Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Questions  >  A wave is propagated in a waveguide at freque... Start Learning for Free
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?
Verified Answer
A wave is propagated in a waveguide at frequency of 9 GHz and separati...
Vg . Vp = C2
where
.
View all questions of this test
Most Upvoted Answer
A wave is propagated in a waveguide at frequency of 9 GHz and separati...
Given:
- Frequency of the wave, f = 9 GHz = 9 x 10^9 Hz
- Separation between walls, d = 2 cm = 0.02 m

To find:
Group velocity for the dominant mode

Formula:
The group velocity (vg) can be calculated using the formula:
vg = c / β

Where:
c is the speed of light in a vacuum = 3 x 10^8 m/s
β is the phase constant

Solution:
1. Calculate the phase constant (β) using the formula:
β = 2πf√(εμ - (λ/2d)^2)

Where:
ε is the permittivity of the waveguide
μ is the permeability of the waveguide
λ is the wavelength of the wave in the waveguide

2. Calculate the wavelength (λ) using the formula:
λ = c / f

3. Substitute the values of ε, μ, λ, and d into the formula for β and calculate its value.

4. Substitute the value of β and the speed of light (c) into the formula for group velocity (vg) and calculate its value.

Now, let's calculate step by step:

Step 1:
- The permittivity of air (ε0) is approximately 8.854 x 10^-12 F/m.
- The permeability of free space (μ0) is approximately 4π x 10^-7 T/m.
- Therefore, the permittivity (ε) and permeability (μ) of the waveguide can be assumed to be ε0 and μ0, respectively.

Step 2:
- λ = c / f
= (3 x 10^8 m/s) / (9 x 10^9 Hz)
= 1/3 m = 0.333 m

Step 3:
- β = 2πf√(εμ - (λ/2d)^2)
= 2π(9 x 10^9 Hz)√(8.854 x 10^-12 F/m)(4π x 10^-7 T/m) - ((0.333 m)/(2 x 0.02 m))^2

Simplifying the equation:
= 2π(9 x 10^9 Hz)√(8.854 x 10^-12 F/m)(4π x 10^-7 T/m) - (0.333/0.04)^2

= 2π(9 x 10^9 Hz)√(35.416 x 10^-19) - (8.325)^2

= 2π(9 x 10^9 Hz)(5.95 x 10^-10) - 69.281

= 2π(5.355 x 10^9) - 69.281

= 33.718 x 10^9π - 69.281

= 106.128 x 10^9 - 69.281

= 106.128 x 10^9 - 69.281

≈ 106.128 x 10^9

Step 4:
- vg = c / β
= (3 x
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

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?
Question Description
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? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about 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? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice Electrical Engineering (EE) tests.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev