Learn4PH1Paper 1P · Paper 1 (core content)WavesGeneral properties of waves

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General Properties of Waves

A wave transfers energy from place to place without transferring matter. In a transverse wave the vibrations are at right angles to the direction of travel; in a longitudinal wave they're along it. Every wave obeys $v=f\lambda$ . Waves reflect off barriers, refract when their speed changes, and diffract (spread out) through gaps.

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Section 1 of 14

Learning objectives

Distinguish transverse and longitudinal waves, with examples.
Define amplitude, wavelength, frequency and period, and read them from diagrams.
Use $v=f\lambda$ and $f=\dfrac1T$ .
Describe reflection, refraction and diffraction of water waves.

Pause and think

At a stadium, fans stand and sit to make a "Mexican wave" that travels all the way round. Does any fan actually travel round the stadium?

Section 2 of 14

Core idea

Start hereA Mexican wave

In a stadium wave, the wave races round the stands, yet every fan just stands up and sits down in their own seat. Nobody travels round the stadium. Waves carry energy from place to place without carrying the material along.

The big idea

$v=f\lambda$ ; $T=\frac1f$ . Transverse: vibration across the travel direction. Longitudinal: along it. Waves reflect, refract and diffract.

1. Describing a wave

A transverse wave moving to the right

time = 0.0

The wave shape travels right, but each particle of the medium just moves up and down about its rest position.

Amplitude: maximum displacement from rest.
Wavelength $\lambda$ : crest to next crest.
Frequency $f$ : waves per second (Hz).

Why

v=f\lambda

$f\text{ waves pass each second}$
Definition of frequency.
$\text{each is }\lambda\text{ long}$
Definition of wavelength.
$v=f\lambda$
Distance the wave moves per second.

v=f\lambda\qquad T=\frac1f

$v$: wave speed (m/s).
$f$: frequency (Hz).
$\lambda$: wavelength (m).
$T$: period (s).

Worked exampleWater waves

5 waves per second, crests 0.4 m apart.

Goal: Speed and period.
Strategy: Formulas.

$v=5\times0.4=2\text{ m/s}$
$f\lambda$ .
$T=\tfrac15=0.2\text{ s}$
Reciprocal.

Answer

2

m/s;

0.2

✓ Check

\lambda/T=0.4/0.2=2

✓.

2. Wave behaviour

Water waves: reflection, refraction and diffraction

Waves bounce off barriers, bunch up (shorter wavelength) when they slow down in shallow water, and spread out through a gap. Diffraction is greatest when the gap is about the size of the wavelength.

Reflection: angle in = angle out.
Refraction: speed changes, so direction changes; frequency stays the same, wavelength changes.
Diffraction: spreading through gaps; strongest when gap ≈ wavelength.

Worked exampleInto shallow water

Speed falls from 2 m/s to 1.5 m/s; $f=5$ Hz.

Goal: New wavelength.
Strategy: $f$ unchanged.

$\lambda=\frac vf=\frac{1.5}5$
Rearrange.
$=0.3\text{ m}$
Evaluate.

Answer

0.3

✓ CheckSlower wave, shorter wavelength ✓.

Common misconceptionFrequency changing Frequency is set by the source; it doesn't change on refraction.

Summary

$v=f\lambda$ ; $T=1/f$ .
Reflect, refract, diffract.

Transverse: Vibration at right angles to travel.
Longitudinal: Vibration along travel.

HistoryHertz proves Maxwell right. In

1887

Heinrich Hertz made invisible electromagnetic waves with sparks and detected them across his lab, measuring their wavelength. Asked what use they were, he said: "It's of no use whatsoever." Within

10

years, they carried the first radio messages. The unit of frequency is named after him.

Fun factTsunamis hide in deep water. In deep ocean, a tsunami travels at up to

800

km/h but may be only

1

m high, unnoticed by ships. Approaching the coast it slows down; its energy crowds into a shorter wavelength and the wave grows to many metres high.

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