# Frequency, Polarity and Phases

## Introduction

Science is an important study. Frequency, Phase, and polarity are three important parameters in both Physics and Geophysics departments. These parameters do important work in Geophysical interpretations. They are also wave properties. This topic stands to give detail explanation of the three. When any mineral is discovered underground, they individually have their roles to play.

**Frequency**

What is frequency? It is the number of complete vibrations or cycles that a particle makes in one second. It is also equivalent to number of complete waves passing a given point in one second. The S. I unit of frequency is Hertz (Hz), which is defined as one cycle or oscillation per second. The reciprocal of period, T, is frequency. Mathematically, F = 1/T. This implies that as the frequency increases, period decreases. Again, as the period increases frequency decreases. The frequency of wave is identical to the frequency of the source that it is sent out.

Frequency as a property of wave is used in Geophysical data processing frequency or wave number (number of waveform per unit distance). In seismic data processing, we make use of sampling frequency and sampled frequency. Sampling frequency is the number of sampling points in unit time or unit distance. Intuitively, it may appear that the digital sampling of a continuous function inevitably leads to loss of information in the resultant digital function. However, there will be no loss of information as long as the sampling frequency is much higher than the highest frequency component in the sample function. Mathematically, it can be proved that if the waveform is a sine curve, this can always be reconstructed provided that there is minimum of two samples per period of the sine wave. Thus if a waveform is sampled every two milliseconds (sampling interval), the sampling frequency is 500 sample per second (or 500Hz). Sampling at this rate will preserve all frequencies up to 250 Hz in the sample function. This frequency of half the sampling frequency is Nyquist frequency (F_{N}) and the Nyquist interval is the frequency range from zero up to F_{N}.

F_{N} = 1/(2Δt), where Δt = sampling interval.

The resolution of subsurface structure depends on the frequency spectrum of the source. The broader the frequency range and the higher the upper frequency, better the resolution power.

**Polarity**

Poles are found at the two ends of a bar magnet, which is positive at one end and negative at the other end. Two like poles repels each other while two unlike poles get attracted to each other.

## Field Lines

There are Geographic poles and Magnetic poles. The most important type of magnetic field and also the dominant component of the Geomagnetic field is that of a magnetic dipole. This is the field of two magnetic poles opposite to each other.

In the study of Geophysics, the polarity can be called geomagnetic polarity. There had been a lot of arguments by many scientists on the reality of the polarity. It is a rare phenomenon. It has been described in lavas in which ferromagnetic minerals are particular forms of titanohematite.

A change of polarity from one sense to the opposite one is called a polarity transition. Paleomagnetic records of polarity transitions have been observed in radiometrically dated lava sequences in a deep-sea sediments with known deposition rates (Fundamentals of Geophysics by William Lowrie). Nobody is completely sure on how geomagnetic field behave during polarity transmission. The irregular pattern of polarity intervals in any sequence provides a kind of geological fingerprint which can be used under favourable circumstances to date and correlate some types of sedimentary rocks.

## Coulomb’s Law of Magnetic Poles

Coulomb’s established that the force between the ends of long thin magnets is inversely proportional to the square of their separation. Gauss expanded Coulomb’s observation and attributed the force of attraction and repulsion to fictitious magnet charges or poles.

**The Field of a Magnetic Pole**

Magnetic poles do not really exist. Nevertheless, many magnetic properties can be described and magnetic problems solved in terms of fictitious poles. A magnetic field B as the force exerted by a pole of strength, P, on a unit pole at a distance, r.

**B = K p/r ^{2}**

**The Magnetic Dipoles**

In fig 1b, the line joining the positive and negative poles (the normal to the plane of the loop or the direction of magnetization of the sphere) defines an axis about which the field has rotational symmetry. Let two equal and opposite poles, +p and –p, be located at a distance, d, apart. The potential, W, at a distance, r, from the midpoint of the pair of poles in a direction that makes an angle, θ, to the axis is the sum of the potentials of the positive and negative poles at the point (r, θ) the distance from the respective poles, r_{+ }and r_{-}.

**Phase**

When do we say that particles are in phase? Particles which are at the same vertical distances from their positions of vertical distances from their positions of rest and are moving in the same direction as shown on the graph, are said to be in phase i.e particle A and B are in phase.

Phase in sinusoidal functions or in waves has two different, but closely related meanings. One is the initial angle of sinusoidal functions at its origin and is sometimes called phase offset or phase difference. Another usage of phase is in the fraction of the wave which has elapsed relative to the origin.

The phase of an oscillation or wave refers to a sinusoidal function such as the following:

X (t) = A Cos (2πft + φ)

Y (t) = A Sin (2πft + φ), where A, f, and φ are constant parameters called amplitude, frequency and phase of the sinusoid respectively.

Phase difference is the difference expressed in electrical degrees or time between two waves having the same frequency and referenced to the same point in time. Two oscillations that have the same frequency and no phase difference are said to be in phase. Two oscillations that have the same frequency and different phases have a phase difference and the oscillations are said to be out of phase with each other. The amount at which such oscillations are out of phase with each other can be expressed in degrees from 0^{0 }to 360^{0 }or in radian from 0 to 2π. If the phase difference is 180^{0} (π in radian), the two oscillations are said to be in anti-phase.

**Phases on a Seismogram **

The seismogram of a distant earthquake contains the arrivals of numerous seismic waves that have travelled along different path through the earth from source to the receiver. Each event that is recorded in the seismogram is referred to as a phase.

**Conclusion **

The topic discussed is very important in the area of science. You cannot effective discuss anything on wave without mentioning the terms explained above. These terms are phase, frequency, and polarity. They were broken into other subheadings for in-depth writing and explanations.

## References

- Fundamentals of Geophysics by William Lowrie
- New School Physics by M. W Anyakoha

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

**© 2014 Okwuagbala Uzochukwu Mike P**

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