Answer key for the "Anatomy of a Wave Worksheet," illustrating wave components and providing definitions for amplitude, wavelength, crest, trough, and frequency.

Let’s go step by step to solve the problems on this worksheet.

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First, look at Fig 1 — it shows a wave with labeled parts A through E. We need to match each letter to its correct definition:

- A: The highest point of the wave → that’s the crest
- B: The lowest point of the wave → that’s the trough
- C: The distance from one crest to the next (or trough to trough) → that’s the wavelength
- D: How tall the wave is from the middle line to the top (or bottom) → that’s the amplitude
- E: Same as C — another full cycle shown → also wavelength

Wait — let’s double-check the definitions given in the worksheet:

> - A = amplitude
> - B = trough
> - C = wavelength
> - D = crest
> - E = wavelength

Hmm… but looking at the diagram:

- Point A is pointing to the vertical height from center to peak → that’s amplitude ✔
- Point B is at the very bottom → trough ✔
- Point C spans from one peak to the next → wavelength ✔
- Point D is at the very top → crest ✔
- Point E spans from one trough to the next → also wavelength ✔

So the matching is already correctly filled in on the worksheet! No changes needed there.

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Now, move to Part 2, Fig 2 — we have four waves (A, B, C, D), and for each, they give frequency and ask us to find period and wavelength.

We’re told:
- Speed of all waves = 5 cm/sec

There are two key formulas we’ll use:

1. Period (T) = 1 / Frequency (f)
→ T = 1/f

2. Wavelength (λ) = Wave Speed (v) × Period (T)
→ λ = v × T
OR since v = f × λ, then λ = v / f

Either way works. Let’s use λ = v / f because it’s direct.

Given: v = 5 cm/sec

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Let’s fill in the table row by row.

Wave A:

Frequency = 1 Hz
→ Period = 1 / 1 = 1 sec
→ Wavelength = 5 cm/sec ÷ 1 Hz = 5 cm

Wave B:

Frequency = 2 Hz
→ Period = 1 / 2 = 0.5 sec
→ Wavelength = 5 ÷ 2 = 2.5 cm

Wave C:

Frequency = 4 Hz
→ Period = 1 / 4 = 0.25 sec
→ Wavelength = 5 ÷ 4 = 1.25 cm

Wave D:

Frequency = 8 Hz
→ Period = 1 / 8 = 0.125 sec
→ Wavelength = 5 ÷ 8 = 0.625 cm

All these match what’s already written in the table — so again, no corrections needed.

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Now, the concluding questions:

> 1. What is the relationship between frequency and period? Explain the reason for the relationship.

As frequency increases, period decreases. Why? Because period is how long one wave takes, and frequency is how many waves happen per second. If more waves happen each second (higher frequency), each individual wave must take less time (shorter period). They are inversely related: T = 1/f.

> 2. What is the relationship between frequency and wavelength? Explain the reason for the relationship.

As frequency increases, wavelength decreases — if speed stays the same. Why? Because wave speed = frequency × wavelength. If speed is fixed (like here, 5 cm/sec), then when frequency goes up, wavelength must go down to keep the product equal to the constant speed.

Example:
If f doubles, λ must halve to keep v = f×λ the same.

> 3. Which wave has the greatest energy? Explain your answer.

Wave D has the greatest energy.

Why? Because energy of a wave depends on both amplitude and frequency. In this case, all waves have the same amplitude (we assume, since not stated otherwise — and in Fig 2, they look similar in height). So the main factor is frequency. Higher frequency means more energy. Wave D has the highest frequency (8 Hz), so it carries the most energy.

Also, in real life, high-frequency waves like gamma rays carry more energy than low-frequency ones like radio waves.

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Final Answer:

The worksheet answers are already correctly filled out. For the concluding questions:

1. Frequency and period are inversely related: as one increases, the other decreases. This is because period is the time for one wave, and frequency is how many waves per second — so T = 1/f.

2. Frequency and wavelength are inversely related when wave speed is constant. As frequency increases, wavelength must decrease to keep speed = frequency × wavelength unchanged.

3. Wave D has the greatest energy because it has the highest frequency, and energy increases with frequency (assuming amplitude is the same).