What does Wave Model cover in IB Physics?

This topic covers the fundamental properties and characteristics of travelling waves, including their classification and how they transfer energy. Waves can be classified as transverse or longitudinal. Key wave properties are wavelength λ, frequency f, time period T, and wave speed v.

Is Wave Model SL or HL?

Both. SL and HL students study Wave Model to the same depth.

How does FourtyFive help me practise Wave Model?

FourtyFive has 20 Wave Model questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

Is FourtyFive free for Wave Model practice?

Yes. A free account gives you 50 marked answers a month, and you do not need a card to sign up.

Can I handwrite Wave Model answers on an iPad?

Yes. In the FourtyFive iPad app you write your working by hand with Apple Pencil, the way you would on paper, and it is marked the same way.

Topic C.2 · SL and HL

Wave Model: notes and practice questions

Q: How do I revise Wave Model for IB Physics?

Start from the core idea: this topic covers the fundamental properties and characteristics of travelling waves, including their classification and how they transfer energy. In the exam: mostly a supporting subtopic: a one-mark v = fλ step inside a longer wave question. May 2025 Paper 2 TZ1 asked, at both levels, for one difference between sound and electromagnetic waves (1 mark, "1 max" from three acceptable marking points) and then a straight calculate the wavelength of a 1700 Hz sound in air (1 mark). Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

10 min read Jump to 20 practice questions

Summary

This topic covers the fundamental properties and characteristics of travelling waves, including their classification and how they transfer energy.
Waves can be classified as transverse or longitudinal.
Key wave properties are wavelength $\lambda$ , frequency $f$ , time period $T$ , and wave speed $v$ .
The wave speed is given by $v = f\lambda = \frac{\lambda}{T}$ .
Sound waves are mechanical, longitudinal waves that require a medium for propagation.
Electromagnetic waves are transverse waves that can travel through a vacuum.
Travelling waves transfer energy without a net displacement of the medium.
The motion of particles in a medium due to a wave can be described by displacement over time.

How it is examined

Mostly a supporting subtopic: a one-mark $v = f\lambda$ step inside a longer wave question. May 2025 Paper 2 TZ1 asked, at both levels, for one difference between sound and electromagnetic waves (1 mark, "1 max" from three acceptable marking points) and then a straight calculate the wavelength of a 1700 Hz sound in air (1 mark). Displacement-position and displacement-time graph reading is the other common shape.

Given in the booklet

$v = f\lambda = \lambda/T$ , the speed of light c, and the electromagnetic spectrum with approximate wavelength orders of magnitude. Students do not have to recall that visible light is around 400 to 700 nm, but they do have to read the booklet's table to find it.

Key ideas

transverse and longitudinal travelling waves
wavelength $\lambda$ , frequency f, time period T and wave speed v applied to wave motion, as given by $v = f\lambda = \dfrac{\lambda}{T}$
the nature of sound waves
the nature of electromagnetic waves

Guiding questions

What are the similarities and differences between different types of waves?
How can the wave model describe the transmission of energy as a result of local disturbances in a medium?
What effect does a change in the frequency of oscillation or medium through which the wave is travelling have on the wavelength of a travelling wave?

Linking questions

How can light be modelled as an electromagnetic wave?
What happens when waves overlap or coincide?
How can the length of a wave be determined using concepts from kinematics?
Why does the intensity of an electromagnetic wave decrease with distance according to the inverse square law?
How are electromagnetic waves able to travel through a vacuum?
How were X-rays discovered? (NOS)
Can the wave model inform the understanding of quantum mechanics? (NOS)
How are waves used in technology to improve society? (NOS)

Practice questions

20 questions · 7 easy · 13 medium

Showing 20 of 20

Question 1

EasyPaper 2 · calculator4 marks

A teacher demonstrates two types of mechanical waves using a long slinky spring stretched out on a smooth floor.

Demonstration 1: The teacher pushes and pulls the end of the slinky back and forth, parallel to the length of the spring. This creates a series of compressions and rarefactions.

Demonstration 2: The teacher moves the end of the slinky up and down, perpendicular to the length of the spring. This creates a series of crests and troughs.

(a) Discuss the similarities and differences between the two waves produced in the demonstrations.

Question 2

MediumPaper 1A · calculator1 mark

A small particle attached to a vibrating speaker cone oscillates with simple harmonic motion. The variation with time $t$ of the displacement $d$ of the particle from its equilibrium position is shown.

Graph showing displacement d/mm on y-axis from -8.0 to 8.0, and time t/ms on x-axis from 0 to 3.0. A sinusoidal wave is shown, starting at d=0, going up to 8.0, down to -8.0, and back to 0 at t=2.5 ms.

What is the frequency and the amplitude of the particle's oscillation?

	Frequency/Hz	Amplitude/mm
A.	$0.40$	$8.0$
B.	$400$	$8.0$
C.	$0.40$	$16.0$
D.	$400$	$16.0$

Question 3

EasyPaper 1A · calculator1 mark

An X-ray is travelling through the air.

What is a possible frequency and what is the nature of the wave?

Wave frequency / $\text{Hz}$	Nature of the wave
A. $10^{18}$	transverse
B. $10^{18}$	longitudinal
C. $10^{-10}$	transverse
D. $10^{-10}$	longitudinal

Question 4

MediumPaper 2 · calculator7 marks

(a)

An earthquake generates seismic waves. A seismograph, located $50 \text{ km}$ from the earthquake's epicentre, records the vertical displacement of the ground. The graph shows the displacement due to the arrival of the primary (P) wave. Time is measured from the instant the earthquake occurs.

Displacement-time graph for a P-wave showing a sinusoidal wave starting at t=10s, with amplitude 2.5 cm and period 0.5s

(a) Determine the amplitude of the P-wave.

[1]

(b)

(b) Calculate the speed of the P-wave.

[2]

(c)

[2]

(d)

(d) Calculate the wavelength of the P-wave.

[2]

Question 5

EasyPaper 1A · calculator1 mark

A sensor records the displacement of a point on a vibrating guitar string as a sound wave propagates. The variation with time $t$ of the displacement $d$ of this point is shown.

Displacement-time graph for a vibrating guitar string. The displacement d/cm ranges from -3.0 to 3.0. The time t/ms ranges from 0 to 10.0. The graph shows one complete oscillation from t=0 to t=8.0 ms, with amplitude 3.0 cm.

What is the frequency and the amplitude of the vibration?

	Frequency/Hz	Amplitude/cm
A.	$125$	$3.0$
B.	$125$	$6.0$
C.	$8.0 \times 10^{-3}$	$3.0$
D.	$8.0 \times 10^{-3}$	$6.0$

Question 6

MediumPaper 1A · calculator1 mark

A musician plucks a guitar string, generating a transverse wave. The wave has an amplitude of $2.5$ cm, a wavelength of $40.0$ cm, and a frequency of $100$ Hz.

What is the average speed of a particle on the string and the direction of its motion relative to the direction of wave propagation during one full oscillation?

Average speed of particle / $\text{m s}^{-1}$ | Direction of particle motion

---|---

A. $10$ | parallel

B. $40$ | perpendicular

C. $40$ | parallel

D. $10$ | perpendicular

Question 7

EasyPaper 1A · calculator1 mark

A ray of monochromatic light travels from air and enters a block of glass. Part of the light is refracted.

Three statements are made about the refracted light compared to the incident light.

I. The speed of the light is different.

II. The frequency of the light is different.

III. The wavelength of the light is different.

Which of the statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Question 8

MediumPaper 2 · calculator6 marks

(a)

A sound engineer is designing a set of organ pipes, each closed at one end. The speed of sound in the concert hall is measured to be $343\ \text{m s}^{-1}$ . One particular pipe is designed to resonate at its fundamental frequency when a sound wave of frequency $440\ \text{Hz}$ is introduced.

(a) Calculate the wavelength of the sound wave produced by the $440\ \text{Hz}$ source.

[2]

(b)

(b) The organ pipe can be adjusted in length to be between $0.30\ \text{m}$ and $1.50\ \text{m}$ . Determine all possible lengths of the pipe for which it would resonate with the $440\ \text{Hz}$ sound wave.

[4]

Question 9

EasyPaper 1A · calculator1 mark

A remote control for a television emits electromagnetic radiation to send signals. The wavelength of this radiation is slightly longer than that of red light.

What region of the electromagnetic spectrum does this radiation belong to?

A. Microwaves

B. Infrared

C. Ultraviolet

D. Radio waves

Question 10

MediumPaper 2 · calculator11 marks

(a)(i)

In a geological survey, a controlled explosion on the surface generates seismic waves that travel through the Earth's crust. Two types of waves are produced: primary (P-waves) and secondary (S-waves). In a particular region of granite bedrock, P-waves travel at a speed of $6.0 \times 10^3 \text{ m s}^{-1}$ and S-waves travel at $3.5 \times 10^3 \text{ m s}^{-1}$ .

(a) (i) Outline the nature of P-waves.

[2]

(a)(ii)

(ii) Outline the nature of S-waves.

[2]

(b)(i)

(b) (i) The explosion generates P-waves with a dominant frequency of $50 \text{ Hz}$ . Calculate the wavelength of these P-waves.

[2]

(b)(ii)

(ii) A particular component of the S-waves has a wavelength of $40 \text{ m}$ . Calculate the frequency of these S-waves.

[2]

(c)

(c) A seismograph station detects the arrival of the P-waves first, followed by the S-waves. The time interval between the arrival of the two wave types is $15 \text{ s}$ . Estimate the distance from the explosion to the seismograph station.

[3]

Question 11

EasyPaper 1A · calculator1 mark

An electromagnetic wave has a wavelength that is about the size of the head of a pin.

What region of the electromagnetic spectrum does the wave belong to?

A. Ultraviolet

B. Visible light

C. Infrared

D. Radio waves

Question 12

MediumPaper 1A · calculator1 mark

A beam of monochromatic light of intensity $I$ is incident on a metal plate. The source of light is changed. The wavelength of the new light is tripled. The number of photons incident on the plate per unit area per unit time is increased by a factor of six.

What is the new intensity of the light beam?

A. $\frac{I}{3}$

B. $2I$

C. $6I$

D. $18I$

Question 13

EasyPaper 1A · calculator1 mark

An electromagnetic wave has a wavelength that is approximately equal to the diameter of a typical human red blood cell.

What region of the electromagnetic spectrum does this wave belong to?

A. Radio waves

B. Microwaves

C. Infrared

D. Ultraviolet

Question 14

MediumPaper 1A · calculator1 mark

A geophone detects a transverse seismic wave propagating through the ground. The wave has a period of $1.0$ ms. The graph shows the instantaneous vertical displacement of the ground particles against the horizontal distance from the geophone at a specific moment.

Graph of displacement versus distance for a transverse wave. Y-axis: Displacement (mm), X-axis: Distance (cm). The wave shows an amplitude of 2.0 mm and a wavelength of 4.0 cm.

What is the average speed of the ground particles and the direction of particle motion relative to the direction of the wave travel during one cycle?

A. $8.0$ m s $^{-1}$ parallel

B. $8.0$ m s $^{-1}$ perpendicular

C. $10.0$ m s $^{-1}$ parallel

D. $10.0$ m s $^{-1}$ perpendicular

Question 15

MediumPaper 1A · calculator1 mark

The diagram shows a snapshot of a transverse wave propagating along a stretched string. The wave travels from right to left.

Graph of displacement y versus position x for a wave on a string. Points A, B, C, D are marked on the wave. Point A is at a crest, B is at the equilibrium position with a negative slope, C is at a trough, D is at the equilibrium position with a positive slope.

At the instant shown, which point on the string has the maximum positive acceleration?

Question 16

MediumPaper 1A · calculator1 mark

The graph shows a snapshot of a transverse wave on a string. The wave is travelling from right to left (in the negative $x$ direction).

Graph of displacement versus position x for a transverse wave. The wave is sinusoidal. Point P is at a crest. Point Q is at the next equilibrium position after P. Point R is at the next trough. Point S is at the next equilibrium position after R.

At this instant, which point has the maximum negative velocity?

A. P

B. Q

C. R

D. S

Question 17

MediumPaper 1A · calculator1 mark

A monochromatic light source illuminates a diffraction grating in air, producing a pattern of principal maxima on a distant screen. A total of 11 principal maxima are observed.

The diffraction grating and the screen are then submerged in water (refractive index $n=1.33$ ). The light source remains in the air, and the beam enters the water before reaching the grating.

What are the changes, if any, to the angular separation of the principal maxima and the total number of principal maxima observed?

Option	Angular separation of maxima	Total number of maxima
A	Decreases	Increases
B	Decreases	Decreases
C	Increases	Increases
D	Increases	Decreases

A. A

B. B

C. C

D. D

Question 18

MediumPaper 1A · calculator1 mark

A loudspeaker S emits sound with a power $P$ . An observer at a distance $r$ from S measures a sound intensity $I$ .

A second loudspeaker T has a power of $\frac{P}{9}$ .

At what distance from T will an observer measure the same sound intensity $I$ ?

A. $9r$

B. $3r$

C. $\frac{r}{3}$

D. $\frac{r}{9}$

Question 19

MediumPaper 1A · calculator1 mark

A longitudinal wave travels through a fluid to the right. The graph shows the variation of the displacement $s$ of the fluid particles with position $x$ along the wave at time $t = 0$ .

Positive values of $s$ represent displacements to the right and negative values represent displacements to the left.

Graph of displacement s in mm versus position x in m. The curve starts at 0 at x = 0, reaches a positive crest of +2.0 mm at x = 0.4 m, crosses zero at x = 0.8 m, reaches a negative trough of -2.0 mm at x = 1.2 m, crosses zero at x = 1.6 m, and reaches a crest at x = 2.0 m.

At which position is there a rarefaction at $t = 0$ ?

A. $0.4\text{ m}$

B. $0.8\text{ m}$

C. $1.2\text{ m}$

D. $1.6\text{ m}$

Question 20

MediumPaper 1A · calculator1 mark

A sound wave travels through a medium with a frequency of $400 \text{ Hz}$ . The shortest distance between two points on the wave that have a phase difference of $90^\circ \left( \frac{\pi}{2} \text{ rad} \right)$ is $0.10 \text{ m}$ . What is the speed of the sound wave?

A. $40 \text{ m s}^{-1}$

B. $80 \text{ m s}^{-1}$

C. $160 \text{ m s}^{-1}$

D. $240 \text{ m s}^{-1}$

Every Wave Model question, marked for you

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Wave Model: notes and practice questions

How it is examined

Guiding questions

Linking questions