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A rectangular air filled waveguide has cross section of 4 cm x 10 cm. The minimum frequency which can propagate in the waveguide is
- a)1.5 GHz
- b)2.0 GHz
- c)2.5 GHz
- d)3.0 GHz
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Cut-off Frequency in a Rectangular Waveguide
Introduction:
In a waveguide, the frequency at which the waveguide can no longer support the propagation of the electromagnetic wave is called the cut-off frequency. For a rectangular waveguide, the cut-off frequency depends on the dimensions of the waveguide. In this question, we are given the dimensions of the rectangular waveguide and we need to find its cut-off frequency.
Given:
Cross-section of the waveguide = 4 cm x 10 cm
Solution:
The cut-off frequency for a rectangular waveguide can be calculated using the formula:
fc = (c/2)*sqrt((m/a)^2 + (n/b)^2)
where,
fc = cut-off frequency
c = speed of light in free space
m, n = mode numbers (integers)
a, b = dimensions of the waveguide
For the TE10 mode, m = 1 and n = 0
Substituting the given values, we get:
fc = (3 x 10^8/2)*sqrt((1/0.04)^2 + (0/0.1)^2)
fc = 1.5 GHz
Therefore, the minimum frequency which can propagate in the given waveguide is 1.5 GHz.
Conclusion:
The cut-off frequency of a rectangular waveguide can be calculated using the formula fc = (c/2)*sqrt((m/a)^2 + (n/b)^2), where m and n are mode numbers and a and b are the dimensions of the waveguide. For the given rectangular waveguide, the minimum frequency which can propagate is found to be 1.5 GHz.
Introduction:
In a waveguide, the frequency at which the waveguide can no longer support the propagation of the electromagnetic wave is called the cut-off frequency. For a rectangular waveguide, the cut-off frequency depends on the dimensions of the waveguide. In this question, we are given the dimensions of the rectangular waveguide and we need to find its cut-off frequency.
Given:
Cross-section of the waveguide = 4 cm x 10 cm
Solution:
The cut-off frequency for a rectangular waveguide can be calculated using the formula:
fc = (c/2)*sqrt((m/a)^2 + (n/b)^2)
where,
fc = cut-off frequency
c = speed of light in free space
m, n = mode numbers (integers)
a, b = dimensions of the waveguide
For the TE10 mode, m = 1 and n = 0
Substituting the given values, we get:
fc = (3 x 10^8/2)*sqrt((1/0.04)^2 + (0/0.1)^2)
fc = 1.5 GHz
Therefore, the minimum frequency which can propagate in the given waveguide is 1.5 GHz.
Conclusion:
The cut-off frequency of a rectangular waveguide can be calculated using the formula fc = (c/2)*sqrt((m/a)^2 + (n/b)^2), where m and n are mode numbers and a and b are the dimensions of the waveguide. For the given rectangular waveguide, the minimum frequency which can propagate is found to be 1.5 GHz.
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A rectangular air filled waveguide has cross section of 4 cm x 10 cm. The minimum frequency which can propagate in the waveguide isa)1.5 GHzb)2.0 GHzc)2.5 GHzd)3.0 GHzCorrect answer is option 'A'. Can you explain this answer?
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