Relationship between frequency and period

The period of a function (voltage versus time, for instance) shows the interval (on time axes) between the points where a given dependence repeats its value. Frequency (f ) on the other hand shows how many times a function attains the same value in a given interval of time. It is apparent that frequency is equal to the reciprocal of the period f =1/T, and is a measure of the periodicity of the function.

There is also angular frequency w = 2p/T = 2pf which is essentially the (linear) frequency f normalized to the frequency of the harmonic (sin, cos) functions, that is equal to 1/2p.

If the basis translations of the real lattice are compared to the period, the basis translation of the reciprocal lattice can be compared to the frequency. The real crystal lattice represents a three-dimensional periodic function (of atomic density versus distance for instance). Therefore the reciprocal lattice is a "three-dimensional frequency" of that function. It reveals the periodicity of real lattice. Therefore if d is the interplanar distance (period of atomic density function ), then 1/d is the analog of linear frequency while 2p/d is the analog of angular frequency.

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