A transmission line has a phase constant β = 29.8 rad/m. At a frequency of 1000 MHz, what will be the wavelength of the signal?

Introduction / Context:
The phase constant β in a transmission line is related to the propagation constant and wavelength. Calculating wavelength from β is a common problem in RF and microwave engineering.

Given Data / Assumptions:

• β = 29.8 rad/m.
• Frequency f = 1000 MHz = 1 GHz.
• Formula: β = 2π / λ.

Concept / Approach:

By definition, wavelength λ = 2π / β. Once β is known, λ can be calculated directly.

Step-by-Step Solution:

Verification / Alternative check:

For 1 GHz in free space, λ ≈ 0.3 m. A phase constant of 29.8 rad/m corresponds to a slightly shorter wavelength due to dielectric or guide effects, consistent with 0.21 m.

Why Other Options Are Wrong:

• 29.8 m, 2.98 m, 2.1 m: too large, do not satisfy β formula.
• 0.0298 m: too small, not matching calculation.

Common Pitfalls:

Using frequency-speed formula instead of β relation; ignoring 2π factor.

Final Answer:

0.21 m