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A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are
- a)0.5 x 1012Hz
- b)6 x 1015Hz
- c)8 x 1014Hz
- d)1 x 1013Hz
Correct answer is option 'A,B,C,D'. Can you explain this answer?
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Most Upvoted Answer
A waveguide consists of two infinite parallel plates (perfect conduct...
Solution:
Given parameters are:
Separation between the plates, d = 10-4 cm = 10-6 m
Speed of light in air, c = 3x108 m/s
We need to calculate the frequency/frequencies of TM waves which can propagate in this waveguide.
TM waves in a waveguide:
TM waves are transverse magnetic waves in which the electric field is perpendicular to the direction of propagation and the magnetic field is parallel to the direction of propagation.
In a waveguide, TM waves have a cutoff frequency below which they cannot propagate. The cutoff frequency depends on the dimensions of the waveguide and the mode of propagation.
The cutoff frequency for the TE10 mode in a rectangular waveguide of width a and height b is given by:
fc = c/2*(a/π) * (b/π) * (m2 + n2)0.5
where m and n are integers and determine the mode of propagation.
For TM waves, the cutoff frequency is given by:
fc = c/2*(a/π) * (b/π) * (m2 + n2 + 1)0.5
where m and n are integers and determine the mode of propagation.
Frequency range for TM waves in the given waveguide:
The waveguide in this problem has two parallel plates of infinite width, so we can assume that a = ∞.
The only dimension that matters is the separation between the plates, d.
For the TM mode, m and n are both integers and determine the number of half-wavelengths of the electric and magnetic fields in the x and y directions, respectively.
The lowest frequency that can propagate in the waveguide is for the TM01 mode, which has one half-wavelength in the y direction and no half-wavelengths in the x direction.
So, for the TM01 mode, m = 0 and n = 1, and the cutoff frequency is:
fc = c/2*(d/π)
Substituting the given values, we get:
fc = 3x108 / 2*(10-6/π) = 1.209x1012 Hz
This is the cutoff frequency for the TM01 mode.
Higher modes will have higher cutoff frequencies, given by the same formula with larger values of m and n.
The given answer options are:
A) 0.5x1012 Hz
B) 6x1015 Hz
C) 8x1014 Hz
D) 1x1013 Hz
All these options are within the frequency range of TM waves that can propagate in the given waveguide.
Therefore, the correct answer is A, B, C, and D.
Given parameters are:
Separation between the plates, d = 10-4 cm = 10-6 m
Speed of light in air, c = 3x108 m/s
We need to calculate the frequency/frequencies of TM waves which can propagate in this waveguide.
TM waves in a waveguide:
TM waves are transverse magnetic waves in which the electric field is perpendicular to the direction of propagation and the magnetic field is parallel to the direction of propagation.
In a waveguide, TM waves have a cutoff frequency below which they cannot propagate. The cutoff frequency depends on the dimensions of the waveguide and the mode of propagation.
The cutoff frequency for the TE10 mode in a rectangular waveguide of width a and height b is given by:
fc = c/2*(a/π) * (b/π) * (m2 + n2)0.5
where m and n are integers and determine the mode of propagation.
For TM waves, the cutoff frequency is given by:
fc = c/2*(a/π) * (b/π) * (m2 + n2 + 1)0.5
where m and n are integers and determine the mode of propagation.
Frequency range for TM waves in the given waveguide:
The waveguide in this problem has two parallel plates of infinite width, so we can assume that a = ∞.
The only dimension that matters is the separation between the plates, d.
For the TM mode, m and n are both integers and determine the number of half-wavelengths of the electric and magnetic fields in the x and y directions, respectively.
The lowest frequency that can propagate in the waveguide is for the TM01 mode, which has one half-wavelength in the y direction and no half-wavelengths in the x direction.
So, for the TM01 mode, m = 0 and n = 1, and the cutoff frequency is:
fc = c/2*(d/π)
Substituting the given values, we get:
fc = 3x108 / 2*(10-6/π) = 1.209x1012 Hz
This is the cutoff frequency for the TM01 mode.
Higher modes will have higher cutoff frequencies, given by the same formula with larger values of m and n.
The given answer options are:
A) 0.5x1012 Hz
B) 6x1015 Hz
C) 8x1014 Hz
D) 1x1013 Hz
All these options are within the frequency range of TM waves that can propagate in the given waveguide.
Therefore, the correct answer is A, B, C, and D.
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Community Answer
A waveguide consists of two infinite parallel plates (perfect conduct...
For parallel plate wave guide
It passes all of the frequency components.
Hence, the correct options are (A), (B), (C) and (D).
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A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer?
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A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of light in air to be 3 x 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/area)0.5 x 1012Hzb)6 x 1015Hzc)8 x 1014Hzd)1 x 1013HzCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
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