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Consider a cavity resonator of dimensions 25 cm × 25 cm × 22 cm. (a) Calculate...
Consider a cavity resonator of dimensions 25 cm × 25 cm × 22 cm. (a) Calculate resonant frequencies for the modes with the four lowest frequencies. (b) Describe how the lowest frequency mode satisfie...
Consider a cavity resonator of dimensions 25 cm × 25 cm × 22 cm. (a) Calculate resonant frequencies for the modes with the four lowest frequencies. (b) Describe how the lowest frequency mode satisfies the electric field boundary conditions at the walls of the cavity. c) Where in the cavity does this mode have its highest intensity? Explain your reasoning.
Consider a cavity resonator of dimensions 25 cm × 25 cm × 22 cm. (a) Calculate resonant frequencies for the...
4-23. A rectangular-cavity resonator has dimensions of a -5 cm, b 2 cm, and d - 15 cm. Compute: a. The resonant frequen...
4-23. A rectangular-cavity resonator has dimensions of a -5 cm, b 2 cm, and d - 15 cm. Compute: a. The resonant frequency of the dominant mode for an air-filled cavity b. The resonant frequency of the dominant mode for a dielectric-filled cavity of , 2.56 l wish to help me in solving this question this the reference book is Microwave Devices and Circuits Third Edition SAMUEL Y. LIAO Professor of Electrical Engineering California State n University, Fresno sec 4...
2. A hollow pipe of length L and square cross-section of side a is ter- minated...
2. A hollow pipe of length L and square cross-section of side a is ter- minated by square faces of side a that are orthogonal to its length dimension which is along the z axis. The walls of the so-formed cavity are perfectly conducting, and the medium filling the cavity is lossless and with a real dielectric permittivity, e'. (a) Calculate the spatial distribution of the longitudinal component of the electric field for the various TM modes of the cavity....
A rectangular waveguide is oriented with its transverse dimensions of width a and height b in the...
A rectangular waveguide is oriented with its transverse dimensions of width a and height b in the z 0 plane, with guided modes propagating along 2. Write a MATLAB program that takes parameters a, b, frequency f (all values to be accepted in SI units), refractive index of the waveguide medium nr, mode indices m and n, and a way to choose whether to plot the TEmm or the TMmn mode fields. With the provided input parameters and the chosen...
Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the...
Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the following. (a) What are the supported mode(s) at 6 GHz? Calculate phase velocity and (b) What are the supported mode(s) at 8 GHz? Calculate phase velocity and (c) Plot the group velocity dispersion parameter β2 (-d+p) for the lowest order (d) Consider the lowest order mode supported in the rectangular waveguid<e group velocity of those mode(s) at 6GHz. group velocity of those mode(s) at...
12. A longitudinal standing wave can be created in a long, thin aluminum rod by stroking...
12. A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an open-open tube. In particular, both ends of the rod are anti-nodes. What is the fundamental frequency of a 2.50 m -long aluminum rod? The speed of sound in...
Quantum Mechanics Thank you! 2 Casimir effect We will derive the Casimir effect in three dimensions,...
Quantum Mechanics
Thank you!
2 Casimir effect We will derive the Casimir effect in three dimensions, making use of the Euler- Maclaurin formula Ž 0,F(n) – [F(n)dn = 67\2F'O) + 30 x , F"(0) -... (1) JO n=0 where On = 1 for n > 0, 0 = 1/2, and on = 0 for n < 0. (You don't need to prove this formula.) Let us consider a square box with conducting walls of length L. Let El be the...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
question 4-7 4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 H...
question 4-7
4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 Hz, and that the wave is subject to the following initial conditions: at x 0 and t = 0: y =-1 cm, and, at x = 0 and t : ar = +20 cm/s (this is the velocity of the point on the rope at horizontal...
2. Consider the following set of complex 2 x 2 matrices where i = -1: H...
2. Consider the following set of complex 2 x 2 matrices where i = -1: H = a + bi -c+dil Ic+dia-bi Put B = {1, i, j, k} where = = {[ctdie met di]|1,3,c,dex} 1-[ ), : = [=]. ; = [i -:], « =(: :] . (a) Show that H is a subspace of the real vector space of 2 x 2 matrices with entries from C, that is, show H is closed under matrix addition and multi-...
Consider a cavity resonator of dimensions 25 cm × 25 cm × 22 cm. (a) Calculate resonant frequencies for the modes with the four lowest frequencies. (b) Describe how the lowest frequency mode satisfies the electric field boundary conditions at the walls of the cavity. c) Where in the cavity does this mode have its highest intensity? Explain your reasoning.
Consider a cavity resonator of dimensions 25 cm × 25 cm × 22 cm. (a) Calculate resonant frequencies for the...
4-23. A rectangular-cavity resonator has dimensions of a -5 cm, b 2 cm, and d - 15 cm. Compute: a. The resonant frequency of the dominant mode for an air-filled cavity b. The resonant frequency of the dominant mode for a dielectric-filled cavity of , 2.56 l wish to help me in solving this question this the reference book is Microwave Devices and Circuits Third Edition SAMUEL Y. LIAO Professor of Electrical Engineering California State n University, Fresno sec 4...
2. A hollow pipe of length L and square cross-section of side a is ter- minated by square faces of side a that are orthogonal to its length dimension which is along the z axis. The walls of the so-formed cavity are perfectly conducting, and the medium filling the cavity is lossless and with a real dielectric permittivity, e'. (a) Calculate the spatial distribution of the longitudinal component of the electric field for the various TM modes of the cavity....
A rectangular waveguide is oriented with its transverse dimensions of width a and height b in the z 0 plane, with guided modes propagating along 2. Write a MATLAB program that takes parameters a, b, frequency f (all values to be accepted in SI units), refractive index of the waveguide medium nr, mode indices m and n, and a way to choose whether to plot the TEmm or the TMmn mode fields. With the provided input parameters and the chosen...
Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the following. (a) What are the supported mode(s) at 6 GHz? Calculate phase velocity and (b) What are the supported mode(s) at 8 GHz? Calculate phase velocity and (c) Plot the group velocity dispersion parameter β2 (-d+p) for the lowest order (d) Consider the lowest order mode supported in the rectangular waveguid<e group velocity of those mode(s) at 6GHz. group velocity of those mode(s) at...
Quantum Mechanics
Thank you!
2 Casimir effect We will derive the Casimir effect in three dimensions, making use of the Euler- Maclaurin formula Ž 0,F(n) – [F(n)dn = 67\2F'O) + 30 x , F"(0) -... (1) JO n=0 where On = 1 for n > 0, 0 = 1/2, and on = 0 for n < 0. (You don't need to prove this formula.) Let us consider a square box with conducting walls of length L. Let El be the...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
question 4-7
4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 Hz, and that the wave is subject to the following initial conditions: at x 0 and t = 0: y =-1 cm, and, at x = 0 and t : ar = +20 cm/s (this is the velocity of the point on the rope at horizontal...
2. Consider the following set of complex 2 x 2 matrices where i = -1: H = a + bi -c+dil Ic+dia-bi Put B = {1, i, j, k} where = = {[ctdie met di]|1,3,c,dex} 1-[ ), : = [=]. ; = [i -:], « =(: :] . (a) Show that H is a subspace of the real vector space of 2 x 2 matrices with entries from C, that is, show H is closed under matrix addition and multi-...
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