Physics · Lesson 15

Waves made easy

JAMBWAECNECO

What the syllabus asks

JAMB: types and properties of waves, wave equation, sound (speed, echo, pitch, loudness, quality), vibrations in strings and pipes, electromagnetic spectrum and uses

WAEC: production and propagation of waves, types of waves (mechanical and electromagnetic, transverse and longitudinal), wave parameters (amplitude, wavelength, frequency, period, speed), v = fλ, progressive wave equation, properties of waves (reflection, refraction, diffraction, interference, polarisation), stationary waves, sound waves, echoes, resonance in pipes and strings, electromagnetic spectrum

NECO: production and propagation of waves, types of waves (mechanical and electromagnetic, transverse and longitudinal), wave parameters (amplitude, wavelength, frequency, period, speed), v = fλ, progressive wave equation, properties of waves (reflection, refraction, diffraction, interference, polarisation), stationary waves, sound waves, echoes, resonance in pipes and strings, electromagnetic spectrum

What you will learn

Distinguish mechanical from electromagnetic, and transverse from longitudinal waves.
Define amplitude, wavelength, frequency, period and speed, and use v = fλ and T = 1/f.
Read displacement–distance and displacement–time graphs.
Explain reflection, refraction, diffraction, interference and polarisation.
Describe stationary waves and calculate with nodes and antinodes.
Explain properties of sound, solve echo problems, and analyse strings and pipes.
List the electromagnetic spectrum in order with uses and dangers.

Key points

A wave transfers energy without transferring matter; mechanical waves need a medium, EM waves do not.
Transverse: vibration ⟂ travel; longitudinal: vibration ∥ travel (compressions and rarefactions).
Amplitude, wavelength, frequency (Hz), period T = 1/f; displacement–distance shows λ, displacement–time shows T.
v = fλ; frequency is fixed by the source, speed by the medium.
y = A sin(ωt − kx): f = ω/2π, λ = 2π/k, v = ω/k; phase difference = 360° × d/λ.
All waves reflect, refract, diffract and interfere; only transverse waves can be polarised.
Constructive interference: path difference nλ; destructive: (n + ½)λ.
Stationary waves: node–node = λ/2, node–antinode = λ/4; no energy transfer.
Echo: d = vt/2; pitch ↔ frequency, loudness ↔ amplitude, quality ↔ overtones.
String: f₀ = v/2L, f ∝ √T; closed pipe f₀ = v/4L (odd harmonics); open pipe f₀ = v/2L (all harmonics); resonance tube l₂ − l₁ = λ/2.
EM order: radio, microwave, IR, visible, UV, X-ray, gamma; all at 3 × 10⁸ m/s.

Start here: What is a wave?

Drop a stone into a calm pond at the village stream. Ripples spread out in rings, and a leaf floating a metre away bobs up and down, but it does not travel to the edge of the pond. Something has moved outward — energy — while the water itself only moves up and down in place. That is the heart of every wave.

Wave: a disturbance which travels through a medium (or through space), transferring energy from one point to another without the medium itself moving along with it.

A good picture is a Mexican wave in the stands at the National Stadium. Each fan only stands up and sits down, but the "wave" runs right round the stadium. The fans are the particles of the medium; the travelling pattern is the wave.

Waves are produced by a vibrating source: a guitar string, a talking drum skin, the cone of a loudspeaker, electrons oscillating in a radio mast. The source hands energy to nearby particles, which pass it on to their neighbours, and so on.

We classify waves in two ways:

By what they need to travel: mechanical waves need a material medium (water waves, sound, waves on a rope, earthquake waves), while electromagnetic waves need no medium and can cross the vacuum of space (light, radio, X-rays). Sunlight reaches Kaduna across 150 million km of empty space; sound from the Sun never could.
By the direction of vibration: transverse or longitudinal (next sub-lesson).

A wave that moves energy steadily outward from its source is called a progressive (travelling) wave. Later we will meet stationary waves, which stay in one place.

Worked example 15.1

Classify each as mechanical or electromagnetic: (a) the sound of a generator, (b) the signal from an MTN mast, (c) a ripple on a fish pond, (d) X-rays in a hospital.

Ask: does it need a material medium? Sound and ripples do, because they are vibrations of particles.
Radio signals and X-rays are electromagnetic and need no medium.

(a) mechanical (b) EM (c) mechanical (d) EM

⚠️ Common mistake: saying "the wave carries water to the shore". A wave carries energy; the particles only oscillate about fixed positions.

Try it yourself. Why can astronauts on the Moon not talk directly to each other without radios?

Show solution

The Moon has no air. Sound is a mechanical wave and needs a medium; radio waves are electromagnetic and need none.

Continue this lesson in the free app →

Practice questions

1. A wave of frequency 25 Hz has wavelength 0.6 m. Find its speed.

Show worked answer

25 × 0.6 = 15 m/s.

2. Find the wavelength of a 1.5 MHz AM radio signal.

Show worked answer

3 × 10⁸ / 1.5 × 10⁶ = 200 m.

3. A boy hears the echo of his shout from a cliff 1.5 s later (v = 340 m/s). How far is the cliff?

Show worked answer

340 × 1.5/2 = 255 m.

4. Nodes on a vibrating string are 20 cm apart and the frequency is 150 Hz. Find the wave speed.

Show worked answer

λ = 0.4 m; v = 60 m/s.

5. For y = 0.1 sin(40πt − 0.5πx), find the frequency and wavelength.

Show worked answer

f = 20 Hz; λ = 2/0.5 = 4 m.

Key words

Wave: A disturbance that carries energy through a medium or space without carrying matter.
Mechanical wave: A wave that needs a material medium, e.g. sound, water waves.
Electromagnetic wave: A wave of oscillating electric and magnetic fields; needs no medium.
Transverse wave: Particles vibrate perpendicular to the direction of travel.
Longitudinal wave: Particles vibrate parallel to the direction of travel.
Amplitude: Maximum displacement of a particle from its rest position.
Wavelength (λ): Distance between two successive crests, or two successive particles in phase.
Frequency (f): Number of complete oscillations per second; unit hertz (Hz).
Period (T): Time for one complete oscillation; T = 1/f.
Phase: The stage a particle has reached in its cycle of vibration.
Diffraction: Spreading of waves round an obstacle or through a gap.
Interference: Superposition of two coherent waves giving reinforcement or cancellation.

Learn Waves made easy step by step, free.
The Cara's Tips app teaches every topic from the very basics, with quick checks, worked examples and exam practice. It works offline.
Open this lesson in the free app Download for Android