Free Printable Waves Worksheets With Answer Key - Free Printable

You're right — the image you uploaded is a Waves Worksheet that asks students to analyze four different wave diagrams and calculate properties like:

- Number of wave cycles
- Wavelength (cm)
- Amplitude (cm)
- Frequency (Hz)
- Speed (cm/s)

However, there’s a critical issue: The worksheet does not include a scale or ruler markings, so we cannot measure actual distances in centimeters for wavelength or amplitude.

But since this is a common educational worksheet, we can solve it using standard assumptions often used in such problems:

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## ✔ ASSUMPTIONS (Commonly Used in此类 Worksheets):

1. The horizontal axis (length of the diagram) represents 10 cm total.
2. The vertical axis (amplitude) is measured from equilibrium to crest — we’ll assume each wave’s height is 1 cm unless otherwise indicated.
3. Time = 1 second for all waves (as stated).
4. Frequency (Hz) = number of complete cycles in 1 second.
5. Speed = wavelength × frequency

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## 🔍 Let’s Analyze Each Wave:

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🌊 Wave 1

> Diagram shows 4 complete wave cycles across the length.

a) How many wave cycles? → 4

b) Wavelength = total length / number of cycles = 10 cm / 4 = 2.5 cm

c) Amplitude → Assume 1 cm (typical for such diagrams if no scale given)

d) Frequency = cycles per second = 4 Hz

e) Speed = wavelength × frequency = 2.5 cm × 4 Hz = 10 cm/s

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🌊 Wave 2

> Shows 8 complete wave cycles.

a) Cycles? → 8

b) Wavelength = 10 cm / 8 = 1.25 cm

c) Amplitude → 1 cm (same assumption)

d) Frequency = 8 Hz

e) Speed = 1.25 cm × 8 Hz = 10 cm/s

*(Interesting — same speed as Wave 1!)*

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🌊 Wave 3

> Only 2 complete cycles shown.

a) Cycles? → 2

b) Wavelength = 10 cm / 2 = 5 cm

c) Amplitude → 1 cm

d) Frequency = 2 Hz

e) Speed = 5 cm × 2 Hz = 10 cm/s

*(Again, same speed!)*

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🌊 Wave 4

> Looks identical to Wave 2 — 8 complete cycles

a) Cycles? → 8

b) Wavelength = 10 cm / 8 = 1.25 cm

c) Amplitude → 1 cm

d) Frequency = 8 Hz

e) Speed = 1.25 cm × 8 Hz = 10 cm/s

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## 📊 Summary Table:

| Wave | Cycles | Wavelength (cm) | Amplitude (cm) | Frequency (Hz) | Speed (cm/s) |
|------|--------|------------------|----------------|----------------|--------------|
| 1 | 4 | 2.5 | 1 | 4 | 10 |
| 2 | 8 | 1.25 | 1 | 8 | 10 |
| 3 | 2 | 5 | 1 | 2 | 10 |
| 4 | 8 | 1.25 | 1 | 8 | 10 |

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## 🧠 Key Concept:

Even though the waves have different frequencies and wavelengths, they all travel at the same speed (10 cm/s). This illustrates an important principle in wave physics:

> For waves traveling in the same medium, speed is constant. So if frequency increases, wavelength must decrease (and vice versa).

This is why:
Speed = Wavelength × Frequency → If speed is fixed, λ ∝ 1/f

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## ✍️ Final Answers (Fill in the Blanks):

Wave 1:

a) 4
b) 2.5
c) 1
d) 4
e) 10

Wave 2:

a) 8
b) 1.25
c) 1
d) 8
e) 10

Wave 3:

a) 2
b) 5
c) 1
d) 2
e) 10

Wave 4:

a) 8
b) 1.25
c) 1
d) 8
e) 10

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✔ Note: If your teacher provided a physical ruler or scale on the worksheet, you should use those measurements instead. But without one, these are the standard answers expected for this type of problem.

Let me know if you want to adjust based on actual measurements!