Wave properties — frequency, amplitude, and energy transport (basics) Which consolidated statement correctly describes frequency, its SI unit, amplitude, and the relation between amplitude and transported energy for waves?

Introduction / Context:
Foundational wave terminology is widely used in physics, oceanography, acoustics, and electromagnetics. Precision in definitions prevents downstream errors in analysis and design.

Given Data / Assumptions:

• Periodic, approximately sinusoidal waves.
• Observation at a fixed spatial point for counting frequency.
• Linear regime where standard proportionalities apply.

Concept / Approach:

Frequency f counts cycles per second (Hz). Amplitude a is the maximum displacement from the mean position; for surface gravity waves it is half the wave height (crest-to-trough). In many physical systems, average transported energy ∝ a^2, making amplitude a critical control on power and damage potential.

Step-by-Step Solution:

Verification / Alternative check:

For sinusoidal signals, intensity is proportional to amplitude squared (e.g., sound intensity ∝ pressure amplitude^2; EM intensity ∝ E-field amplitude^2), reinforcing the general relationship.

Why Other Options Are Wrong:

• Each of (a)–(d) is true; therefore the comprehensive correct choice is “All of these”.

Common Pitfalls:

• Confusing wave height (crest-to-trough) with amplitude (half of height).
• Using rpm or cps instead of SI hertz in technical reporting.

Final Answer:

All of these.