Physics Lesson 5 — Waves

Wave Speed Equation: v = f × λ

Spec 3.5

Learning Objective:

3.5 – Know and use: wave speed = frequency × wavelength → v = f × λ

Navigation: Arrow Keys or Spacebar

🖨️ Pupil Packs

⏱️ 40-Minute Pacing Guide

Core path (40 min): Arrival → Starter → I Do 1 → We Do 1 → I Do 2 → We Do 2 → Independent → Exit Ticket

FLEX slides (I Do 3 + We Do 3): Use if time allows, or as next-lesson warm-up. Marked with 🟠 FLEX badge.

⏱️ 4 min

Arrival Task

Arrival Task – Recall from Lesson 4

Instructions: Answer from memory. Q1–3 recall wave definitions from L4.

1. 🟢

What is the amplitude of a wave?

The maximum displacement from the rest position (the height).

2. 🟢

What unit is frequency measured in?

Hertz (Hz).

3. 🟢

Do waves transfer energy or matter?

Energy (and information). Not matter.

4. Lead-in 🌊

If a wave has a frequency of 10 Hz and each wave is 2 m long, how far do you think the wave travels in 1 second?

10 waves × 2 m = 20 m per second. This is the wave speed!

1. 🟠

Define wavelength and state its unit.

Distance from one point to the same point on the next wave (e.g. crest to crest). Measured in metres (m).

2. 🟠

A wave has a frequency of 4 Hz. Calculate the period.

T = 1/f = 1/4 = 0.25 s.

3. 🟠

Explain why a duck on a pond doesn't travel with the wave.

Waves transfer energy not matter. Water particles bob up and down but don't travel forward.

4. Lead-in 🌊

If you know how many waves arrive per second (frequency) and how long each wave is (wavelength), how could you calculate the speed?

Multiply them: speed = frequency × wavelength. v = f × λ.

1. 🔵

Distinguish between a wavefront and a wavelength.

Wavefront: line joining points at the same vibration stage. Wavelength: distance between two consecutive wavefronts.

2. 🔵

A wave has T = 0.005 s. Calculate frequency.

f = 1/T = 1/0.005 = 200 Hz.

3. 🔵

Explain how a tsunami transfers energy 10,000 km without moving water that distance.

Each particle passes energy to the next by vibrating — energy is transferred through the water without the water itself travelling.

4. Lead-in 🌊

All electromagnetic waves travel at 3 × 10⁸ m/s. Radio waves have λ ≈ 1 m, visible light λ ≈ 5 × 10⁻⁷ m. Which has the higher frequency? Explain.

Visible light. If v is constant and v = fλ, then f = v/λ. Smaller λ means larger f.

⏱️ 3 min

Starter

Starter: Crack the Code 🔍

Instructions: Look at the wave data in the table. Your mission: work out the pattern that links f, λ, and v.

📝 Spot the pattern

f (Hz)	λ (m)	v (m/s)
2	3	6
5	4	20
10	0.5	5
100	0.02	2

What do you do to f and λ to get v?

Write it in your book: v = _______ _______ _______

💡 Step-by-step guide

Step 1: Look at row 1 only. f = 2, λ = 3, v = 6.

Step 2: Ask yourself: what does 2 and 3 do to make 6? Try: +, −, ×, ÷

Step 3: Check your answer works for row 2: does it also give 20?

Step 4: If yes — that's the formula! Write it down.

💡 Did You Know?

Light from the Sun takes 8 minutes 20 seconds to reach Earth — even at 3 × 10⁸ m/s! You can calculate the distance using today's formula: v × t = 3×10⁸ × 500 = 1.5 × 10¹¹ m (150 billion metres).

🌟 Stretch: Can you predict v if f = 8 Hz and λ = 0.5 m? (v = 4 m/s)

✅ The pattern: v = f × λ
Check: 2 × 3 = 6 ✅ 5 × 4 = 20 ✅ 10 × 0.5 = 5 ✅

🧠 Quick Recall (from L4)

What is the wavelength of a wave?

Try it in your head before we start. Answer: The distance from one crest to the next. Measured in metres.

⏱️ 4 min

I Do

I Do: The Wave Equation (3.5)

Key Equation: wave speed = frequency × wavelength → v = f × λ

📜 The Equation & Rearrangements

v = f × λ

f = v ÷ λ

λ = v ÷ f

v = wave speed (m/s) f = frequency (Hz) λ = wavelength (m)

✏️ Worked Example

Q: A wave has f = 5 Hz and λ = 3 m. Find v.

Step 1: v = f × λ

Step 2: v = 5 × 3

Step 3: v = 15 m/s

The vfλ Formula Triangle

Cover what you want — the rest is the formula!

Cover v → f × λ | Cover f → v ÷ λ | Cover λ → v ÷ f

🌍 Why This Matters

This one equation — v = f × λ — explains why thunder arrives after lightning (sound is slow), how radar catches speeding cars (EM waves are fast), and why submarines use sonar not radio (sound travels in water, radio doesn't). One formula, hundreds of uses.

💡 Step-by-step: 1. Write formula 2. Substitute numbers 3. Calculate 4. Write the unit (m/s, Hz, or m)

🔑 Keywords to Know

Wave speed (v)	How fast the wave travels. Measured in m/s.
Frequency (f)	Waves per second. Measured in hertz (Hz).
Wavelength (λ)	Length of one complete wave. Measured in metres.
Equation	v = f × λ (speed = frequency × wavelength).

⏱️ 5 min

We Do

We Do: Guided Wave Calculations 🧮

Instructions: Work through each question together. Type the answer and check!

👥 Think-Pair-Share: Try it yourself → discuss with your partner → agree on the answer.

1. f = 4 Hz, λ = 2 m. Find v.

2. v = 330 m/s, f = 110 Hz. Find λ.

3. v = 1500 m/s, λ = 0.5 m. Find f.

4. A sound wave: f = 256 Hz, λ = 1.3 m. Find v.

5. All EM waves: v = 3 × 10⁸ m/s, f = 1 × 10⁶ Hz. Find λ.

⏱️ 4 min

I Do

I Do: Real-World Wave Calculations

Key Context: Speed of sound in air ≈ 330 m/s. Speed of light / all EM waves ≈ 3 × 10⁸ m/s.

✏️ Sound Example

Q: A tuning fork vibrates at 440 Hz. Sound travels at 330 m/s. Find λ.

λ = v ÷ f = 330 ÷ 440 = 0.75 m

✏️ Water Wave Example

Q: A ripple tank produces waves with λ = 0.03 m at 8 Hz. Find v.

v = f × λ = 8 × 0.03 = 0.24 m/s

✏️ EM Wave Example

Q: A radio wave has λ = 1500 m. All EM waves travel at 3 × 10⁸ m/s. Find f.

f = v ÷ λ = 3 × 10⁸ ÷ 1500 = 200,000 Hz = 200 kHz

📋 Key Wave Speeds to Know

Wave Type	Speed
Sound in air	~330 m/s
Sound in water	~1500 m/s
All EM waves (light, radio, etc.)	3 × 10⁸ m/s

🌟 Exam Tip: If the question mentions "electromagnetic" or "light" — use v = 3 × 10⁸ m/s. If it says "sound in air" — use v ≈ 330 m/s. The question will always tell you or give you the speed.

⏱️ 5 min

We Do

We Do: vfλ Triangle Challenge ⚡

Instructions: The triangle covers the unknown. Calculate the answer and type it in. Get all 6!

👥 Think-Pair-Share: Try it yourself → discuss with your partner → agree on the answer.

Ready? Let's go!

Click Start to begin!

Score: 0 / 6

⏱️ 4 min · FLEX

I Do

I Do: Combining v = fλ with Definitions

Key Skill: Some questions give you period (T) instead of frequency. Use f = 1/T first, then v = fλ.

✏️ Two-Step Example

Q: A wave has T = 0.2 s and λ = 4 m. Find v.

Step 1: f = 1/T = 1/0.2 = 5 Hz

Step 2: v = f × λ = 5 × 4 = 20 m/s

✏️ Finding Period from v and λ

Q: v = 330 m/s, λ = 1.5 m. Find T.

Step 1: f = v ÷ λ = 330 ÷ 1.5 = 220 Hz

Step 2: T = 1/f = 1/220 = 0.0045 s

📋 Full Summary

Find	Formula
Wave speed	v = f × λ
Frequency	f = v ÷ λ
Wavelength	λ = v ÷ f
Period from f	T = 1 ÷ f
Frequency from T	f = 1 ÷ T

🌟 Common exam trap: They give you period instead of frequency, hoping you'll put T straight into v = fλ. Always convert T → f first using f = 1/T!

⏱️ 5 min · FLEX

We Do

We Do: Wave Detective 🔍

Instructions: Each wave card shows 2 values. Calculate the missing one. Type your answer and check!

👥 Think-Pair-Share: Try it yourself → discuss with your partner → agree on the answer.

🎵

Guitar String

f = 440 Hz

λ = 0.75 m

v = ?

m/s

🌊

Ocean Wave

v = 8 m/s

f = 0.5 Hz

λ = ?

📡

Wi-Fi Signal

v = 3×10⁸ m/s

λ = 0.12 m

f = ?

🦇

Bat Echolocation

f = 50000 Hz

v = 330 m/s

λ = ?

🔊

Bass Speaker

v = 330 m/s

λ = 5.5 m

f = ?

🏥

Ultrasound

f = 3×10⁶ Hz

v = 1500 m/s

λ = ?

Cases Solved:

0/6

⏱️ 8 min

Independent Work

Instructions: Complete the tasks in your printed pack independently.

📝 Your Pack Contains:

A: Multiple Choice (4 Qs)

B: Short Answer — calculations

C: Long Answer — explain + calculate

D: Exam-Style Question

Need help? Check the Scaffolding Sheet for the vfλ triangle and step-by-step method.

📝 Exam Command Words:
State = write a fact, no explanation needed.
Calculate = show the formula, substitute, get the answer + unit.
Explain = say what happens AND why (use "because").
Describe = say what happens step by step (no "why" needed).

🏆 Success Criteria

Foundation (Grades U–1): I can use v = f × λ to find wave speed when given f and λ.

Middle (Grades 1–2): I can rearrange v = fλ to find any unknown and apply it to sound and water waves.

Higher (Grades 3–5): I can solve two-step problems involving T and f, apply v = fλ to EM waves, and evaluate real-world scenarios.

✅ Tick as you go — Success checklist

I can write v = f × λ

I know the units for each

I can calculate v when given f and λ

I can rearrange to find f or λ (Middle/Higher)

⏱️ 3 min

Exit Ticket

Exit Ticket – Lessons 4–5 Recap

6 questions — 3 from each lesson. No notes.

🟢 I'm confident — I could teach this

🟡 I'm getting there — need a bit more practice

🔴 I'm stuck — I need help with this

1. What is the amplitude of a wave?

Maximum displacement from rest position.

2. What unit is frequency measured in?

Hertz (Hz).

3. Do waves transfer energy or matter?

Energy (and information). Not matter.

4. Write the wave speed equation.

v = f × λ

5. f = 5 Hz, λ = 2 m. Find v.

v = 5 × 2 = 10 m/s

6. What unit is wave speed measured in?

Metres per second (m/s).

Knowledge Organiser: Wave Speed Equation (L5)

How to use: Read this before starting. Refer back during independent work. Cover it up for the exit ticket — that tests what you actually remember!

Concept	Details
Wave equation	v = f × λ. Wave speed = frequency × wavelength.
v (wave speed)	How fast the wave travels. Unit: m/s.
f (frequency)	Waves per second. Unit: Hz. f = 1/T.
λ (wavelength)	Length of one complete wave. Unit: m.
Rearranged	f = v ÷ λ \| λ = v ÷ f
Sound in air	≈ 330 m/s
All EM waves	3 × 10⁸ m/s in free space (speed of light)
Period trap	If given T, convert first: f = 1/T, then use v = fλ.
Triangle	v on top, f × λ on bottom. Cover what you need.

🧠 Memory Tricks

"Very Fast Lamborghini" = v = f × λ

Sound is Slow = 330 m/s. Light is Lightning fast = 3×10⁸ m/s.

Period trap: If they give you T, ALWAYS convert to f first: f = 1/T. Then use v = fλ.

Arrival Task – Foundation (U–1) 🟢

1. What is the amplitude of a wave?

2. What unit is frequency measured in?

3. Do waves transfer energy or matter?

4. f = 10 Hz, λ = 2 m. How far does the wave travel in 1 second?

Arrival Task – Middle (1–2) 🟠

1. Define wavelength and state its unit.

2. f = 4 Hz. Calculate T.

3. Explain why a duck doesn't travel with a wave.

4. If you know f and λ, how could you calculate speed?

Arrival Task – Higher (3–5) 🔵

1. Distinguish between wavefront and wavelength.

2. T = 0.005 s. Calculate f.

3. How does a tsunami transfer energy without moving water?

4. Radio λ ≈ 1 m, light λ ≈ 5×10⁻⁷ m. Both at 3×10⁸ m/s. Which has higher f?

Starter: Build the Formula

Spot the pattern and write the formula for wave speed.

f (Hz)	λ (m)	v (m/s)
2	3	6
5	4	20
10	0.5	5
100	0.02	2

The formula is: v = _______ × _______

We Do Worksheet

Part A: Guided Calculations

#	Given	Find
1	f=4 Hz, λ=2 m	v
2	v=330, f=110 Hz	λ
3	v=1500, λ=0.5 m	f

Part B: Wave Detective

Wave	v	f	λ
🎵 Guitar	?	440 Hz	0.75 m
🌊 Ocean	8 m/s	0.5 Hz	?
🦇 Bat	330 m/s	50000 Hz	?

Scaffolding Sheet

vfλ Formula Triangle

Find	Formula	Example
Speed (v)	v = f × λ	v = 5 × 3 = 15 m/s
Frequency (f)	f = v ÷ λ	f = 330 ÷ 3 = 110 Hz
Wavelength (λ)	λ = v ÷ f	λ = 330 ÷ 110 = 3 m

Cover what you want — the rest is the formula!

Step-by-Step

1. Write formula 2. Substitute 3. Calculate 4. Unit (m/s, Hz, or m)

Period trap: If given T, find f first: f = 1/T. Then use v = fλ.

Key Speeds

Sound in air ≈ 330 m/s | All EM waves = 3 × 10⁸ m/s

Independent Work – Foundation (Grades U–1)

You've got this! Use your scaffolding sheet. Write the formula first every time. Show your working — even partial working earns marks.

Section A: Multiple Choice

1. The wave equation is… [ ] v = f + λ [ ] v = f × λ [ ] v = f ÷ λ

2. Wave speed is measured in… [ ] Hz [ ] m [ ] m/s

3. f = 10 Hz, λ = 3 m. v = … [ ] 30 m/s [ ] 13 m/s [ ] 3.3 m/s

4. The Greek letter λ stands for… [ ] Frequency [ ] Wavelength [ ] Speed

Section B: Short Answer

5. Write the wave speed equation in words and symbols.

6. Calculate v for each:

f (Hz)	λ (m)	v (m/s)
2	5
4	3
10	0.5

Section C: Long Answer (Grade 2 Challenge — scaffolded)

7. (4 marks) A sound wave has f = 256 Hz and travels at 330 m/s.

Hint: To find wavelength, use λ = v ÷ f

(a) Write the formula for wave speed. [1 mark]

(b) Which formula finds wavelength? Tick one: [1 mark]

[ ] λ = v × f [ ] λ = v ÷ f [ ] λ = f ÷ v

Section D: Exam-Style

8. (3 marks) Water waves in a ripple tank have f = 8 Hz and λ = 0.03 m.

(a) Calculate the wave speed. [2 marks]

(b) State the unit of wave speed. [1 mark]

Independent Work – Middle (Grades 1–2)

Push yourself! Show full working for every calculation. Section D is your Grade 3 stretch — give it your best shot.

Section A: Recall

1. Write v = fλ and state what each letter represents with units.

2. Rearrange v = fλ to find: (a) f = _______ (b) λ = _______

3. State the speed of sound in air.

4. State the speed of all EM waves.

Section B: Application

5. Complete the table. Show working.

v (m/s)	f (Hz)	λ (m)
?	440	0.75
330	?	1.5
1500	3000	?

Section C: Long Answer

6. (4 marks) A student counts 20 waves passing in 10 seconds. λ = 0.04 m.

(a) Calculate f. [2 marks]

(b) Calculate v. [2 marks]

Section D: Exam-Style (Grade 3 Stretch)

7. (5 marks) A radio station broadcasts at f = 200 kHz. EM waves travel at 3 × 10⁸ m/s.

(a) Convert 200 kHz to Hz. [1 mark]

(b) Calculate the wavelength. [2 marks]

Independent Work – Higher (Grades 3–5)

Aim high! Full sentences for explanations. Section D includes Grade 5 challenges — these go beyond the basics. Show the examiner you can reason, not just calculate.

Section A: Recall

1. State v = fλ and explain how to find f if given T and λ. [2 marks]

2. Explain why increasing frequency decreases wavelength when speed is constant. [2 marks]

Section B: Application

3. Complete. Show full working.

v	f	λ	T
?		4 m	0.2 s
3×10⁸	?	0.01 m
330		?	0.005 s

Section C: Long Answer

4. (5 marks) Ultrasound used in pregnancy has f = 3 MHz and travels at 1500 m/s in body tissue.

(a) Convert 3 MHz to Hz. [1 mark]

(b) Calculate λ. [2 marks]

Section D: Exam-Style (includes Grade 5 Challenge)

5. (6 marks) A student uses a ripple tank. She measures λ = 0.02 m and counts 40 waves in 8 s.

(a) Calculate f. [1 mark]

(b) Calculate v. [2 marks]

(d) Explain why the speed stayed constant even though she changed the frequency. [1 mark]

Exit Ticket – Foundation (U–1) (L4–L5 Recap)

Name: _________________________ Date: _____________

1) What is amplitude?

2) What unit is frequency?

3) Waves transfer energy or matter?

4) Write the wave speed equation.

5) f=5 Hz, λ=2 m. Find v.

6) Unit of wave speed?

Exit Ticket – Middle (1–2) (L4–L5 Recap)

1) Define wavelength + unit.

2) f=10 Hz. Find T.

3) Why doesn't a duck travel with a wave?

4) v=330, f=110. Find λ.

5) λ=0.5, v=1500. Find f.

6) Speed of all EM waves?

Exit Ticket – Higher (3–5) (L4–L5 Recap)

1) Wavefront vs wavelength?

2) T=0.002 s. Find f.

3) Tsunami energy transfer explanation.

4) T=0.2 s, λ=4 m. Find v (two steps).

5) v=3×10⁸, λ=0.01. Find f.

6) f↑ but v constant. What happens to λ?

Wave Speed Equation: v = f × λ

🖨️ Pupil Packs

⏱️ 40-Minute Pacing Guide

Arrival Task – Recall from Lesson 4

1. 🟢

2. 🟢

3. 🟢

4. Lead-in 🌊

1. 🟠

2. 🟠

3. 🟠

4. Lead-in 🌊

1. 🔵

2. 🔵

3. 🔵

4. Lead-in 🌊

Starter: Crack the Code 🔍

📝 Spot the pattern

💡 Step-by-step guide

💡 Did You Know?

🧠 Quick Recall (from L4)

I Do: The Wave Equation (3.5)

📜 The Equation & Rearrangements

✏️ Worked Example

The vfλ Formula Triangle

🌍 Why This Matters

🔑 Keywords to Know

We Do: Guided Wave Calculations 🧮

I Do: Real-World Wave Calculations

✏️ Sound Example

✏️ Water Wave Example

✏️ EM Wave Example

📋 Key Wave Speeds to Know

We Do: vfλ Triangle Challenge ⚡

I Do: Combining v = fλ with Definitions

✏️ Two-Step Example

✏️ Finding Period from v and λ

📋 Full Summary

We Do: Wave Detective 🔍

Independent Work

📝 Your Pack Contains:

🏆 Success Criteria

✅ Tick as you go — Success checklist

Exit Ticket – Lessons 4–5 Recap

Knowledge Organiser: Wave Speed Equation (L5)

🧠 Memory Tricks

Arrival Task – Foundation (U–1) 🟢

Arrival Task – Middle (1–2) 🟠

Arrival Task – Higher (3–5) 🔵

Starter: Build the Formula

We Do Worksheet

Part A: Guided Calculations

Part B: Wave Detective

Scaffolding Sheet

vfλ Formula Triangle

Step-by-Step

Key Speeds

Independent Work – Foundation (Grades U–1)

Section A: Multiple Choice

Section B: Short Answer

Section C: Long Answer (Grade 2 Challenge — scaffolded)

Section D: Exam-Style

Independent Work – Middle (Grades 1–2)

Section A: Recall

Section B: Application

Section C: Long Answer

Section D: Exam-Style (Grade 3 Stretch)

Independent Work – Higher (Grades 3–5)

Section A: Recall

Section B: Application

Section C: Long Answer

Section D: Exam-Style (includes Grade 5 Challenge)

Exit Ticket – Foundation (U–1) (L4–L5 Recap)

Exit Ticket – Middle (1–2) (L4–L5 Recap)

Exit Ticket – Higher (3–5) (L4–L5 Recap)

We Do – Class Evidence

📋 Exam Technique — Every Mark Counts!