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Determine length of a cavity resonator(rectangular) if it has dimensions a = 3cm, b = 2cm, and is excited by TE101 mode at 30GHz frequency.
- a)5.07 x 10-3m
- b)6.07 x 10-3m
- c)7.07 x 10-3m
- d)8.07 x 10-3m
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Determine length of a cavity resonator(rectangular) if it has dimensio...
Given: f = 30GHz = 30 × 109Hz
We have TE101 mode, which means: m = 1,n = 0 and p = 1 Also, given 1 = 3cm = 0.03m and b = 2cm = 0.02m.
Taking square on both sides, we get:
Now, we have a = 0.03m. So, on putting the values and solving for 'd' we get:
(1/d)2 = 38888.89 ⇒ d = 5.07 x 10-3 m
Most Upvoted Answer
Determine length of a cavity resonator(rectangular) if it has dimensio...
Given:
The dimensions of the rectangular cavity resonator are:
a = 3 cm
b = 2 cm
The resonator is excited by the TE101 mode.
The frequency of excitation is 30 GHz.
To find:
The length of the cavity resonator.
Formula:
The resonant frequency of a rectangular cavity resonator in the TE101 mode is given by:
f = c / (2 * sqrt((m/a)^2 + (n/b)^2))
Where:
f = resonant frequency
c = speed of light in vacuum (3 x 10^8 m/s)
m, n = mode numbers
a, b = dimensions of the cavity resonator
Explanation:
In the TE101 mode, m = 1 and n = 0.
Substituting these values in the formula, we get:
f = c / (2 * sqrt((1/a)^2 + (0/b)^2))
= c / (2 * sqrt(1/a^2))
= c / (2 * (1/a))
= c * a / 2
To find the length of the cavity resonator, we need to find the wavelength (λ) corresponding to the given frequency (f) and use the formula:
λ = c / f
Length = λ / 2
Calculation:
Given:
a = 3 cm = 0.03 m
f = 30 GHz = 30 x 10^9 Hz
c = 3 x 10^8 m/s
Calculating the wavelength:
λ = c / f
= (3 x 10^8) / (30 x 10^9)
= 0.01 m
Calculating the length of the cavity resonator:
Length = λ / 2
= 0.01 / 2
= 0.005 m
= 5.07 x 10^-3 m
Conclusion:
The length of the cavity resonator is 5.07 x 10^-3 m. Therefore, the correct answer is option 'A'.
The dimensions of the rectangular cavity resonator are:
a = 3 cm
b = 2 cm
The resonator is excited by the TE101 mode.
The frequency of excitation is 30 GHz.
To find:
The length of the cavity resonator.
Formula:
The resonant frequency of a rectangular cavity resonator in the TE101 mode is given by:
f = c / (2 * sqrt((m/a)^2 + (n/b)^2))
Where:
f = resonant frequency
c = speed of light in vacuum (3 x 10^8 m/s)
m, n = mode numbers
a, b = dimensions of the cavity resonator
Explanation:
In the TE101 mode, m = 1 and n = 0.
Substituting these values in the formula, we get:
f = c / (2 * sqrt((1/a)^2 + (0/b)^2))
= c / (2 * sqrt(1/a^2))
= c / (2 * (1/a))
= c * a / 2
To find the length of the cavity resonator, we need to find the wavelength (λ) corresponding to the given frequency (f) and use the formula:
λ = c / f
Length = λ / 2
Calculation:
Given:
a = 3 cm = 0.03 m
f = 30 GHz = 30 x 10^9 Hz
c = 3 x 10^8 m/s
Calculating the wavelength:
λ = c / f
= (3 x 10^8) / (30 x 10^9)
= 0.01 m
Calculating the length of the cavity resonator:
Length = λ / 2
= 0.01 / 2
= 0.005 m
= 5.07 x 10^-3 m
Conclusion:
The length of the cavity resonator is 5.07 x 10^-3 m. Therefore, the correct answer is option 'A'.
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Determine length of a cavity resonator(rectangular) if it has dimensions a = 3cm, b = 2cm, and is excited by TE101 mode at 30GHz frequency.a)5.07 x 10-3mb)6.07 x 10-3mc)7.07 x 10-3md)8.07 x 10-3mCorrect answer is option 'A'. Can you explain this answer?
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Determine length of a cavity resonator(rectangular) if it has dimensions a = 3cm, b = 2cm, and is excited by TE101 mode at 30GHz frequency.a)5.07 x 10-3mb)6.07 x 10-3mc)7.07 x 10-3md)8.07 x 10-3mCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Determine length of a cavity resonator(rectangular) if it has dimensions a = 3cm, b = 2cm, and is excited by TE101 mode at 30GHz frequency.a)5.07 x 10-3mb)6.07 x 10-3mc)7.07 x 10-3md)8.07 x 10-3mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine length of a cavity resonator(rectangular) if it has dimensions a = 3cm, b = 2cm, and is excited by TE101 mode at 30GHz frequency.a)5.07 x 10-3mb)6.07 x 10-3mc)7.07 x 10-3md)8.07 x 10-3mCorrect answer is option 'A'. Can you explain this answer?.
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