# Fourier Series and Absorption Questions?

• arianna1012
In summary, the conversation discusses the use and application of Fourier series with different types of waves, including sound and light waves. The speaker also inquires about the measurement of absorption and penetration of waves through materials. It is noted that a Fourier transformation can be applied to nearly any function on the real axis, and while recording sound waves is possible, it is not feasible for visible light due to its high frequency. To measure absorption and penetration, one can direct waves onto a material and measure the amount going through multiple times with varying thickness.
arianna1012
Sorry if I am posting in the wrong place.

I'm really interested in the Fourier series, but I'm not an expert on it yet. I am very well aware yoy can do it with sound waves, but can you manipulate any other waves? What about light waves?

And for absorption, how can you measure the absorption of light/sound waves of a material? Or better yet, how can you measure the amount of penetration through a material of light/sound waves?

You can do a Fourier transformation on nearly (!) every function defined on the real axis, or even defined in a multidimensional space.
Visible light oscillates so fast that you cannot record it in the same way you can record sound, but with longer wavelengths (and therefore lower frequencies) this is possible.

And for absorption, how can you measure the absorption of light/sound waves of a material? Or better yet, how can you measure the amount of penetration through a material of light/sound waves?
Direct sound / light onto the material, measure the amount going through, do the measurement multiple times with variable thickness of the material.

## 1. What is a Fourier series?

A Fourier series is a mathematical tool used to represent a periodic function as a sum of sine and cosine functions. It is named after the French mathematician Joseph Fourier who introduced the concept in the early 19th century.

## 2. How is a Fourier series used in science?

Fourier series are commonly used in many fields of science, including physics, engineering, and signal processing. They are used to analyze and approximate a wide range of periodic phenomena, such as sound waves, electromagnetic waves, and vibrations.

## 3. What is the difference between a Fourier series and a Fourier transform?

A Fourier series is used to represent a periodic function as a sum of sine and cosine functions, while a Fourier transform is used to represent a non-periodic function as a combination of sinusoidal functions with varying frequencies.

## 4. What is absorption and how does it relate to Fourier series?

Absorption is a process in which energy, such as light or sound, is absorbed by a material. In the context of Fourier series, absorption is related to the coefficient of absorption, which is a measure of how much energy is absorbed by a material at a given frequency. This coefficient can be represented as a term in the Fourier series for a material's absorption spectrum.

## 5. How does the number of terms in a Fourier series affect its accuracy?

The more terms included in a Fourier series, the more accurate the representation of the original function will be. However, including too many terms can lead to overfitting and loss of generalizability. The number of terms needed for a desired level of accuracy depends on the complexity of the function being represented.

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