Consider a traveling wave having the amplitude (A) and phase (φ) of A= 10 , φ=π/4 at x1= 2 and A =5, φ=π/3 at x1=3. Find the attenuation constant (α), wavenumber (β), and initial phase (0φ).
Consider a traveling wave having the amplitude (A) and phase (φ) of A= 10 , φ=π/4...
Two waves having the same frequency, wavelength, and amplitude are traveling in the same direction. If they differ in phase by π/2 and each has an amplitude of 0.060 m, what is the amplitude of the resultant wave? cm
2A uniform electromagnetic plane wave is normally incident norm the air region (medium #1 with intrinsic medium (medium #2 with intrinsic k,- and wavenumber k ) upon the planar interface separating air from a lossy dielectric impedance 'h-%(I + J) and wavenumber (1-)).The incident plane wave in air has a phasor electric field given by 2. Find (leave all answers in terms ofm: (a) value of the wavenumber in air, ko (b) attenuation constant α and phase constant β (c)...
Consider phase A winding only of a 3-Φ AC machine with one winding per phase. The mmf it produces is given by the expression F = Fmcos(θa), where Fm = (4/π)⋅(N/2)⋅i. Show that when the winding is excited by a sinusoidal current i = Iacos(ωt), it generates two travelling waves. In which direction does each wave travel?
2. (a) State, without proof, the compound angle formulae for sin(a + β) and sin(α-β). 2 marks (b) Let θ be a fixed real number with 0 < θ < π. Show that, for all real x, sin(z+θ)- sin(z-Asin(z + φ) where φ (π + θ)/2 and A-2 sin(θ/2) (Hint: use part (a) above). 10 marks] (c) Determine φ if A = V2 and if A = V3. [9 marks] The physical interpretation of the result in part (b) above...
Example: er a wave of frequency 1 MHz incident on seawater, having conductivity of 4 S/m, and relative permittivity of 81. Find: The skin depth Phase velocity Attenuation constant Propagation constant
Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m)....
Problem 2.6 Although the overall phase constant of the wave function is of no physical significance (it cancels out whenever you calculate a measurable quantity), the relative phase of the coefficients in Equation 2.17 does matter. For example, suppose we change the relative phase of ψι and in Problem 2.5: where ф įs some constant. Find ų,(x,t), Ux.t)12, and (x), and compare your results with what you got before. Study the special cases φ = π/2 and φ = π....
Consider a vertically incoming (incident) P-wave striking a
horizontally stratified earth (Fig. 2). The amplitude of the
transmitted P-wave at the top boundary of layer 1 is 1 (don’t worry
about units for amplitude). What is the amplitude of the P-wave
reflected from the boundary between layers 3 and 4? What is the
amplitude of the P-wave transmitted into layer 4? What are the
amplitudes of the corresponding S-waves? Express amplitudes in
relative terms (relative to the amplitude of the...
For the wave function Ψ(x) = ((α/π)^ 1/4) * exp((−αx^2) /2) a) Calculate <x> ) Calculate <x^2> c) Calculate φ(p) and <p>
Problem 1 Ho and&r9. A 25-MHz uniform plane wave is traveling in a nonmagnetic medium with Find: 1. 2. 3. 4. The phase velocity, the wavenumber, the wavelength in the medium, the intrinsic impedance of the medium.