Grade 8 · Unit 4 · Mechanical Waves

Why does sound
travel?

⚡ You see lightning. Then — 8 seconds later — you hear thunder.

They happened at the exact same moment. So why the delay? What does this tell us about how energy moves?

E2 · Explore

Discover it yourself

No formulas yet. Just drag the sliders and watch what happens. Try to figure out the relationship between these three mystery quantities before moving on.

Mystery Controls — what do you notice?

🔵 Mystery A5.0
🟠 Mystery B2.0
🟣 Mystery C343

What do you notice about these hidden results?

Result X
0.50
Result Y
171.5
Result Z
25.0

Live Wave Shape

↕ Changes with Mystery A ← → Cycles change with Mystery B
E3 · Explain

The Formula Reference

Now that you've seen the patterns, here are the names and formulas. Notice how they match what you discovered above.

Wave Speed
v = f × λ
v = speed (m/s) · f = frequency (Hz) · λ = wavelength (m)
Frequency ↔ Period
f = 1 / T
f = frequency (Hz) · T = period (s) · They are reciprocals
Period
T = 1 / f
T = time for one full cycle · f = frequency
Wavelength
λ = v / f
λ = wavelength (m) · v = speed · f = frequency
Energy & Amplitude
E ∝ A²
Double the amplitude → 4× the energy
Distance (d = vt)
d = v × t
d = distance (m) · v = speed · t = time (s)
Speed of Sound
343 m/s
In dry air at 20°C. The answer to the lightning mystery!
Wave Types
T vs L
Transverse: vibration ⊥ travel (light, water) · Longitudinal: vibration ∥ travel (sound)
💡 Back to the mystery:

Lightning and thunder happen simultaneously. Light reaches you almost instantly (3×10⁸ m/s). Sound travels at only 343 m/s. Using d = v × t: 343 × 8 = 2,744 metres away. That's the power of wave speed!

E3 · Wave Types

Transverse vs. Longitudinal

The direction particles vibrate relative to the wave's travel defines everything. Master this distinction — it appears in every wave question.

Transverse vibration ⊥ direction of travel

Particles move up and down (perpendicular) while the wave energy travels horizontally. Think of a rope being flicked — each point rises and falls while the pulse moves forward.

Key features
Crest
Highest point above equilibrium
Trough
Lowest point below equilibrium
Amplitude
Max displacement from centre
Wavelength λ
Crest to next crest
Real-world examples
🌊
Water waves
Surface ripples — water moves up/down, wave travels outward
💡
Light (electromagnetic)
Electric & magnetic fields oscillate perpendicular to direction
🎸
Guitar string vibration
String moves up/down while wave travels along its length
🌍
Seismic S-waves
Secondary earthquake waves — shake ground side to side
Ahmad's Note:

"We rise and fall, yet we stay grounded — transferring energy forward without moving from our position."

Live simulation — Transverse wave
Each ● dot represents a particle.
Notice: dots move up and down while the wave travels left to right →
Quick comparison
Transverse Longitudinal
Vibration direction ⊥ perpendicular ∥ parallel
Features Crests & troughs Compression & rarefaction
Examples Light, water, strings Sound, ultrasound, P-waves
Needs medium? Not always Always
✦ Quick check — wave type identification
E4 · Elaborate

Apply & Challenge

Each problem comes with a live simulation. Study the wave, then solve. Watch out — one question contains a common misconception trap!

Problem 01 · Fill in the blank · Wave Speed
The wave above has a frequency of 4 Hz and a wavelength of 2 m.
Calculate the wave speed using v = f × λ
m/s
Problem 02 · Fill in the blank · Period
The wave above completes 5 full cycles per second.
Find its period using T = 1 / f
s
Problem 03 · Drag & Drop · Match the formula
Drag each formula to the correct description.
v = f × λ
T = 1 / f
λ = v / f
E ∝ A²
Calculates how fast a wave travels
Drop here
Time for one complete cycle
Drop here
Distance between two crests
Drop here
Energy depends on this wave property
Drop here
⚠ Common Misconception Trap
Problem 04 · Multiple Choice · Think carefully!
Wave A has a larger amplitude than Wave B. Both waves travel in the same medium.
Which statement is TRUE?
AWave A travels faster because it has more energy
BBoth waves travel at the same speed — amplitude doesn't affect speed
CWave A has a longer wavelength
DWave B carries more energy because it's faster
Problem 05 · Fill in the blank · Storm Distance
You see lightning. Thunder arrives 9 seconds later. Speed of sound = 343 m/s.
How far is the storm? Use d = v × t
km
Bonus · Open Question · AI Tutor
A doctor uses ultrasound (v = 1540 m/s, f = 3.5 MHz) to scan a patient.
What is the wavelength? What type of wave is ultrasound and why? What happens to wavelength if the doctor increases the frequency?
E5 · Evaluate

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