GATE EC 2021 Set 1 — Question 64
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumRectangular & Circular WaveguidesWaveguides & Optical FibersElectromagneticsCutoff Frequency & Guide Wavelength
Electromagnetics → Waveguides & Optical Fibers → Cutoff Frequency & Guide Wavelength
Last updated
Question
A standard air-filled rectangular waveguide with dimensions cm, cm, operates at 3.4 GHz. For the dominant mode of wave propagation, the phase velocity of the signal is . The value (rounded off to two decimal places) of , where denotes the velocity of light, is __________.
Correct answer
1.15 to 1.25
Solution
Given:
Waveguide dimensions: cm m, cm m
Operating frequency GHz Hz
Velocity of light m/s
GHz
Waveguide dimensions: cm m, cm m
Operating frequency GHz Hz
Velocity of light m/s
1.For a standard air-filled rectangular waveguide, the dominant mode is .
2.The cutoff frequency for the mode is given by:
GHz
3.Since the operating frequency GHz is greater than the cutoff frequency GHz, the wave propagates.
4.The phase velocity in a waveguide is related to the velocity of light and the cutoff frequency by the formula:
5.Calculate the ratio :
6.Calculate :
7.Now, substitute this into the phase velocity formula to find :
8.Rounded off to two decimal places, .
The final answer is Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Waveguides & Optical Fibers
2026 Set 1 Q21Consider the Friis' transmission equation , where…2026 Set 1 Q24The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous…2026 Set 1 Q28Which option(s) represents/ represent the dielectric loss tangent of a substrate?2026 Set 1 Q33The cutoff frequency (in GHz) for the dominant mode of an air-filled rectangular…2026 Set 1 Q34For a lossless passive two-port network, and intersect at -3 dB. For a lossy…