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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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A wave is propagated in a waveguide at frequency of 9 GHz and separati...
Given:
- Frequency of the wave: 9 GHz
- Separation between walls: 2 cm
To find:
Cut off wavelength for the dominant mode.
Solution:
The cutoff wavelength is the minimum wavelength at which a particular mode can propagate in a waveguide. For a dominant mode, the wave travels in a straight line and bounces off the walls of the waveguide.
Step 1: Calculate the wavelength:
The wavelength of the wave can be calculated using the formula:
λ = c / f
where:
λ is the wavelength,
c is the speed of light (approximately 3 x 10^8 m/s),
f is the frequency of the wave.
Converting the frequency to Hz:
f = 9 GHz = 9 x 10^9 Hz
Plugging the values into the formula:
λ = (3 x 10^8 m/s) / (9 x 10^9 Hz)
Calculating the wavelength:
λ = 1/3 m = 0.333 m = 33.3 cm
Step 2: Calculate the cut off wavelength:
The cutoff wavelength for the dominant mode in a rectangular waveguide is given by the formula:
λc = 2a / sqrt(m^2 + n^2)
where:
a is the separation between the walls,
m and n are the mode numbers.
In the dominant mode, m = 1 and n = 0.
Plugging the values into the formula:
λc = 2(2 cm) / sqrt(1^2 + 0^2)
Calculating the cutoff wavelength:
λc = 4 cm
Therefore, the cut off wavelength for the dominant mode in the given waveguide is 4 cm (option A).
- Frequency of the wave: 9 GHz
- Separation between walls: 2 cm
To find:
Cut off wavelength for the dominant mode.
Solution:
The cutoff wavelength is the minimum wavelength at which a particular mode can propagate in a waveguide. For a dominant mode, the wave travels in a straight line and bounces off the walls of the waveguide.
Step 1: Calculate the wavelength:
The wavelength of the wave can be calculated using the formula:
λ = c / f
where:
λ is the wavelength,
c is the speed of light (approximately 3 x 10^8 m/s),
f is the frequency of the wave.
Converting the frequency to Hz:
f = 9 GHz = 9 x 10^9 Hz
Plugging the values into the formula:
λ = (3 x 10^8 m/s) / (9 x 10^9 Hz)
Calculating the wavelength:
λ = 1/3 m = 0.333 m = 33.3 cm
Step 2: Calculate the cut off wavelength:
The cutoff wavelength for the dominant mode in a rectangular waveguide is given by the formula:
λc = 2a / sqrt(m^2 + n^2)
where:
a is the separation between the walls,
m and n are the mode numbers.
In the dominant mode, m = 1 and n = 0.
Plugging the values into the formula:
λc = 2(2 cm) / sqrt(1^2 + 0^2)
Calculating the cutoff wavelength:
λc = 4 cm
Therefore, the cut off wavelength for the dominant mode in the given waveguide is 4 cm (option A).
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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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