C.2 Wave model

Learning objectives

—C.2.1—Transverse and longitudinal travelling waves• Distinguish transverse and longitudinal travelling waves by comparing particle or field oscillation with the direction of propagation and energy transfer.• Describe the motion of particles in a medium using displacement with position and with time.—C.2.2—Wave quantities and wave equation• Apply wavelength λ, frequency f, time period T and wave speed v to wave motion using v=fλ=λ/T.—C.2.3—Nature of sound waves• Explain sound as a mechanical longitudinal wave, including particle oscillations, compressions and rarefactions, and energy transfer through a medium.—C.2.4—Nature of electromagnetic waves• Explain electromagnetic waves as transverse oscillating electric and magnetic fields that can propagate through a vacuum.• Use the approximate wavelength orders of magnitude in the Physics data booklet without treating them as sharp boundaries.—C.2.5—Mechanical and electromagnetic wave models• Compare mechanical waves, which require a medium, with electromagnetic waves, which can travel through a vacuum.• Travelling waves transfer energy even when there is no resultant displacement of the medium.• Apply the wave model to both mechanical and electromagnetic waves.

Feature	Transverse wave	Longitudinal wave
Oscillation direction	perpendicular to propagation	parallel to propagation
Snapshot features	crests and troughs	compressions and rarefactions
Mechanical example	wave on a stretched rope	sound in air

Follow one particle, not the drawn shape

At a fixed position, a medium particle oscillates with time about equilibrium. In a position snapshot, different particles have different displacements at the same instant. The travelling pattern and energy move through the medium; the particles do not travel with the pattern.

Classification rule

Compare the particle or field oscillation direction with the propagation direction. A sinusoidal-looking graph alone does not determine whether a wave is transverse or longitudinal.

2 marks

Outline what is meant by a travelling wave.

Define the quantities

Wavelength $\lambda$ is the shortest distance between points in phase. Frequency $f$ is cycles per second, period $T$ is the time for one cycle, and amplitude is maximum displacement from equilibrium. Wave speed $v$ is the speed at which the disturbance and energy propagate.

Connect time and space

For a travelling wave, $v=f\lambda=\lambda/T$ . Use a spatial wavelength measured in metres and a temporal frequency measured in hertz; the result is in metres per second.

Read the same ideas in both wave types

For transverse waves, wavelength can be measured crest-to-crest or trough-to-trough. For longitudinal waves, measure compression-to-compression or rarefaction-to-rarefaction. In both cases the points are in phase.

Common trap

Do not use the distance from a crest to the next trough as one wavelength; that is half a wavelength. Do not confuse the speed of the medium particles with the propagation speed $v$ .

2 marks

State the wavelength and the period of the sound wave.

Sound needs a mechanical medium

Sound is produced by a vibrating source and travels through matter as a mechanical wave. In air it is longitudinal: air molecules oscillate back and forth parallel to the direction in which the disturbance and energy propagate.

Compressions and rarefactions

A compression is a region of higher particle density and pressure; a rarefaction is a region of lower density and pressure. One wavelength is the distance between neighbouring compressions or neighbouring rarefactions.

Exam-language calibration from local practice question 2

A complete description connects all four ideas: longitudinal particle motion, propagation through air, alternating compressions/rarefactions, and energy transfer away from the source.

Boundary

The air molecules oscillate locally; they are not carried from loudspeaker to listener. Sound cannot propagate through a vacuum because there are no particles to sustain the mechanical disturbance.

1 mark

The loudspeaker and the detector are now stationary and above a surface of water. The loudspeaker is at point L and the detector is at point D. L and D are at the same height above the surface of the water. The sound reaches D by two routes: along the direct path LD and the reflection-path LPD.

The following data are given:

\begin{aligned} \text { Frequency of the sound wave } & =1700 \mathrm{~Hz} \\ \text { Speed of sound in air } & =340 \mathrm{~m} \mathrm{~s}^{-1} \\ \text { Speed of sound in water } & =1500 \mathrm{~m} \mathrm{~s}^{-1} \\ \text { Distance LD } & =0.70 \mathrm{~m} \\ \text { Distance LP } & =0.50 \mathrm{~m} \end{aligned}

Calculate the wavelength of the sound wave in air.

Oscillating fields

An electromagnetic wave consists of oscillating electric and magnetic fields. The two fields are perpendicular to each other and both are perpendicular to the direction of propagation and energy transfer, so the wave is transverse.

No material medium is required

Electromagnetic fields can propagate through a vacuum. Every electromagnetic wave travels in vacuum at $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$ , with $c=f\lambda$ .

One spectrum, approximate regions

Radio, microwave, infrared, visible, ultraviolet, X-ray and gamma radiation are all electromagnetic waves. Use the approximate wavelength orders of magnitude supplied in the Physics data booklet; the named regions do not have perfectly sharp physical boundaries.

Common trap

Different spectrum regions do not have different vacuum speeds. They differ in frequency and wavelength while satisfying the same value of $c$ .

1 mark

An ultraviolet wave is travelling in a vacuum.

What is the frequency and the nature of the wave?

Wave frequency / Hz

Nature of the wave

$10^{15}$

transverse

$10{ }^{15}$

longitudinal

$10^{-7}$

transverse

$10^{-7}$

longitudinal

Feature	Mechanical wave	Electromagnetic wave
What oscillates	particles of a material medium	electric and magnetic fields
Vacuum propagation	impossible	possible
Transverse/longitudinal	may be either	transverse
Shared wave model	has $f$ , $T$ , $\lambda$ , $v$ and transfers energy	has $f$ , $T$ , $\lambda$ , $v$ and transfers energy

Energy moves without net medium displacement

In a travelling mechanical wave, particles oscillate about equilibrium and pass the disturbance onward, so energy moves even though the medium has no resultant displacement after a complete cycle. In an electromagnetic wave, oscillating fields carry energy through space.

Use the same relationship carefully

Both models obey $v=f\lambda$ , but $v$ is set by the relevant medium or, for electromagnetic waves in vacuum, by $c$ . The source frequency links the spatial pattern to how rapidly the local oscillation repeats.

Common trap

“Transfers energy” does not mean matter must travel from source to receiver. It also does not mean mechanical and electromagnetic waves have the same physical oscillator.

1 mark

An electromagnetic wave enters a medium of lower refractive index.

Three statements are made:

I. The wavelength of the wave has increased.
II. The frequency of the wave has decreased.
III. The speed of the wave has increased.

What is true about the properties of the wave?

Model the transfer

A travelling wave propagates a disturbance and transfers energy without a resultant transport of the medium. Use the local particle/field motion to describe oscillation, and the wave direction to describe propagation.

Connect the quantities

Describe waves with wavelength $\lambda$ , frequency $f$ , period $T$ , amplitude and speed $v$ , linked by $v=f\lambda=\lambda/T$ . Measure wavelength between adjacent in-phase points.

Classify the wave

Transverse oscillations are perpendicular to propagation; longitudinal oscillations are parallel. Mechanical waves require a medium, while electromagnetic waves are transverse field oscillations and travel at $c$ in vacuum.

Final check

At a boundary, identify which quantity is fixed by the source and which properties change in the new medium. Keep units consistent and distinguish propagation speed from the local oscillation speed.

Next Topic

—C.3 Wave phenomenaRead

C.2 Wave model

Learning objectives

Distinguish Transverse and Longitudinal Travelling Waves

Describe Wave Quantities

Explain the Nature of Sound Waves

Explain the Nature of Electromagnetic Waves

Compare Mechanical and Electromagnetic Wave Models

Retrieve the C.2 Wave Model

Next Topic

C.2.1 Exam Analysis

C.2.2 Exam Analysis

C.2.3 Exam Analysis

C.2.4 Exam Analysis

C.2.5 Exam Analysis