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A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls find cut off wavelength for dominant mode.
- a)4 cm
- b)1 cm
- c)2 cm
- d)8 cm
Correct answer is option 'A'. Can you explain this answer?
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A wave is propagated in a waveguide at frequency of 9 GHz and separati...
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Explanation:
To find the cut-off wavelength for the dominant mode in a waveguide, we can use the following formula:
\(\lambda_c = \frac{2a}{m}\)
where:
\(\lambda_c\) is the cut-off wavelength,
\(a\) is the separation between the walls of the waveguide, and
\(m\) is the mode number.
In this case, the frequency of the wave is given as 9 GHz and the separation between the walls is 2 cm.
Step 1: Convert the frequency to wavelength:
The speed of light (\(c\)) can be approximated as \(3 \times 10^8\) m/s.
The wavelength (\(\lambda\)) can be calculated using the formula:
\(\lambda = \frac{c}{f}\)
where:
\(\lambda\) is the wavelength,
\(c\) is the speed of light, and
\(f\) is the frequency.
Substituting the values, we have:
\(\lambda = \frac{3 \times 10^8}{9 \times 10^9}\)
\(\lambda = \frac{1}{3} \times 10^{-1}\)
\(\lambda = 0.1\) m
Step 2: Convert the separation between walls to meters:
The separation between the walls (\(a\)) is given as 2 cm.
Converting cm to meters, we have:
\(a = 2 \times 10^{-2}\) m
Step 3: Calculate the cut-off wavelength:
Using the formula mentioned earlier:
\(\lambda_c = \frac{2a}{m}\)
Substituting the values, we have:
\(\lambda_c = \frac{2 \times 10^{-2}}{1}\)
\(\lambda_c = 2 \times 10^{-2}\)
\(\lambda_c = 0.02\) m
Converting the cut-off wavelength to centimeters, we have:
\(\lambda_c = 0.02 \times 100\)
\(\lambda_c = 2\) cm
Therefore, the cut-off wavelength for the dominant mode in the waveguide is 2 cm.
To find the cut-off wavelength for the dominant mode in a waveguide, we can use the following formula:
\(\lambda_c = \frac{2a}{m}\)
where:
\(\lambda_c\) is the cut-off wavelength,
\(a\) is the separation between the walls of the waveguide, and
\(m\) is the mode number.
In this case, the frequency of the wave is given as 9 GHz and the separation between the walls is 2 cm.
Step 1: Convert the frequency to wavelength:
The speed of light (\(c\)) can be approximated as \(3 \times 10^8\) m/s.
The wavelength (\(\lambda\)) can be calculated using the formula:
\(\lambda = \frac{c}{f}\)
where:
\(\lambda\) is the wavelength,
\(c\) is the speed of light, and
\(f\) is the frequency.
Substituting the values, we have:
\(\lambda = \frac{3 \times 10^8}{9 \times 10^9}\)
\(\lambda = \frac{1}{3} \times 10^{-1}\)
\(\lambda = 0.1\) m
Step 2: Convert the separation between walls to meters:
The separation between the walls (\(a\)) is given as 2 cm.
Converting cm to meters, we have:
\(a = 2 \times 10^{-2}\) m
Step 3: Calculate the cut-off wavelength:
Using the formula mentioned earlier:
\(\lambda_c = \frac{2a}{m}\)
Substituting the values, we have:
\(\lambda_c = \frac{2 \times 10^{-2}}{1}\)
\(\lambda_c = 2 \times 10^{-2}\)
\(\lambda_c = 0.02\) m
Converting the cut-off wavelength to centimeters, we have:
\(\lambda_c = 0.02 \times 100\)
\(\lambda_c = 2\) cm
Therefore, the cut-off wavelength for the dominant mode in the waveguide is 2 cm.
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A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls find cut off wavelength for dominant mode.a)4 cmb)1 cmc)2 cmd)8 cmCorrect answer is option 'A'. Can you explain this answer?
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