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Data

A power spectrum provides information about how much of the power of a given signal falls within a given frequency. In other words, the power spectrum determines the strength of each note. So the power spectrum is similar to the display on a graphic equalizer.


To reconstruct the sound of the little bang we first determined the power spectrum at the last moment of the collision from the STAR correlations data. Just like the sound at any moment of a song is made up of the sum a number of frequencies, the correlations can represented as how much power is present in different frequencies. The figure shows how the correlation taken from a slice of the data (at zero separation in rapidity) can be reproduced by adding up a sequence of different wavelengths or frequencies.


The power spectrum is then related to the amplitude required at each frequency such that the sum of the frequencies recreates the correlations. A French Mathematician and Physicists born in 1768, Joseph Fourier was the first to think up the idea of representing complicated shapes in terms of a series of simple sine or cosine waves with integer values of frequency. This is called a Fourier Series. And  piece of info for your trivia night out: Fourier was also the first to discover the greenhouse effect. The process of transforming a function of some variable into the summation of different frequencies is called a Fourier Transform. The power spectrum below is the Fourier transform of the correlations above. It tells us what notes are present and at what strength in the final sound.

Power Spectrum
Speed of Sound
Acoustic Horizon
The Sound