Wave model HL Paper 1&2

C.2 Wave Model Papers 1&2

Extended Question Bank: Multiple Choice and Extended Responses

These original IB-style practice questions are not official IB examination questions. Show your working, include units and explain your reasoning. Attempt each question before opening its answer.

Instructions

Use $v=f\lambda$ and $f=\frac{1}{T}$ where appropriate.
Give numerical answers to 2–3 significant figures unless stated otherwise.
Convert lengths and times to consistent units before substituting.
Distinguish wave speed from particle speed.
For graphs, check whether the horizontal axis is distance or time.
Assume linear waves and stationary boundaries unless stated otherwise.

Part A — Multiple-Choice Questions

A1 — Energy transfer

Which statement best describes an ideal travelling wave?

A. It transports every particle of the medium from source to receiver.
B. It always requires a material medium.
C. It transfers matter without transferring energy.
D. It transfers energy without net transport of matter.

Show answer and explanation

Answer: D. In the ideal wave model, the disturbance carries energy while particles of a medium oscillate locally. Electromagnetic waves can propagate without a material medium.

A2 — Longitudinal waves

In a longitudinal wave, particles of the medium oscillate:

A. parallel to the direction of wave propagation.
B. perpendicular to the direction of wave propagation.
C. only in the direction of wave propagation, without returning.
D. in circles around the direction of propagation.

Show answer and explanation

Answer: A. Longitudinal oscillations are parallel to the direction of energy transfer. In sound in air, they produce compressions and rarefactions.

A3 — Wave speed

A wave has frequency $12\,\mathrm{Hz}$ and wavelength $0.25\,\mathrm{m}$ . What is its speed?

A. 0.0208 m s⁻¹
B. 3.0 m s⁻¹
C. 48 m s⁻¹
D. 12.25 m s⁻¹

Show answer and explanation

Answer: B. $v=f\lambda=12(0.25)=3.0\,\mathrm{m\,s^{-1}}$ .

A4 — Period and frequency

A particle completes one oscillation every $0.020\,\mathrm{s}$ . What is the frequency?

A. 0.020 Hz
B. 20 Hz
C. 50 Hz
D. 2.0 Hz

Show answer and explanation

Answer: C. $f=\frac{1}{T}=\frac{1}{0.020}=50\,\mathrm{Hz}$ .

A5 — Reading wavelength

A displacement–distance graph shows that a crest and the nearest trough are separated by $0.90\,\mathrm{m}$ . What is the wavelength?

A. 1.80 m
B. 0.90 m
C. 0.45 m
D. 3.60 m

Show answer and explanation

Answer: A. The distance from a crest to the nearest trough is $\lambda/2$ . Therefore $\lambda=2(0.90)=1.80\,\mathrm{m}$ .

A6 — Propagation through a vacuum

Which wave can propagate through a vacuum?

A. Sound in air.
B. A wave on a rope.
C. Visible light.
D. A pressure wave in water.

Show answer and explanation

Answer: C. Visible light is an electromagnetic wave and does not require a material medium. The other examples are mechanical waves.

A7 — Changing frequency

In a non-dispersive medium, the source frequency is doubled while wave speed stays constant. What happens to wavelength?

A. It doubles.
B. It stays constant.
C. It becomes four times greater.
D. It halves.

Show answer and explanation

Answer: D. From $\lambda=v/f$ , wavelength is inversely proportional to frequency at constant wave speed.

A8 — Particle motion and wave motion

A particle in a medium completes one full oscillation. Which statement about its motion over that cycle is correct?

A. Its average velocity equals the wave speed.
B. Its average velocity is zero, although its average speed is non-zero.
C. Its total distance travelled is zero.
D. It moves forward by one wavelength.

Show answer and explanation

Answer: B. The particle returns to its starting position, so its net displacement and average velocity are zero. It travels a non-zero distance, so its average speed is non-zero.

Part B — Extended-Response Questions

Question 1 — Wave definition and energy transfer

(a) State what is meant by a wave.
(b) Explain “a wave transfers energy without net transfer of matter”, using one example.

Show answer and explanation

(a) A wave is a disturbance that transfers energy through space or a medium without net transport of matter in the ideal wave model.

(b) In sound in air, molecules oscillate back and forth about their equilibrium positions. Energy travels away from the source, while the molecules vibrate locally rather than travelling with the wave from source to receiver.

Question 2 — Transverse and longitudinal waves

(a) Describe the difference between transverse and longitudinal waves.
(b) Explain why sound in air is longitudinal, using the terms compression and rarefaction.

Show answer and explanation

(a) In a transverse wave, oscillations are perpendicular to the direction of energy transfer. In a longitudinal wave, oscillations are parallel to that direction.

(b) Air molecules oscillate parallel to the direction of propagation. Compressions are regions of higher pressure and density; rarefactions are regions of lower pressure and density.

Question 3 — Using the wave equation

A wave on a string has frequency $7.5\,\mathrm{Hz}$ and wavelength $0.80\,\mathrm{m}$ . Calculate the wave speed.

Show answer and explanation

$\displaystyle v=f\lambda=(7.5)(0.80)=6.0\,\mathrm{m\,s^{-1}}$

Answer: $6.0\,\mathrm{m\,s^{-1}}$ .

Question 4 — Using a time period

A ripple tank produces water waves with wavelength $0.25\,\mathrm{m}$ . A floating marker completes one oscillation in $0.40\,\mathrm{s}$ .

(a) Determine the frequency.
(b) Determine the wave speed.

Show answer and explanation

(a) $\displaystyle f=\frac{1}{T}=\frac{1}{0.40}=2.5\,\mathrm{Hz}$

(b) $\displaystyle v=f\lambda=2.5(0.25)=0.625\,\mathrm{m\,s^{-1}}\approx0.63\,\mathrm{m\,s^{-1}}$

Question 5 — A displacement–distance graph

A displacement–distance graph shows that consecutive crests are separated by $1.5\,\mathrm{m}$ . The maximum displacement from equilibrium is $0.040\,\mathrm{m}$ .

(a) State the wavelength and amplitude.
(b) Explain why this graph does not directly show the period.

Show answer and explanation

(a) Wavelength: $\lambda=1.5\,\mathrm{m}$ . Amplitude: $A=0.040\,\mathrm{m}$ .

(b) This graph is a snapshot at one instant. It shows displacement against position, rather than time. The period cannot be obtained without additional information such as speed or frequency.

Question 6 — Tracking a crest

A crest moves $4.8\,\mathrm{m}$ in $2.0\,\mathrm{s}$ .

(a) Determine the wave speed.
(b) If the wavelength is $0.60\,\mathrm{m}$ , determine the frequency.

Show answer and explanation

(a) $\displaystyle v=\frac{\Delta x}{\Delta t}=\frac{4.8}{2.0}=2.4\,\mathrm{m\,s^{-1}}$

(b) $\displaystyle f=\frac{v}{\lambda}=\frac{2.4}{0.60}=4.0\,\mathrm{Hz}$

Question 7 — Mechanical and electromagnetic waves

(a) State two differences between mechanical and electromagnetic waves.
(b) A student says: “Sound and light are both waves, so both can travel through a vacuum.” Explain why this statement is incorrect.

Show answer and explanation

(a) Mechanical waves require a material medium and involve disturbances of that medium. Electromagnetic waves involve oscillating electric and magnetic fields and can propagate through a vacuum. Electromagnetic waves in vacuum are transverse; mechanical waves can be transverse or longitudinal.

(b) Sound is mechanical and requires particles to oscillate. In a vacuum there are no particles to support sound propagation. Light is electromagnetic and does not require a material medium.

Question 8 — Sound entering another medium

A sound wave in air has frequency $440\,\mathrm{Hz}$ and wave speed $340\,\mathrm{m\,s^{-1}}$ .

(a) Calculate its wavelength.
(b) Classify the wave as transverse or longitudinal and explain.
(c) The sound crosses a stationary boundary into a medium where its speed is $510\,\mathrm{m\,s^{-1}}$ . State what happens to frequency and calculate the new wavelength.

Show answer and explanation

(a) $\displaystyle \lambda=\frac{v}{f}=\frac{340}{440}=0.773\,\mathrm{m}$

(b) It is longitudinal: air particles oscillate parallel to the propagation direction, producing compressions and rarefactions.

(c) Frequency remains unchanged at $440\,\mathrm{Hz}$ because it is set by the source.

$\displaystyle \lambda'=\frac{v'}{f}=\frac{510}{440}=1.16\,\mathrm{m}$

The wavelength increases because speed increases at constant frequency.

Question 9 — Counting oscillations

A floating marker completes 24 full oscillations in $12.0\,\mathrm{s}$ . The wavelength of the water wave is $0.75\,\mathrm{m}$ .

(a) Calculate the frequency.
(b) Calculate the period.
(c) Calculate the wave speed.
(d) State whether the marker’s oscillation frequency equals the wave frequency.

Show answer and explanation

(a) $\displaystyle f=\frac{N}{t}=\frac{24}{12.0}=2.00\,\mathrm{Hz}$

(b) $\displaystyle T=\frac{1}{f}=0.500\,\mathrm{s}$

(c) $\displaystyle v=f\lambda=2.00(0.75)=1.5\,\mathrm{m\,s^{-1}}$

(d) Yes. In the ideal model, the marker follows the local surface motion and completes one oscillation for each wave cycle.

Question 10 — A displacement–time graph

A displacement–time graph for one point on a string shows a maximum displacement of $6.0\,\mathrm{mm}$ . Consecutive positive maxima occur at $t=0.10\,\mathrm{s}$ and $t=0.50\,\mathrm{s}$ . The wave speed is $8.0\,\mathrm{m\,s^{-1}}$ .

(a) State the amplitude and calculate the peak-to-peak displacement.
(b) Determine the period and frequency.
(c) Calculate the wavelength.
(d) Explain why this time graph cannot directly show wavelength.

Show answer and explanation

(a) $A=6.0\,\mathrm{mm}$ . Peak-to-peak displacement is $2A=12.0\,\mathrm{mm}$ .

(b) $\displaystyle T=0.50-0.10=0.40\,\mathrm{s}$

$\displaystyle f=\frac{1}{0.40}=2.5\,\mathrm{Hz}$

(c) $\displaystyle \lambda=\frac{v}{f}=\frac{8.0}{2.5}=3.2\,\mathrm{m}$

(d) The horizontal axis is time at a fixed position. It gives the time between cycles, rather than the distance between points of equal phase. Speed is needed to relate the time information to wavelength.

Question 11 — Combining distance and time information

For the same travelling wave, a displacement–distance snapshot shows consecutive crests at $x=0.20\,\mathrm{m}$ and $x=0.80\,\mathrm{m}$ . A displacement–time graph at a fixed point shows consecutive positive maxima at $t=0.10\,\mathrm{s}$ and $t=0.40\,\mathrm{s}$ . The amplitude is $3.0\,\mathrm{cm}$ .

(a) Determine the wavelength and period.
(b) Calculate the frequency and wave speed.
(c) Express the amplitude in metres.
(d) Determine the distance between a crest and its nearest trough.

Show answer and explanation

(a) $\lambda=0.80-0.20=0.60\,\mathrm{m}$ and $T=0.40-0.10=0.30\,\mathrm{s}$ .

(b) $\displaystyle f=\frac{1}{0.30}=3.33\,\mathrm{Hz}$

$\displaystyle v=\frac{\lambda}{T}=\frac{0.60}{0.30}=2.0\,\mathrm{m\,s^{-1}}$

(c) $A=0.030\,\mathrm{m}$ .

(d) The separation is $\lambda/2=0.30\,\mathrm{m}$ .

Question 12 — Comparing two sound waves

Two sound waves travel in the same air at $340\,\mathrm{m\,s^{-1}}$ . Wave P has frequency $170\,\mathrm{Hz}$ and wave Q has frequency $680\,\mathrm{Hz}$ .

(a) Calculate the wavelength of each.
(b) Calculate the period of each.
(c) State which has the higher pitch.
(d) The amplitude of P increases while its frequency stays fixed. State what happens to its wavelength and speed in the linear wave model.

Show answer and explanation

(a) $\displaystyle \lambda_P=\frac{340}{170}=2.0\,\mathrm{m}$

$\displaystyle \lambda_Q=\frac{340}{680}=0.50\,\mathrm{m}$

(b) $\displaystyle T_P=\frac{1}{170}=5.88\times10^{-3}\,\mathrm{s}$

$\displaystyle T_Q=\frac{1}{680}=1.47\times10^{-3}\,\mathrm{s}$

(c) Wave Q has higher pitch because it has higher frequency.

(d) Both speed and wavelength remain unchanged. In the linear model, wave speed is set by the medium, and wavelength remains $v/f$ .

Question 13 — Wave speed and particle speed

A transverse travelling wave on a string has amplitude $0.015\,\mathrm{m}$ , frequency $5.0\,\mathrm{Hz}$ and wave speed $20\,\mathrm{m\,s^{-1}}$ . Each particle oscillates between displacements $+A$ and $-A$ .

(a) Calculate the wavelength and period.
(b) Calculate the total distance travelled by one particle during a complete cycle.
(c) Calculate the particle’s average speed over that cycle.
(d) State its average velocity over the cycle.
(e) Explain why neither result should be identified with wave speed.

Show answer and explanation

(a) $\lambda=v/f=20/5.0=4.0\,\mathrm{m}$ and $T=1/f=0.20\,\mathrm{s}$ .

(b) In one complete cycle the particle travels a total distance of $4A$ .

$\displaystyle \text{distance}=4(0.015)=0.060\,\mathrm{m}$

(c) $\displaystyle \text{average speed}=\frac{0.060}{0.20}=0.30\,\mathrm{m\,s^{-1}}$

(d) Average velocity is zero because the particle returns to its initial position.

(e) Wave speed describes propagation of the disturbance along the string. Particle speed describes local motion perpendicular to that direction. These are different motions.

Question 14 — Phase relationships (extension)

A sinusoidal travelling wave has wavelength $1.20\,\mathrm{m}$ and frequency $4.0\,\mathrm{Hz}$ . Use $\Delta\phi=2\pi\Delta x/\lambda$ for the magnitude of a spatial phase difference.

(a) Calculate the phase difference between points separated by $0.30\,\mathrm{m}$ .
(b) Describe the phase relationship for points separated by $0.60\,\mathrm{m}$ .
(c) Describe the phase relationship for points separated by $1.20\,\mathrm{m}$ .
(d) At one point, determine the shortest positive time interval corresponding to a phase change of $\pi/2$ .

Show answer and explanation

(a) $\displaystyle \Delta\phi=\frac{2\pi(0.30)}{1.20}=\frac{\pi}{2}\,\mathrm{rad}$

This is a quarter-cycle phase difference.

(b) The separation is half a wavelength, giving a phase difference of $\pi$ radians: the points are in antiphase.

(c) The separation is one wavelength, giving a phase difference of $2\pi$ radians: the points are in phase.

(d) A phase change of $\pi/2$ corresponds to one quarter of a period.

$\displaystyle T=\frac{1}{4.0}=0.25\,\mathrm{s}$

$\displaystyle \Delta t=\frac{T}{4}=0.0625\,\mathrm{s}$

Question 15 — An electromagnetic wave

Light has vacuum wavelength $750\,\mathrm{nm}$ . Take $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$ . It enters a stationary transparent medium where its speed is $2.00\times10^8\,\mathrm{m\,s^{-1}}$ .

(a) Calculate its frequency in vacuum.
(b) Calculate its period.
(c) State its frequency in the medium and calculate its new wavelength.
(d) Explain what oscillates in this wave.

Show answer and explanation

(a) $\displaystyle f=\frac{c}{\lambda_0}=\frac{3.00\times10^8}{750\times10^{-9}}=4.00\times10^{14}\,\mathrm{Hz}$

(b) $\displaystyle T=\frac{1}{f}=2.50\times10^{-15}\,\mathrm{s}$

(c) Frequency remains $4.00\times10^{14}\,\mathrm{Hz}$ .

$\displaystyle \lambda=\frac{v}{f}=\frac{2.00\times10^8}{4.00\times10^{14}}=5.00\times10^{-7}\,\mathrm{m}=500\,\mathrm{nm}$

(d) Electric and magnetic fields oscillate. For a plane electromagnetic wave in an isotropic medium, the fields are perpendicular to each other and to the propagation direction.

Question 16 — Water waves changing speed

A source produces water waves at $10\,\mathrm{Hz}$ . Their speed is $0.80\,\mathrm{m\,s^{-1}}$ in one region and $0.50\,\mathrm{m\,s^{-1}}$ in a second region. The boundary is stationary.

(a) Calculate the wavelength in each region.
(b) State the period in each region.
(c) Describe the change in wavefront spacing.
(d) Explain why frequency stays constant although speed changes.

Show answer and explanation

(a) $\displaystyle \lambda_1=\frac{0.80}{10}=0.080\,\mathrm{m}$

$\displaystyle \lambda_2=\frac{0.50}{10}=0.050\,\mathrm{m}$

(b) In both regions, $T=1/10=0.10\,\mathrm{s}$ .

(c) Adjacent crest wavefronts are closer together in the slower region: their separation decreases from $0.080\,\mathrm{m}$ to $0.050\,\mathrm{m}$ .

(d) The source sets the rate of successive cycles. A stationary boundary preserves that rate, while the medium determines propagation speed. Wavelength adjusts so that $v=f\lambda$ remains satisfied.

Question 17 — Wave measurements and uncertainty

A crest travels a measured distance $1.20\pm0.02\,\mathrm{m}$ in a measured time $0.50\pm0.01\,\mathrm{s}$ . The wavelength is $0.60\pm0.01\,\mathrm{m}$ . Estimate uncertainties in products and quotients by adding the fractional uncertainties.

(a) Calculate wave speed.
(b) Estimate its percentage and absolute uncertainties.
(c) Calculate frequency.
(d) Estimate the absolute uncertainty in frequency.

Show answer and explanation

(a) $\displaystyle v=\frac{1.20}{0.50}=2.4\,\mathrm{m\,s^{-1}}$

(b) $\displaystyle \frac{\delta v}{v}\approx\frac{0.02}{1.20}+\frac{0.01}{0.50}=0.0367$

The percentage uncertainty is approximately $3.7\%$ .

$\displaystyle \delta v\approx2.4(0.0367)=0.088\,\mathrm{m\,s^{-1}}$

Report approximately $v=2.40\pm0.09\,\mathrm{m\,s^{-1}}$ .

(c) $\displaystyle f=\frac{v}{\lambda}=\frac{2.4}{0.60}=4.0\,\mathrm{Hz}$

(d) $\displaystyle \frac{\delta f}{f}\approx0.0367+\frac{0.01}{0.60}=0.0533$

$\displaystyle \delta f\approx4.0(0.0533)=0.213\,\mathrm{Hz}$

Report approximately $f=4.0\pm0.2\,\mathrm{Hz}$ .

Question 18 — Investigating frequency and wavelength

A student varies the frequency of a wave generator in a ripple tank. Over the selected range, the water depth is constant and the wave speed is approximately $1.5\,\mathrm{m\,s^{-1}}$ . Treat this range as non-dispersive.

(a) Predict the wavelengths at frequencies $6.0\,\mathrm{Hz}$ and $10\,\mathrm{Hz}$ .
(b) State how wavelength depends on frequency.
(c) Explain why a graph of wavelength against reciprocal frequency should be a straight line, and state its gradient.
(d) Describe how to improve the measurement of wavelength.
(e) State one control variable and one possible source of measurement error.

Show answer and explanation

(a) $\displaystyle \lambda_6=\frac{1.5}{6.0}=0.25\,\mathrm{m}$

$\displaystyle \lambda_{10}=\frac{1.5}{10}=0.15\,\mathrm{m}$

(b) At constant wave speed, wavelength is inversely proportional to frequency.

(c) $\displaystyle \lambda=v\left(\frac{1}{f}\right)$

A graph of $\lambda$ against $1/f$ is a straight line through the origin. Its gradient is the wave speed, $1.5\,\mathrm{m\,s^{-1}}$ .

(d) Measure the distance across several complete wavelengths and divide by the number of wavelength intervals. Repeat measurements and average them. Remember that six consecutive crests span five wavelengths.

(e) Keep water depth constant. Possible errors include parallax, blurred crest positions, incorrect counting of wavelength intervals, or reflections from the tank sides disturbing the pattern.

Exam readiness checklist

I can define waves as energy transfers without net transport of matter in the ideal model.
I can distinguish transverse and longitudinal waves.
I can use $v=f\lambda$ , $f=1/T$ and $v=\Delta x/\Delta t$ .
I can read amplitude and wavelength from distance graphs, and amplitude and period from time graphs.
I can distinguish wave motion from the local oscillation of particles.
I can explain why frequency stays constant at a stationary boundary.
I can compare mechanical and electromagnetic waves.
I can interpret proportional relationships and estimate measurement uncertainties.

Learning with Wonder and Integrity

Memory verse — Psalm 19:1 (KJV):
“The heavens declare the glory of God; and the firmament sheweth his handywork.”

Creation: A world we can investigate

Sound, light and water waves reveal patterns that we can observe, measure and describe. As Christians, we receive the created world and our ability to understand it as gifts from God. Psalm 19 invites us to recognise His glory, while Colossians 1:16–17 teaches that all things were created through Jesus Christ and for Him, and that in Him all things hold together.

The Fall: Our need for honesty and grace

Sin affects our choices and relationships. In our studies, we may be tempted to copy work, conceal mistakes or seek success without integrity. God calls us to walk in truth, acknowledge our failures and treat others with love. Admitting an error and correcting it is an opportunity to practise humility.

Redemption: New life through Jesus Christ

Jesus Christ died for our sins and rose again. Through Him, we can receive forgiveness and a restored relationship with God. Turn to Him in repentance and faith, receiving Him as your personal God, Saviour and Lord. His grace gives us a foundation for growth in both character and learning.

Restoration: Grow in faith and serve others

Revelation 21:3–5 promises a future in which God dwells with His people and makes all things new. As we look forward to that hope, we can honour Him through faithful study, honest work and loving service. Read and study the Bible, spend time in prayer, and connect with other believers in a local church to grow in faith and knowledge of God.

Reflection: How can you use your understanding of science to help another learner while showing patience, honesty and gratitude?

Prayer: Lord Jesus, thank You for the world You created and the opportunity to learn. Forgive my sins and help me follow You. Give me understanding, perseverance and honesty in my studies. Help me grow through Your Word, prayer and fellowship, and use my learning to serve others. Amen.

IB Physics HL Book 2025; Papers 1 & 2 Practice 5 Sections65 Lessons54 Weeks

Curriculum

Wave model HL Paper 1&2

C.2 Wave Model Papers 1&2

Instructions

Part A — Multiple-Choice Questions

A1 — Energy transfer

A2 — Longitudinal waves

A3 — Wave speed

A4 — Period and frequency

A5 — Reading wavelength

A6 — Propagation through a vacuum

A7 — Changing frequency

A8 — Particle motion and wave motion

Part B — Extended-Response Questions

Question 1 — Wave definition and energy transfer

Question 2 — Transverse and longitudinal waves

Question 3 — Using the wave equation

Question 4 — Using a time period

Question 5 — A displacement–distance graph

Question 6 — Tracking a crest

Question 7 — Mechanical and electromagnetic waves

Question 8 — Sound entering another medium

Question 9 — Counting oscillations

Question 10 — A displacement–time graph

Question 11 — Combining distance and time information

Question 12 — Comparing two sound waves

Question 13 — Wave speed and particle speed

Question 14 — Phase relationships (extension)

Question 15 — An electromagnetic wave

Question 16 — Water waves changing speed

Question 17 — Wave measurements and uncertainty

Question 18 — Investigating frequency and wavelength

Exam readiness checklist

Learning with Wonder and Integrity

Creation: A world we can investigate

The Fall: Our need for honesty and grace

Redemption: New life through Jesus Christ

Restoration: Grow in faith and serve others

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