Waves Worksheet - Name: Date: ______ Period: ______ 1 Wave ... - Free Printable

Let's go through the Wave Worksheet step by step, solve the problems, and explain each solution clearly.

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🔹 Understanding Key Concepts

Before solving, recall the wave equation:

> Speed (v) = Wavelength (λ) × Frequency (f)
> or
> v = λ × f

Also:
- Amplitude: Height from rest position to crest (or trough).
- Wavelength (λ): Distance of one full wave cycle.
- Frequency (f): Number of waves passing a point per second (in Hz).
- Time given: 1 second for all wave trains → frequency = number of waves in 1 second.

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## ✔ Wave 1

Given:
- Time = 1 second
- Amplitude = 2 cm (from diagram)
- Waveform shows 5 complete cycles

a) How many waves are there in this wave train?

→ There are 5 full waves in 1 second.
✔ Answer: 5

b) Wavelength

From the diagram: The horizontal distance between two consecutive crests is 4 cm.
So, wavelength = 4 cm
✔ Answer: 4 cm

c) Amplitude

Vertical distance from rest line to crest = 2 cm
✔ Answer: 2 cm

d) Frequency

Since 5 waves pass in 1 second → frequency = 5 Hz
✔ Answer: 5 Hz

e) Speed

Use formula:
Speed = Wavelength × Frequency
= 4 cm × 5 Hz = 20 cm/s
✔ Answer: 20 cm/s

✔️ All answers for Wave 1 are correct.

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## ✔ Wave 2

Given:
- Time = 1 second
- Amplitude = 1 cm (from diagram – height from rest to crest)
- Horizontal length shown: 5 cm per cycle?

Wait — look carefully at the diagram.

It shows 3 full waves, and the total horizontal length is marked as 5 cm per wave? No — actually, it says "5 cm" under the first crest, but that seems to be the wavelength.

But let’s analyze:

- There are 3 full waves in the wave train.
- The horizontal distance from start to end of one wave cycle (crest to next crest) appears to be 10 cm.

Wait — the label says "5 cm", but it's placed under just half a wave? Let's interpret correctly.

Looking closely:
- The first crest to the next crest spans 10 cm? But the red bar labeled "5 cm" goes from the start to the peak — that's amplitude, not wavelength.

Wait — no! The red bar is vertical, labeled “5 cm”, but it's drawn from the baseline to the crest — so that would be amplitude?

But then it says "Type your text" below — possibly a mistake in labeling.

But the student has filled in:
- Amplitude = 1 cm
- Wavelength = 10 cm
- 3 waves

Let’s check consistency.

From the diagram:
- The wave has 3 full cycles → 3 waves in 1 second → frequency = 3 Hz ✔️
- Each wavelength appears to be 10 cm (distance between crests), so wavelength = 10 cm ✔️
- Amplitude: From rest to crest = 1 cm (not 5 cm) — so likely the "5 cm" label is wrong or misplaced.

Possibly the "5 cm" was meant to be the wavelength, but it's drawn vertically? That doesn't make sense.

Alternatively, maybe the vertical arrow is mislabeled.

But the student wrote:
- Amplitude = 1 cm → that’s correct if the peak is only 1 cm high.
- Wavelength = 10 cm → matches 3 waves over what looks like 30 cm total length → 30 / 3 = 10 cm → yes.

So probably the "5 cm" label is incorrect or refers to something else.

Assuming:
- Amplitude = 1 cm
- Wavelength = 10 cm
- Number of waves = 3
- Time = 1 s → frequency = 3 Hz

Now calculate speed:

a) How many waves? → 3 ✔

b) Wavelength → 10 cm ✔

c) Amplitude → 1 cm ✔

d) Frequency → 3 Hz ✔

e) Speed = λ × f = 10 cm × 3 Hz = 30 cm/s ✔

✔️ All answers for Wave 2 are correct.

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## ✔ Problems

Problem 1:

> What is the wavelength of a sound wave with a frequency of 50 Hz? The speed of sound is 342 m/s.

Use:
> v = λ × f
> ⇒ λ = v / f

Plug in:
> λ = 342 m/s ÷ 50 Hz = 6.84 meters

✔ Answer: 6.84 m (not cm!) — the student wrote 6.84 cm, which is wrong.

✘ Mistake: Unit error. Should be meters, not centimeters.

Correct answer: 6.84 m

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Problem 2:

> A sound wave in a steel rail has a frequency of 620 Hz and a wavelength of 10.5 m. What is the speed of sound in steel?

Use:
> v = λ × f
> = 10.5 m × 620 Hz
> = 6,510 m/s

✔ Student answer: 6.510 m/s — but that’s too small!

They wrote 6.510 m/s, but actual value is 6,510 m/s.

✘ Mistake: Missing decimal place.

Correct answer: 6,510 m/s

(Or written as 6.51 × 10³ m/s)

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## ✔ Final Summary

| Section | Correct Answer | Student's Answer | Status |
|--------|----------------|------------------|--------|
| Wave 1a | 5 | 5 | ✔ |
| Wave 1b | 4 cm | 4 cm | ✔ |
| Wave 1c | 2 cm | 2 cm | ✔ |
| Wave 1d | 5 Hz | 5 Hz | ✔ |
| Wave 1e | 20 cm/s | 20 cm/s | ✔ |
| Wave 2a | 3 | 3 | ✔ |
| Wave 2b | 10 cm | 10 cm | ✔ |
| Wave 2c | 1 cm | 1 cm | ✔ |
| Wave 2d | 3 Hz | 3 Hz | ✔ |
| Wave 2e | 30 cm/s | 30 cm/s | ✔ |
| Problem 1 | 6.84 m | 6.84 cm ✘ | ✘ (unit error) |
| Problem 2 | 6,510 m/s | 6.510 m/s ✘ | ✘ (missing magnitude) |

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## ✔ Corrected Answers:

Problem 1:

> λ = v / f = 342 / 50 = 6.84 meters

Problem 2:

> v = λ × f = 10.5 × 620 = 6,510 m/s

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## 📝 Explanation of Errors:

- Problem 1: The student wrote 6.84 cm, but since speed is in m/s, and frequency in Hz, wavelength must be in meters. So 6.84 m is correct.
- Problem 2: The student wrote 6.510 m/s, but 10.5 × 620 = 6,510, not 6.510. They missed three zeros.

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## ✔ Final Answers:

Problem 1:

Wavelength = 6.84 meters

Problem 2:

Speed of sound in steel = 6,510 m/s

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