In basic wave propagation, if the frequency of a radio wave is increased while the propagation speed remains constant (approximately c in free space), how does its wavelength change?

Introduction:
This question probes the inverse relationship between frequency and wavelength for electromagnetic waves such as radio signals. Understanding this relationship is crucial for antenna design, spectrum planning, and interpreting datasheets for RF systems.

Given Data / Assumptions:

• Propagation in free space or a fixed medium with constant phase velocity v (≈ c in free space).
• Frequency f is increased.
• We seek the qualitative change in wavelength λ.

Concept / Approach:
The fundamental relation is v = f * λ. For constant v, increasing f must reduce λ so that their product remains constant. This is an exact inverse proportionality: λ = v / f.

Step-by-Step Solution:
Start with v = f * λHold v constant (medium unchanged).Solve for λ: λ = v / fIf f increases, the denominator increases, so λ decreases.

Verification / Alternative check:
Example: In free space, v ≈ 3.0 * 10^8 m/s. At 100 MHz, λ = 3 m; at 200 MHz, λ = 1.5 m. Doubling frequency halves wavelength, confirming the inverse relationship.

Why Other Options Are Wrong:

• Increase / remain the same: Contradicts λ = v / f for constant v.
• Cannot tell: The relationship is deterministic given constant propagation speed.
• First increase then decrease: No such behavior in a fixed medium.

Common Pitfalls:

• Forgetting that this relation assumes constant medium and neglects dispersion; in many RF cases, the approximation is valid.
• Confusing group velocity with phase velocity; here we consider the standard phase relation.

Final Answer:
decrease