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?
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AFrequency is the number of crests passing a fixed point per second
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BFrequency is measured in hertz (Hz)
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CAmplitude is the height of the crest measured from the midline (mean level)
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DEnergy transported by a wave is proportional to the square of the amplitude
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EAll of these
Answer
Correct Answer: All of these
Explanation
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:
1) Define frequency: count crests at a point in 1 s ⇒ f (Hz).2) Define amplitude: vertical distance from mean level to crest (or trough).3) State energy proportionality: energy ∝ amplitude^2 in linear wave theory.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.