Properties of Waves

Throw a stone in a lake and ripples spread, but the water itself does not travel far; the shake carries energy. That is a wave. Transverse waves vibrate perpendicular to travel, longitudinal ones parallel, and speed links frequency and wavelength by v = fλ. When two waves meet, their phase difference gives constructive or destructive interference. Slide frequency, amplitude, and phase difference here to watch the waveform and interference pattern.

What is a Wave?

🌊 Intuition of a Wave

①Throw a stone in a lake — ripples spread out

②Water itself does not travel; the "vibration" is transmitted

③A wave = a vibration in one place transmitting energy outward

④Important: the medium (water) only vibrates in place, it does not move!

Classification

ChartTransverse vs Longitudinal

Item	Transverse	Longitudinal
Direction of vibration	Perpendicular to propagation	Parallel to propagation
Examples	Light, string waves, EM waves	Sound, spring waves
Medium required	EM waves: not needed	Required (sound)
Features	Polarization possible	Compressions/rarefactions repeat

Transverse Waves and v = fλ

Frequency f5 Hz

Amplitude A5

Wave Speed

v = fλ

Wave speed (m/s) = frequency (Hz) × wavelength (m)

💡 Why v = fλ

①f vibrations per second → f waves created in 1 s

②Each wave has length λ

③So the distance a wave travels in 1 s = f × λ = v

④v is set by the medium! Changing f or A does not change v

Superposition and Interference

Phase shift (°)0°

Period and Frequency

T = 1f

Period (s) = 1/frequency (Hz) — time for one vibration

🔑 Principle of Superposition

①When two waves meet, displacements add (superposition)

②Same phase (0°) → constructive: amplitude doubles

③Opposite phase (180°) → destructive: amplitude 0

④After the waves pass, the medium returns to its original shape

Four Properties of Waves

🔄 Reflection · Refraction · Interference · Diffraction

①Reflection: wave bounces back at a boundary (angle in = angle out)

②Refraction: speed changes in a new medium → direction bends

③Interference: two waves meet → constructive or destructive

④Diffraction: wave bends around obstacles (larger λ → more bending)

⑤These four are common to all waves!

Worked Examples

Example 1

What is the speed of a wave with frequency 50 Hz and wavelength 4 m?

Use the wave speed equation v = fλ.

v = fλ

Substitute f = 50 Hz, λ = 4 m.

v = 50 × 4 = 200 m/s

▸ 200 m/s

v = fλ is the most basic wave equation. Multiplying frequency (Hz) by wavelength (m) gives speed (m/s).

Example 2

A sound wave travels at 340 m/s with a period of 0.002 s. What is its wavelength?

First find the frequency: f = 1/T.

f = 1T = 10.002 = 500 Hz

From v = fλ, compute λ = v/f.

λ = vf = 340500 = 0.68 m

▸ 0.68 m

When the period T is given, find the frequency with f = 1/T first, then substitute into v = fλ.

Summary

Wave Core Formula

v = fλ = λ/T

Speed = frequency × wavelength = wavelength / period

CSAT-style

If the frequency of a wave in the same medium is doubled, how does the wavelength change?

①Doubles

②Quadruples

③Stays the same

④Halves

⑤Becomes one quarter

▸ ④ Halves

In the same medium the speed v is constant; v = fλ is fixed.

v = fλ = constant

If f doubles, λ is inversely proportional and halves.

λ = vf ⇒ f×2 ⇒ λ÷2

🎯 Exam Points

①v = fλ: speed = frequency × wavelength (must memorize!)

②Wave speed is set by medium — independent of f or A

③Transverse: vibration⊥propagation (light); longitudinal: vibration∥propagation (sound)

④Superposition: total displacement = sum of individuals

⑤Universal wave properties: reflection, refraction, interference, diffraction

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Light and EM Waves

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