physics terms?

Question

can somone explain these terms in plain english?
1.harmonics
2.Fourier synthesis
3.Fourier's theorem
4.periodicity
5.fundamental frequency
6.resonance
7.Fourier analysis

Answer 1

In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For a sine wave, it is an integer multiple of the frequency of the wave. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.

Fourier analysis, named after Joseph Fourier's introduction of the Fourier series, is the decomposition of a function in terms of a sum of sinusoidal basis functions (vs. their frequencies) that can be recombined to obtain the original function. That process of recombining the sinusoidal basis functions is also called Fourier synthesis (in which case Fourier analysis refers specifically to the decomposition process).

In mathematics, the Fourier theorem is a theorem stating that a periodic function f(x), which is reasonably continuous, may be expressed as the sum of a series of sine and cosine terms (called the Fourier series), each of which has specific amplitude and phase coefficients known as Fourier coefficients. The theorem was developed by the French mathematician J.B. Fourier around 1800.

Periodicity is the quality of occurring at regular intervals (e.g. of time) and can occur in different contexts:

A clock marks time at periodic intervals.
A metronome ticks at periodic intervals.
A publication published at periodic intervals can be called a "periodical", though it can also be called magazine.
In mathematics, a function whose output contains values that repeat periodically is called periodic function.
In chemistry, a table which classifies elements by means of periodicity is the periodic table.
In physics, period is the number of cycles as a result of time (time/cycle). The amount of time it takes to complete one full revolution. Period is also the inverse of frequency.
In music theory, periodicity is described as "predictability gives rise to expectations".

The fundamental tone, often referred to simply as the fundamental, is the lowest frequency in a harmonic series.

The fundamental frequency (also called a fundamental) of a periodic signal is the inverse of the pitch period length. The pitch period is, in turn, the smallest repeating unit of a signal. One pitch period thus describes the periodic signal completely.

In physics, resonance is the tendency of a system to oscillate with high amplitude when excited by energy at a certain frequency. This frequency is known as the system's natural frequency of vibration or resonant frequency.

Fourier analysis, named after Joseph Fourier's introduction of the Fourier series, is the decomposition of a function in terms of a sum of sinusoidal basis functions (vs. their frequencies) that can be recombined to obtain the original function. That process of recombining the sinusoidal basis functions is also called Fourier synthesis (in which case Fourier analysis refers specifically to the decomposition process).

Answer 2

Fourier Synthesis
A periodic signal can be described by a Fourier decomposition as a Fourier series, i. e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal wave


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Answer 3

The answer is MAN is lazy and smart.

So, he decides to find a way to explain event in terms of some basic events and apply easy maths on basic events and thus the complete event - and nature comes to help.

Its like any word of english is a combination of known baisc alphabets. So, any signal, or wave, or event is a combination of the FOURIER alphabets. Only, we need infinite number of FOURIER alphabets to explain each event. But, the good news is that each new alphabet is integral multiple of the one basic alphabet.

With this brief jargon, now, the basic events are just sine and cos of some frequencies. The most basic frequency( ie the least frequency component) is the FUNDAMNETAL FREQUENCY.
All other sines and cosines are on m x Fundamental frequency, where m is integer from 2 to infinity ( m=1 is the basic mode itself). All these Multiples of Funadamental frequency are called HArmonics.
The Trick of representing any event in terms of sine and cosine of infinite mulitples of one basic frequency is Fourier's theorem. To put an event in terms of sines and cosines is Analysis.
Now to see what happens to an event in given circumstances, we need to represent it as sum of sines and cosines of multiples of frequency....analyse what happens to these simple mathematical events in these circumstances( analysing for a general term is sufficient ... then putting in the value of m gives result for each term)----and finally add them up just in the manner u split them up---this gives us the accurate picture of what would happen to our initial event.This is Synthesis
Of course, because we are having all frequencies as multiple of one frequency...that frequency also determines the periodicity(1/f).
The last term not explained is RESONANCE. In most simple words, resonance is a case in which the fundamnetal frequency component is strongest....ie, in the analysis...the magnitude of coefficient of fundamnetal frequency is highest (ideally everythng else will be zero)
This was mathematical insight, practically, resonance occurs when a system is doing only what it is supposed to do and nothing else...ie a resonating inductor will not dissipate energy or store it as electrical charge, a resistor will only dissipate and a capacitor will store only electrical energy....thus each providing its best efficiency

Answer 4

Terminal velocity is the maximum velocity a falling body can reach. This limitation is due to air resistance. Initial velocity is the velocity that a value has when the problem starts.