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A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls Calculate group velocity for dominant mode.
- a)1.8 x 108 m/sec
- b)5 x 108 m/sec
- c)3 x 108 m/sec
- d)1.5 x 108 m/sec
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...
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 group velocity for the dominant mode in a waveguide, we need to use the formula:
Vg = λg * fg
Where:
Vg = Group velocity
λg = Wavelength of the dominant mode
fg = Frequency of the dominant mode
Given:
Frequency (fg) = 9 GHz = 9 x 10^9 Hz
Separation between walls = 2 cm = 0.02 m
Step 1: Calculate the wavelength (λg)
The wavelength can be calculated using the formula:
λg = 2 * separation
Substituting the given values:
λg = 2 * 0.02 m = 0.04 m
Step 2: Calculate the group velocity (Vg)
Now we can substitute the values of λg and fg into the formula for group velocity:
Vg = λg * fg
Vg = 0.04 m * 9 x 10^9 Hz
Step 3: Convert the answer to the desired unit
The answer is given in meters per second, so we need to convert Hz to per second. Since 1 Hz = 1/s, we have:
Vg = 0.04 m * 9 x 10^9 s^-1
Simplifying the expression:
Vg = 0.36 x 10^9 m/s
Step 4: Express the answer in scientific notation
To express the answer in scientific notation, we can write it as:
Vg = 3.6 x 10^8 m/s
Comparing this with the given options, we can see that the correct answer is option 'A' - 1.8 x 10^8 m/s.
Vg = λg * fg
Where:
Vg = Group velocity
λg = Wavelength of the dominant mode
fg = Frequency of the dominant mode
Given:
Frequency (fg) = 9 GHz = 9 x 10^9 Hz
Separation between walls = 2 cm = 0.02 m
Step 1: Calculate the wavelength (λg)
The wavelength can be calculated using the formula:
λg = 2 * separation
Substituting the given values:
λg = 2 * 0.02 m = 0.04 m
Step 2: Calculate the group velocity (Vg)
Now we can substitute the values of λg and fg into the formula for group velocity:
Vg = λg * fg
Vg = 0.04 m * 9 x 10^9 Hz
Step 3: Convert the answer to the desired unit
The answer is given in meters per second, so we need to convert Hz to per second. Since 1 Hz = 1/s, we have:
Vg = 0.04 m * 9 x 10^9 s^-1
Simplifying the expression:
Vg = 0.36 x 10^9 m/s
Step 4: Express the answer in scientific notation
To express the answer in scientific notation, we can write it as:
Vg = 3.6 x 10^8 m/s
Comparing this with the given options, we can see that the correct answer is option 'A' - 1.8 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 group velocity for dominant mode.a)1.8 x 108 m/secb)5 x 108 m/secc)3 x 108 m/secd)1.5 x 108 m/secCorrect answer is option 'A'. Can you explain this answer?
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