Waves, Sound & Light — Science Sage

What is a Wave?

A wave is a disturbance that transfers energy through a medium (or through space for electromagnetic waves) without transferring matter. The material through which the wave travels is called the medium.

Pulse: a single disturbance moving through a medium (e.g. flicking a rope once).
Continuous wave: a regular, repeated disturbance (e.g. shaking a rope up and down continuously).

Key Idea: Waves transfer energy, not matter. The medium particles vibrate around their rest positions — they don't travel with the wave.

Transverse Waves

In a transverse wave, particles vibrate perpendicular to the direction of wave travel. Examples: light, water surface waves, waves on a string.

Crest: highest point above rest position
Trough: lowest point below rest position
Amplitude (A): maximum displacement from rest; measured in metres (m)
Wavelength (λ): distance between two consecutive identical points (e.g. crest to crest); unit: metres (m)
Rest position: the undisturbed position of the medium

Longitudinal Waves

In a longitudinal wave, particles vibrate parallel to the direction of wave travel. Sound is the most important example. Longitudinal waves cannot travel through a vacuum — they need a medium.

Compression: region where particles are bunched together (high pressure)
Rarefaction: region where particles are spread apart (low pressure)

Remember: Sound cannot travel through a vacuum because there are no particles to compress and rarefy.

Wave Properties and Equations

Quantity	Symbol	Unit	Definition
Amplitude	A	m	Max displacement from rest
Wavelength	λ (lambda)	m	Length of one complete wave
Frequency	f	Hz (hertz)	Number of complete waves per second
Period	T	s	Time for one complete wave
Wave speed	v	m/s	Distance travelled per second

T = 1/f v = f × λ

Example: f = 200 Hz, λ = 1.7 m → v = 200 × 1.7 = 340 m/s

Sound Waves

Sound is a longitudinal pressure wave that requires a medium. Its speed depends on the properties of the medium:

Sound travels fastest in solids, then liquids, then gases (slowest)
Speed in air ≈ 340 m/s at 20°C
Pitch is determined by frequency (higher f → higher pitch)
Loudness is determined by amplitude (larger A → louder)
Quality (timbre) is determined by the waveform shape

Echo: reflection of sound off a hard surface. Used in sonar (mapping ocean floor) and ultrasound (medical imaging, typically 1–20 MHz, above human hearing range of 20–20,000 Hz).

IEB Extension — Doppler Effect

When a source of sound moves relative to an observer, the observed frequency differs from the emitted frequency. Moving toward each other → higher pitch; moving apart → lower pitch.

f_o = f_s × (v ± v_o) / (v ∓ v_s)

v = speed of sound; v_o = speed of observer; v_s = speed of source. Use + for approach, − for recession (top/bottom swap accordingly).

Light — Electromagnetic Waves

Light is a transverse electromagnetic wave. It does not require a medium and travels at c = 3 × 10⁸ m/s in a vacuum. Visible light has wavelengths from approximately 400 nm (violet) to 700 nm (red).

Reflection of Light

When light strikes a surface, it bounces off according to the Law of Reflection:

Angle of incidence = Angle of reflection (both measured from the normal to the surface)

A plane mirror forms an image that is: virtual, upright, laterally inverted, the same size as the object, and the same distance behind the mirror as the object is in front.

Refraction of Light

Refraction is the bending of light as it crosses the boundary between two media with different optical densities. The speed of light changes, causing the direction to change (unless it hits the boundary at 90°).

The refractive index of a medium:

n = c / v

where c = speed of light in vacuum, v = speed in the medium. A higher n means slower light and more bending.

Snell's Law relates the angles at a boundary:

n₁ sin θ₁ = n₂ sin θ₂

Light bends toward the normal when entering a denser medium (higher n) and away from the normal when entering a less dense medium.

Total Internal Reflection

When light travels from a denser to a less dense medium, if the angle of incidence exceeds the critical angle (θ_c), all light is reflected back into the denser medium — no refraction occurs.

n₁ sin θ_c = n₂ (when n₂ = 1 for air: sin θ_c = 1/n₁)

Applications: optical fibres (data transmission, endoscopes), diamond cutting, periscopes using prisms.

Dispersion

White light is a mixture of all visible wavelengths. When it passes through a prism, different wavelengths refract by different amounts (violet bends most, red least), splitting white light into a spectrum: ROYGBIV.

IEB Extension — Huygens' Principle & Thin Lenses

Huygens' Principle: every point on a wavefront acts as a source of secondary wavelets; the new wavefront is the envelope of all secondary wavelets. Explains diffraction and refraction geometrically.

Thin Lens Equation:

1/f = 1/d_o + 1/d_i m = −d_i/d_o

f = focal length; d_o = object distance; d_i = image distance; m = magnification. Converging lens: f > 0. Diverging lens: f < 0.

Wave & Optics Simulator

Simulation Mode

Controls

Frequency 2.0 Hz

Amplitude 35 px

Wavelength λ

— m

Wave Speed v

— m/s

Period T

— s

Frequency f

— Hz

Question 1 — Wave Equation

A wave has a frequency of 5 Hz and a wavelength of 2 m. What is its speed?

Correct! v = f × λ = 5 × 2 = 10 m/s.

Not quite. Use v = f × λ: 5 Hz × 2 m = 10 m/s.

Question 2 — Wave Types

Which of the following is a longitudinal wave?

Correct! Sound is a longitudinal wave — particles vibrate parallel to the direction of propagation.

Not quite. Light, guitar strings, and water ripples are transverse. Sound is longitudinal.

Question 3 — Sound Properties

A sound wave has a period of 0.004 s. What is its frequency and what property of sound does a higher frequency affect?

Correct! f = 1/T = 1/0.004 = 250 Hz. Higher frequency → higher pitch.

f = 1/T = 1/0.004 = 250 Hz. Frequency determines pitch; amplitude determines loudness.

Question 4 — Reflection

A ray of light strikes a plane mirror at an angle of 35° to the mirror surface. What is the angle of reflection (measured from the normal)?

Correct! Angle from surface = 35°, so angle from normal = 90° − 35° = 55°. By law of reflection, angle of reflection = 55°.

Angles are measured from the normal. If the ray is 35° from the mirror surface, it is 55° from the normal. The angle of reflection equals the angle of incidence = 55°.

Question 5 — Snell's Law

Light travels from water (n = 1.33) into air (n = 1.00) at an angle of incidence of 30°. What is the angle of refraction?

Correct! n₁sinθ₁ = n₂sinθ₂ → 1.33 × sin30° = 1.00 × sinθ₂ → sinθ₂ = 0.665 → θ₂ ≈ 41.7°. Light bends away from normal when entering less dense medium.

Apply Snell's Law: 1.33 × sin30° = 1.00 × sinθ₂ → sinθ₂ = 1.33 × 0.5 = 0.665 → θ₂ = sin⁻¹(0.665) ≈ 41.7°.

Question 6 — Total Internal Reflection

Glass has a refractive index of 1.5. What is the critical angle for a glass–air boundary?

Correct! sinθ_c = n₂/n₁ = 1/1.5 = 0.667 → θ_c = sin⁻¹(0.667) ≈ 41.8°.

Use sinθ_c = 1/n = 1/1.5 = 0.667 → θ_c = sin⁻¹(0.667) ≈ 41.8°.

Question 7 — Echo Sounding (Analysis)

A ship's sonar sends a sound pulse straight down toward the sea floor. The pulse returns to the ship's detector 4 seconds after it was sent. Sound travels at 1500 m/s in seawater. Calculate the depth of the sea floor below the ship.

Correct! The key insight is that the 4 seconds covers the ROUND TRIP — down to the sea floor AND back up to the ship. Total distance travelled by the pulse = speed × time = 1500 × 4 = 6000 m. Since this is there-and-back, the depth is only half of that: 6000 ÷ 2 = 3000 m.

Don't forget the pulse makes a ROUND TRIP: down to the sea floor and back up again. Total distance = speed × time = 1500 × 4 = 6000 m. This is twice the depth, so depth = 6000 ÷ 2 = 3000 m.

Question 8 — Critical Angle Between Two Non-Air Media (Analysis)

Light travels from glass (n = 1.50) into water (n = 1.33) — note that neither medium is air. Calculate the critical angle for this glass-water boundary.

Correct! The critical angle formula n₁sinθ_c = n₂ (light going from the denser medium, n₁ = 1.50, toward the less dense medium, n₂ = 1.33) gives sinθ_c = n₂/n₁ = 1.33/1.50 = 0.887 → θ_c = sin⁻¹(0.887) ≈ 62.5°. The critical angle formula works for ANY two media where light moves from a denser (n₁) to a less dense (n₂) medium — it does not require one of them to be air; 41.8° would be the (wrong) answer if you mistakenly assumed the second medium was air.

The critical angle condition is n₁sinθ_c = n₂, where n₁ is the denser medium the light starts in (glass, 1.50) and n₂ is the less dense medium (water, 1.33) — air does not need to be involved at all. sinθ_c = 1.33/1.50 = 0.887 → θ_c ≈ 62.5°.

IEB Extension Practice IEB ONLY

IEB Question 1 — Doppler Effect

An ambulance emits a siren at 800 Hz and moves toward a stationary observer at 30 m/s. The speed of sound is 340 m/s. What frequency does the observer hear?

Correct! f_o = f_s × v/(v − v_s) = 800 × 340/(340 − 30) = 800 × 340/310 ≈ 873 Hz. Source approaching → frequency increases.

f_o = f_s × v/(v − v_s) = 800 × 340/310 ≈ 873 Hz. The observer is stationary (v_o = 0); source moves toward observer so denominator decreases, increasing frequency.

IEB Question 2 — Critical Angle & Optical Fibres

An optical fibre core has n = 1.62. What is the critical angle, and why must light hit the core-cladding boundary at an angle greater than this value for the fibre to work?

Correct! sinθ_c = 1/1.62 = 0.617 → θ_c ≈ 38.1°. When light hits the boundary at angles greater than θ_c, total internal reflection occurs, keeping all light inside the fibre core for lossless transmission.

sinθ_c = 1/n = 1/1.62 ≈ 0.617 → θ_c ≈ 38.1°. For total internal reflection (needed in optical fibres), incidence angle must exceed θ_c so no light escapes into the cladding.

Complete these questions in your notebook. Show all working for calculation questions. Draw clearly labelled diagrams where requested.

Question 1 — Wave Equation Calculation

A radio station broadcasts at a frequency of 94.5 MHz. The speed of electromagnetic waves is 3 × 10⁸ m/s. Calculate the wavelength of the radio waves. Show all working including the formula used, substitution, and units in your answer.

Question 2 — Snell's Law Calculation

A ray of light passes from air (n₁ = 1.00) into a glass block (n₂ = 1.52) at an angle of incidence of 45°.
(a) Calculate the angle of refraction inside the glass.
(b) State whether the refracted ray bends toward or away from the normal, and explain why.
(c) Calculate the speed of light inside the glass block.

Question 3 — Reflection Diagram

Draw a clearly labelled diagram showing a ray of light striking a plane mirror at an angle of 40° to the normal. Include: the incident ray, the normal, the reflected ray, the angle of incidence, and the angle of reflection. State the law of reflection and explain how it applies to your diagram.

Question 4 — Total Internal Reflection

Diamond has a refractive index of 2.42.
(a) Calculate the critical angle for diamond in air.
(b) Explain what total internal reflection is and the two conditions required for it to occur.
(c) Explain why diamonds are cut with many facets (flat surfaces at specific angles).

Question 5 — Sound Properties

A tuning fork produces a sound wave with a frequency of 440 Hz (musical note A). The speed of sound in air is 340 m/s.
(a) Calculate the wavelength of this sound wave.
(b) Calculate the period of this wave.
(c) If the amplitude of the wave is increased, what property of the sound changes? Explain.
(d) Explain why this sound cannot be heard in outer space.