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Phase refers to the argument of a sine or cosine function in a wave equation and depends on position and time, while the phase constant is determined by initial conditions. The phase difference between two points on a wave is the difference between their phases and is equal to the product of the wavenumber and their distance separation. If this distance separation is an integer multiple of the wavelength, the phases are in phase, but if it is an odd half-integer multiple, the phases are out of phase.
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Physics 2 notes: WAVES ONLY- Notes on the difference between longitudinal, t...
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The document discusses phase and phase difference in waves. It defines phase as being dependent on position and time, represented by the Greek symbol φ in the equation D(x,t) = Asin(kx±ωt+φ). Phase difference is the difference in phase between two positions at the same time. Points an integer number of wavelengths apart are in phase, while half-integer wavelengths apart are out of phase. The equation for phase difference is derived as ∆Φ=k(x2-x1).
Standing waves
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Properties of dft
The document summarizes key properties of the discrete Fourier transform (DFT). It describes linearity, periodicity, time/frequency shifts, conjugation, multiplication, convolution, correlation, and Parseval's theorem. Linearity means the DFT of a linear combination of signals is the linear combination of the DFTs. Periodicity means an N-point DFT is periodic with N samples. Shifts change the time or frequency domain representation. Multiplication in the time domain is convolution in the frequency domain. Correlation relates the time and frequency domain representations. Parseval's theorem relates the energy in the time and frequency domains.
Coincidence points for mappings under generalized contraction
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PaperNo8-HabibiSafari-IJAM-CHAOTICITY OF A PAIR OF OPERATORS
This document summarizes research on chaotic pairs of operators on Frechet spaces. It defines key concepts such as hypercyclic pairs and chaotic pairs of operators. The main results proven are:
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Phase refers to the position of a wave in terms of where it starts and crosses the x-axis, measured in radians. Phase difference is the difference between the phases of two points on a wave. If two points have a phase difference of π/2 radians and a wavelength of 20 cm, the distance between points (Δx) is 5 cm. Therefore, in a distance of 6 m there will be 120 points with a phase difference of π/2 between consecutive points.
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Jeremy soroka lo 1
- 2. What is a phase? Phase is the argument of the sine (or cosine) function and is usually given by Φ So for the equation: sin(kx+ωt+ɸ) kx+ωt+ɸ is the phase AND ɸ is the phase constant
- 3. Important Differences ɸ (phase constant) is not the same as Φ (phase) Phase is a variable that is dependant on position and time The phase constant is a constant determined by the initial conditions
- 4. Phase Difference ● The difference between two points (X1 and X2) that are a distance apart (ΔX) at the same time ● Denoted as ΔΦ
- 5. so: ΔΦ = phase of wave at X2 - phase of wave at X1 = (kX2+ωt+ɸ) - (kX1+ωt+ɸ) = k(X2 - X1) = kΔX = (2ᴨ/ƛ)(Δx)
- 6. If ΔX is an integer multiple of wavelengths apart (such as 2ƛ, 3ƛ, etc.), there is a phase difference of an even multiple of pi (such as 2ᴨ, 4ᴨ, …) and the two phases are IN PHASE with each other
- 7. Phase of the wave at X2 (red) - Phase of the wave at X1(black) = ƛ (an integer multiple) Notice that they have equal displacements
- 8. If ΔX is an odd half-integer multiple of wavelength apart (such as 0.5ƛ, 2.5ƛ, etc.) there is a phase difference of an odd multiple of pi (such as 3ᴨ, 5ᴨ, …) and the two phases are OUT OF PHASE with each other
- 9. Phase of the wave at X2 (red) - Phase of the wave at X1(black) = ƛ/2 (an odd half integer multiple) Notice that they have equal displacements in opposite directions