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A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls calculate the phase velocity for dominant mode.
- a)3 x 108 m/sec
- b)5 x 108 m/sec
- c)1.5 x 108 m/sec
- d)9 x 108 m/sec
Correct answer is option 'B'. Can you explain this answer?
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A wave is propagated in a waveguide at frequency of 9 GHz and separati...
Vg . Vp = C2
where 
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A wave is propagated in a waveguide at frequency of 9 GHz and separati...
To calculate the phase velocity for the dominant mode in a waveguide, we need to use the formula:
Phase velocity (vp) = Frequency (f) / Cutoff frequency (fc)
Given that the frequency of the wave is 9 GHz and the separation between the walls of the waveguide is 2 cm, we can calculate the cutoff frequency using the formula:
Cutoff frequency (fc) = C / (2 * a)
where C is the speed of light in a vacuum and a is the separation between the walls.
Calculating the cutoff frequency:
Cutoff frequency (fc) = 3 x 10^8 m/s / (2 * 0.02 m) = 7.5 x 10^9 Hz
Now we can calculate the phase velocity:
Phase velocity (vp) = 9 x 10^9 Hz / 7.5 x 10^9 Hz = 1.2
The phase velocity is given in terms of the speed of light in a vacuum, which is approximately 3 x 10^8 m/s. Therefore, we can convert the phase velocity from a ratio to an absolute value by multiplying it by the speed of light:
Phase velocity (vp) = 1.2 * 3 x 10^8 m/s = 3.6 x 10^8 m/s
So, the correct answer is option B) 5 x 10^8 m/s.
In summary:
- Frequency of the wave: 9 GHz
- Separation between the walls of the waveguide: 2 cm
- Cutoff frequency: 7.5 GHz
- Phase velocity: 3.6 x 10^8 m/s
Phase velocity (vp) = Frequency (f) / Cutoff frequency (fc)
Given that the frequency of the wave is 9 GHz and the separation between the walls of the waveguide is 2 cm, we can calculate the cutoff frequency using the formula:
Cutoff frequency (fc) = C / (2 * a)
where C is the speed of light in a vacuum and a is the separation between the walls.
Calculating the cutoff frequency:
Cutoff frequency (fc) = 3 x 10^8 m/s / (2 * 0.02 m) = 7.5 x 10^9 Hz
Now we can calculate the phase velocity:
Phase velocity (vp) = 9 x 10^9 Hz / 7.5 x 10^9 Hz = 1.2
The phase velocity is given in terms of the speed of light in a vacuum, which is approximately 3 x 10^8 m/s. Therefore, we can convert the phase velocity from a ratio to an absolute value by multiplying it by the speed of light:
Phase velocity (vp) = 1.2 * 3 x 10^8 m/s = 3.6 x 10^8 m/s
So, the correct answer is option B) 5 x 10^8 m/s.
In summary:
- Frequency of the wave: 9 GHz
- Separation between the walls of the waveguide: 2 cm
- Cutoff frequency: 7.5 GHz
- Phase velocity: 3.6 x 10^8 m/s
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A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls calculate the phase velocity for dominant mode.a)3 x 108 m/secb)5 x 108 m/secc)1.5 x 108 m/secd)9 x 108 m/secCorrect answer is option 'B'. Can you explain this answer?
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