mentions the equation v=ƒλ and explains how it relates to an inverse exponential function. It is noted that exponential functions can also be written as 1/x^n.
  • #1
tenbee
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Homework Statement



A practice problem showed the relationship between frequency and wavelength to be inversely exponential. I don't understand why is the graphical relationship is not [instead] inversely linear. What concept am I missing? (No calculus please... I'd be clueless :biggrin:).

Homework Equations



v = ƒ[itex]\lambda[/itex]

The Attempt at a Solution



Reading my textbook to no avail.
 
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  • #2
What do you mean by inversely linear? If you express frequency in terms of wavelength, for example, you get an inverse exponential function (i.e. variable is in the denominator).

[itex]f=\frac{v}{\lambda}[/itex]
 
  • #3
http://en.wikipedia.org/wiki/Exponential_function"

how is it exponential function then?

OP is right.
it is inversely proportional function (or inversely linear)
 
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  • #4
Exponential functions could also be referring to functions of the from

[itex]y=\large\frac{1}{x^{n}}[/itex]
 
  • #5


The graphical relationship between frequency and wavelength is not inversely linear because it is based on the fundamental equation v = ƒλ, where v represents the speed of light. This equation shows that as the frequency increases, the wavelength decreases, but not in a linear fashion. The inverse exponential relationship is a result of the mathematical relationship between frequency and wavelength. This concept is known as the wave-particle duality, where light behaves both as a wave and a particle. In order to fully understand this concept, a deeper understanding of calculus and quantum mechanics may be necessary. However, for practical purposes, it is sufficient to know that the frequency-wavelength relationship is not linear and is fundamental to the behavior of light.
 

FAQ: Graph of the Frequency(Wavelength) Relationship

What is a graph of the frequency-wavelength relationship?

A graph of the frequency-wavelength relationship, also known as a graph of the electromagnetic spectrum, is a visual representation of the different types of electromagnetic radiation and their corresponding wavelengths and frequencies. It shows the relationship between wavelength and frequency, with longer wavelengths having lower frequencies and shorter wavelengths having higher frequencies.

How is the frequency-wavelength relationship determined?

The frequency-wavelength relationship is determined by the speed of light, which is a constant at approximately 299,792,458 meters per second. This means that the product of the wavelength and frequency of an electromagnetic wave will always equal the speed of light. In other words, as the wavelength increases, the frequency decreases, and vice versa.

What are the different types of electromagnetic radiation shown on the frequency-wavelength graph?

The frequency-wavelength graph shows the entire electromagnetic spectrum, which includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Each type of radiation has a specific wavelength and frequency that determines its position on the graph.

How is the frequency-wavelength graph useful?

The frequency-wavelength graph is useful for understanding the properties and behaviors of electromagnetic radiation. It helps scientists and engineers to categorize and study different types of radiation, as well as to determine how they interact with matter.

Can the frequency-wavelength relationship be applied to other types of waves?

Yes, the frequency-wavelength relationship can be applied to other types of waves, such as sound waves and water waves. In these cases, the speed of the wave would be determined by the medium it is traveling through rather than the speed of light. However, the concept of longer wavelengths having lower frequencies and vice versa still applies.

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