sine wave equation physics Sine waves occur often in physics including wind waves sound waves and light waves such as monochromatic radiation In engineering signal processing and mathematics Fourier analysis decomposes general functions into a sum of sine waves of various frequencies relative phases and magnitudes
Physicists actually like to write the equation for a sine wave in a slightly simpler form Defining the wavenumber as k 2 pi lambda and the angular frequency as omega 2 pi T we write h x t h 0 sin k x omega t label 1 4 Combining the dependencies on space and time in a single expression we can write for the sinusoidal wave u x t A cos k x omega t label 9 1 Figure PageIndex 1 Two basic types of waves
sine wave equation physics
sine wave equation physics
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Definition A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation A sine wave is a continuous wave It is named after the trigonometric function sine of which it is the graph It occurs often in both pure and applied mathematics as well as physics engineering signal processing and many other fields Section 14 1 Sinusoidal Waves When a string is shaken sinusoidally i e it is vibrated such that the oscillations are sine or cosine function of time the wave propagated in the string also has sinusoidal shape as illustrated in Figure 14 1 1
To find the amplitude wavelength period and frequency of a sinusoidal wave write down the wave function in the form y x t Asin kx t y x t A sin k x t The amplitude can be read straight from the equation and is equal to A The mathematical equation of a standing wave is y x t sin 2 x cos 2 ft The shape term sin 2 x describes the sinusoidal shape of the wave pattern of wavelength The flip flop term cos 2 ft describes the up down oscillatory motion
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Let sine enter your mental toolbox Hrm I need a formula to make smooth changes Eventually we ll understand the foundations intuitively e pi radians imaginaries sine and they can be mixed into a scrumptious math salad We have seen that the wave equation is solved by the d Alembert solution y x t f x ct g x ct A particularly interesting option for f u and g v are sines and
The above equation is known as the wave equation It states the mathematical relationship between the speed v of a wave and its wavelength and frequency f Using the symbols v and f the equation can be rewritten as v f A simple example to prove this is a square waveform It s not common in mechanics but it plays a big role in circuits for computation The equation is A times sign sin omega t where the sign function is self explanatory There s nothing sine like about the wave but we still see sin
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sine wave equation physics - The mathematical equation of a standing wave is y x t sin 2 x cos 2 ft The shape term sin 2 x describes the sinusoidal shape of the wave pattern of wavelength The flip flop term cos 2 ft describes the up down oscillatory motion