Waves Sound and Light — Free IB MYP4 Physics Questions

1QuestionComparing EM Waves Speed Wavelength FrequencyConcept Practice

2 marks~3 minCriterion D

The image shows the penetration of different types of ultraviolet (UV) radiation through the Earth's atmosphere. UV-A radiation penetrates most deeply, while UV-C is almost entirely absorbed by the ozone layer.

Outline ONE environmental impact related to the ozone layer's absorption of UV radiation.

Solutions

2QuestionOrder and Properties of EM WavesConcept Practice

2 marks~3 minCriterion A

Emergency services such as police and ambulance crews rely on radio wave communication to coordinate responses in real time.

a

Identify one property of radio waves that makes them suitable for this communication application. [1]

b

A paramedic crew reports that radio communication fails when their vehicle enters a long road tunnel. Explain, using the wave properties of radio waves, why signal loss occurs in this situation. [1]

Solutions

3QuestionComparing EM Waves Speed Wavelength FrequencyConcept Practice

2 marks~3 minCriterion B

A student sets up an experiment to observe diffraction patterns of light. The setup includes a laser, a diffraction grating, and a screen, as shown in the diagram below.

Outline the steps of the experiment to determine the wavelength of the laser light using the diffraction grating.

Solutions

4QuestionComparing EM Waves Speed Wavelength FrequencyConcept Practice

3 marks~5 minCriterion C

The electromagnetic spectrum spans frequencies from approximately

10^{4}

Hz (radio waves) to

10^{20}

Hz (gamma rays), yet all regions travel at

c = 3 \times 10^{8}

m/s in a vacuum.

a

State the value of the speed of all electromagnetic waves in a vacuum and identify what type of property this represents. [1]

b

Using the wave equation

v = f\lambda

, explain how wavelength must change as frequency increases, given that wave speed remains constant. [1]

c

A student claims: "Higher-frequency gamma rays must travel faster than radio waves because they carry more energy." Evaluate this claim using your understanding of electromagnetic wave behaviour in a vacuum. [1]

Solutions

5QuestionDigital vs Analog Signals IntroductoryConcept Practice

2 marks~3 minCriterion A

The diagram shows two electrical signals plotted on voltage–time axes.

Signal X is a smooth, continuous wave that varies sinusoidally between

-5\ \text{V}

and

+5\ \text{V}

.

Signal Y alternates sharply between exactly

0\ \text{V}

and

5\ \text{V}

.

a

Identify which signal is digital. [1]

b

State one characteristic of digital signals that distinguishes them from analog signals. [1]

Solutions

6QuestionFiber Optics and Total Internal ReflectionConcept Practice

2 marks~3 minCriterion D

Fiber optic cables transmit light signals by total internal reflection. Internet providers use fiber optics to deliver high-speed broadband, yet coverage remains uneven across different regions.

a

Identify one real-world application of fiber optic cables beyond internet provision. [1]

b

Explain one reason why fiber optic cables are difficult to deploy for internet access in rural communities. [1]

Solutions

7QuestionSpeed of a Wave v = f lambdaConcept Practice

2 marks~3 minCriterion D

In 2004, the Indian Ocean tsunami travelled approximately 1 600 km from its earthquake epicentre to the Sri Lankan coast. Seismologists estimated the tsunami's wavelength at 200 km and its frequency at

5.6 \times 10^{-4}

Hz.

a

Calculate the wave speed of the tsunami using

v = f\lambda

. [1]

b

Explain one reason why this calculated wave speed may not accurately predict the tsunami's actual arrival time at the coast. [1]

Solutions

8QuestionSpeed of a Wave v = f lambdaConcept Practice

4 marks~6 minCriterion C

During a coastal engineering survey, instruments detect ocean surface waves travelling at

v = 24\ \text{m/s}

with a wavelength of

\lambda = 3\ \text{m}

. A junior technician claims the wave frequency is

f = 0.125\ \text{Hz}

.

a

State the formula that relates wave speed, frequency, and wavelength. [1]

b

Calculate the frequency of the ocean wave. [1]

c

Evaluate the technician's claim of

f = 0.125\ \text{Hz}

. Identify the mathematical error made and justify the correct value using

v = f\lambda

. [2]

Solutions

9QuestionWave Parameters Wavelength Frequency AmplitudeConcept Practice

4 marks~6 minCriterion A

The graph below shows a displacement–distance graph for a transverse wave at a fixed time.

a

Determine the amplitude and wavelength of the wave from the graph. [2]

b

The wave travels at

4.0\ \text{m s}^{-1}

. Deduce the frequency of the wave and explain what a higher amplitude would mean for the energy carried by the wave. [2]

Solutions

10QuestionApplications Sonar Ultrasound and Musical InstrumentsConcept Practice

2 marks~3 minCriterion A

Ultrasound scanners used in hospitals emit sound waves at frequencies above 20 000 Hz to produce images of internal structures.

a

State one medical application of ultrasound technology. [1]

b

Explain one limitation that reduces the effectiveness of ultrasound imaging in a specific clinical situation. [1]

Solutions

11QuestionSpeed of Sound in Solids Liquids and GasesConcept Practice

2 marks~3 minCriterion D

Earthquake early-warning systems rely on the speed difference between seismic wave types. P-waves (primary, compressional) travel through rock at approximately 6 km s

^{-1}

, while S-waves (secondary, shear) travel at approximately 3.5 km s

^{-1}

. S-waves cause significantly greater ground displacement and structural damage than P-waves.

a

Explain how seismic early-warning systems use the arrival-time difference between P-waves and S-waves to issue warnings before destructive shaking begins. [1]

b

Explain one limitation of earthquake early-warning systems that reduces their effectiveness in protecting people. [1]

Solutions

12QuestionRefraction Through Glass Blocks and WaterConcept Practice

2 marks~3 minCriterion D

A spear-fisher observes a fish beneath the surface of a still lake. Light from the fish travels from water (

n = 1.33

) into air (

n = 1.00

), bending away from the normal at the boundary.

Explain why the fish appears to be at a different position from its true location. [1]

Describe one practical consequence of this effect for the spear-fisher. [1]

Solutions

13QuestionPlane Concave and Convex MirrorsConcept Practice

2 marks~3 minCriterion C

The diagram shows parallel rays of light striking a concave mirror. After reflection, the rays pass through a single point on the principal axis.

a

Identify the type of mirror shown. [1]

b

Explain why parallel rays incident on this mirror converge at one specific point rather than being reflected in random directions. [1]

Solutions

14QuestionLenses Converging and Diverging IntroductoryConcept Practice

2 marks~3 minCriterion A

A ray diagram shows three parallel rays of light entering a lens. After passing through the lens, the rays diverge. When extended backwards, the diverging rays appear to meet at a single point on the same side of the lens as the incoming rays.

a

Identify the type of lens shown and explain how the behaviour of the rays supports your answer. [1]

b

Deduce the name given to the point at which the extended rays appear to meet, and state whether this point is real or virtual. [1]

Solutions

15QuestionComparing EM Waves Speed Wavelength FrequencyAssessment Practice

4 marks~6 minCriterion B

A double-slit experiment is performed using visible light with a wavelength of

500 \times 10^{-9}

meters and a frequency of

6 \times 10^{14}

Hz. The resulting interference pattern is observed on a screen, with the fringe spacing (distance between bright fringes) recorded as

d

.

Now, the visible light source is replaced with an ultraviolet (UV) light source. The distance

L

to the screen and the slit separation

s

remain unchanged. The UV light has a wavelength of

250 \times 10^{-9}

meters and a frequency of

12 \times 10^{14}

Hz.

a

Investigate the relationship between wavelength and fringe spacing in a double-slit experiment.

b

Predict the new fringe spacing,

d'

, in terms of the original fringe spacing

d

.

c

Justify your prediction, explaining how the change in wavelength affects the fringe spacing, given that the speed of electromagnetic waves remains constant.

Solutions

16QuestionOrder and Properties of EM WavesAssessment Practice

4 marks~6 minCriterion C

A student measures the frequency and wavelength of five electromagnetic waves travelling in a vacuum. The results are recorded below.

Wave A	frequency $= 3.0 \times 10^{9}$ Hz	wavelength $= 0.10$ m
Wave B	frequency $= 6.0 \times 10^{14}$ Hz	wavelength $= 5.0 \times 10^{-7}$ m
Wave C	frequency $= ?$	wavelength $= 4.0 \times 10^{-7}$ m
Wave D	frequency $= 1.0 \times 10^{18}$ Hz	wavelength $= 3.0 \times 10^{-10}$ m
Wave E	frequency $= 3.0 \times 10^{19}$ Hz	wavelength $= 1.0 \times 10^{-11}$ m

a

Deduce the frequency of wave C. [2]

b

Identify which region of the electromagnetic spectrum wave C belongs to, and justify your answer using its wavelength. [1]

c

A communications engineer claims that radio waves travel more slowly than gamma rays in a vacuum because radio waves carry less energy. Evaluate this claim using evidence from the data table. [1]

Solutions

17QuestionOrder and Properties of EM WavesAssessment Practice

6 marks~9 minCriterion A

A hospital uses X-rays to diagnose bone fractures and MRI (Magnetic Resonance Imaging) to image soft tissues such as the brain and muscles. X-rays are ionizing radiation with frequencies around

10^{18}

Hz. MRI uses non-ionizing radio waves and detects signals from hydrogen nuclei in water molecules within body tissues.

a

State one physical property of X-rays that makes them suitable for imaging bones, and state one risk associated with their use. [2]

b

Explain why MRI is considered safer than X-rays, and explain one reason why MRI is not always chosen as the first imaging method. [2]

c

Discuss the limitation of MRI for diagnosing bone fractures, linking your answer to the physics principle by which MRI produces an image. [2]

Solutions

18QuestionOrder and Properties of EM WavesAssessment Practice

10 marks~15 minCriterion D

A student investigates how the energy of electromagnetic (EM) waves depends on their frequency. The table below shows data for four types of EM radiation.

EM wave type	Frequency (Hz)	Energy per photon (J)
Radio	$1 \times 10^{8}$	$6.6 \times 10^{-26}$
Infrared	$3 \times 10^{12}$	$2.0 \times 10^{-21}$
Visible light	$6 \times 10^{14}$	$4.0 \times 10^{-19}$
Ultraviolet	$1 \times 10^{15}$	$6.6 \times 10^{-19}$

Planck's constant:

h = 6.6 \times 10^{-34}

J s

a

State the independent variable and the dependent variable in this investigation. [2]

b

Deduce the relationship between frequency and energy per photon using values from the table. [2]

c

Calculate the energy per photon of an EM wave with a frequency of

2 \times 10^{15}

Hz. Show your working. [2]

d

A medical imaging team argues that a higher-frequency EM wave is always more harmful to human tissue than a lower-frequency one. Evaluate this claim, using your knowledge of EM wave properties and at least one factor beyond frequency. [4]

Solutions

19QuestionApplications of Light and Sound in Modern TechAssessment Practice

7 marks~11 minCriterion B

A fiber-optic cable carries a signal from a transmitter. The table shows the measured signal-to-noise ratio (SNR) at different distances.

Distance (km)	1	2	3	4	5	7	9
SNR (dB)	30.0	24.0	19.2	15.4	12.3	7.9	5.0

a

Calculate the decrease in SNR for each 1 km step from 1 km to 5 km. Describe the pattern you observe in these decreases. [2]

b

Deduce the SNR at 6 km. Show your working. [2]

c

Explain why the SNR decreases by a constant factor per kilometre rather than a constant amount, and analyse what this implies about how the fiber affects the signal as it travels further from the transmitter. [3]

Solutions

20QuestionDigital vs Analog Signals IntroductoryAssessment Practice

8 marks~12 minCriterion D

A city is evaluating two communication systems for emergency broadcasts: analog radio towers and digital fiber-optic cables. Analog signals lose

0.5\ \text{dB}

of signal-to-noise ratio per kilometre travelled. Digital fiber-optic cables maintain signal quality over any distance, but their installation requires

500\ \text{kg}

of carbon-intensive materials per kilometre of cable. The city spans

20\ \text{km}

and requires dependable communication across its entire area.

a

Calculate the total reduction in signal-to-noise ratio for an analog signal transmitted across the full

20\ \text{km}

city. [2]

b

Explain how the value calculated in part (a) affects the reliability of emergency broadcasts at the far edge of the city. [2]

c

Evaluate the trade-off between communication reliability and environmental impact when choosing between the two systems. In your response, identify one assumption in the data provided and discuss the ethical responsibility of infrastructure planners making this decision. [4]

Solutions

21QuestionFiber Optics and Total Internal ReflectionAssessment Practice

6 marks~9 minCriterion C

A semicircular acrylic block (refractive index

n_1 = 1.50

), a ray box with a single slit, a protractor, and a ruler are available. The critical angle for the acrylic–air interface is approximately

42°

.

a

Construct a labeled diagram of the experimental setup showing the path of light through the acrylic block at the point of total internal reflection at the flat face. [2]

b

Explain how you would measure the critical angle first for the acrylic–air interface and then for the acrylic–water interface, including one safety precaution. [2]

c

Analyse how plotting

\sin\theta_c

against the refractive index of the second medium

n_2

allows you to determine the refractive index of acrylic

n_1

from your graph, referencing Snell's law. [2]

Solutions

22QuestionAssessment Practice

6 marks~9 minCriterion D

In satellite communication, a phone transmits at 2.4 GHz. Signal strength follows the inverse-square law,

P_r \propto \frac{1}{d^2}

, where

d

is distance from the transmitter. In decibels, the change in signal strength relative to 1 m is given by

\Delta S = 10\log_{10}\!\left(\frac{1}{d^2}\right)

dB. The signal strength at 1 m is

-30

dBm.

Measured data:

Distance (m)	1	2	3	4	5
Measured signal (dBm)	$-30$	$-38$	$-44$	$-49$	$-53$

a

Calculate the theoretical signal strength (dBm) at distances of 2 m, 3 m, 4 m, and 5 m. [2]

b

Deduce the percentage deviation of the measured signal from the theoretical value at each distance using:

\text{deviation} = \frac{\text{measured} - \text{theoretical}}{\lvert\text{theoretical}\rvert} \times 100\%

[2]

c

Evaluate the validity of the inverse-square law as a model for this data, identifying at least one physical reason for any systematic trend in the deviations. [2]

Solutions

23QuestionLasers and Optical DevicesAssessment Practice

5 marks~8 minCriterion C

A laser beam travels from air into an unknown transparent medium. The angles of incidence

\theta_1

(in air) and refraction

\theta_2

(in the medium) are measured across several trials and plotted as

\sin\theta_2

versus

\sin\theta_1

. The graph is a straight line through the origin with gradient

0.667

.

Snell's law:

n_1 \sin\theta_1 = n_2 \sin\theta_2

, where

n_1 = 1.00

for air.

Refractive indices of candidate media:
Crown glass: 1.52 — Flint glass: 1.62 — Diamond: 2.42 — Water: 1.33

a

Deduce the relationship between the gradient of the graph and the refractive index

n_2

of the medium. [1]

b

Calculate the refractive index of the medium. [2]

c

A technician claims the medium is crown glass. Evaluate this claim using your calculated value and the data provided. [2]

Solutions

24QuestionFiber Optics and Total Internal ReflectionAssessment Practice

8 marks~12 minCriterion A

An optical fibre carries light signals through a glass core (refractive index

n_{\text{core}} = 1.52

) surrounded by cladding (refractive index

n_{\text{clad}} = 1.39

).

a

State the two conditions required for total internal reflection to occur at the core–cladding boundary. [2]

b

Construct a ray diagram showing light undergoing total internal reflection inside the optical fibre. Label the core, cladding, angle of incidence

\theta_i

, and angle of reflection

\theta_r

. [2]

c

Explain how total internal reflection allows an optical fibre to transmit communication signals over long distances with minimal signal loss. [2]

d

The critical angle

\theta_c

for this fibre is given by

\sin\theta_c = \dfrac{n_{\text{clad}}}{n_{\text{core}}}

. Calculate

\theta_c

and analyse whether a ray striking the boundary at 68° will undergo total internal reflection. [2]

Solutions

25QuestionSpeed of a Wave v = f lambdaAssessment Practice

4 marks~6 minCriterion B

An earthquake produces P-waves and S-waves simultaneously at the same source. Seismologists record the following data:

- P-wave speed:

6000 \ \text{m/s}

- S-wave speed:

3500 \ \text{m/s}

- Frequency of both waves:

2 \ \text{Hz}

a

Calculate the wavelength of the P-waves. [1]

b

The S-wave wavelength is calculated to be

1750 \ \text{m}

. Deduce what this difference in wavelength tells you about the relationship between wave speed and wavelength when frequency is constant. [1]

c

A seismograph plots displacement against distance for both waves on the same axes. Analyse which wave appears more spread out on this graph and evaluate whether a higher wave speed always produces a more spread-out wave pattern. [2]

Solutions

26QuestionWave Parameters Wavelength Frequency AmplitudeAssessment Practice

7 marks~11 minCriterion B

A student uses a frequency generator to investigate how wavelength varies with frequency in three media. Wave speed remains constant within each medium.

Medium A, wave speed

= 10

m/s

Frequency (Hz)	2.0	4.0	6.0	8.0	10.0
Wavelength (m)	5.0	2.5	1.67	1.25	1.0

Medium B, wave speed

= 20

m/s

Frequency (Hz)	2.0	4.0	6.0	8.0	10.0
Wavelength (m)	10.0	5.0	3.33	2.5	2.0

Medium C, wave speed

= 30

m/s

Frequency (Hz)	2.0	4.0	6.0	8.0	10.0
Wavelength (m)	15.0	7.5	5.0	3.75	3.0

a

Deduce the mathematical relationship between wavelength, frequency, and wave speed, using calculations from at least two media to support your answer. [2]

b

A wave of frequency 5.0 Hz travels through Medium D, where wave speed

= 25

m/s. Show that the wavelength in Medium D is 5.0 m. [2]

c

A second student claims that the prediction for Medium D would be unreliable if the wave speed were not fixed by the medium but instead changed with frequency. Evaluate this claim by analysing what would happen to the relationship

v = f\lambda

under those conditions. [3]

Solutions

27QuestionTransverse vs Longitudinal WavesAssessment Practice

8 marks~12 minCriterion C

A student investigates wave speed in a long spring by generating transverse and longitudinal pulses. Each pulse travels distances of 0.50 m, 1.00 m, 1.50 m, and 2.00 m. The stopwatch uncertainty is

\pm 0.10

s; the ruler uncertainty is

\pm 0.005

m.

Transverse — Distance (m): 0.50, 1.00, 1.50, 2.00 | Time (s): 0.45, 0.92, 1.38, 1.84

Longitudinal — Distance (m): 0.50, 1.00, 1.50, 2.00 | Time (s): 0.48, 0.95, 1.42, 1.89

a

Using

v = \dfrac{d}{t}

and the 2.00 m data, calculate the speed of each wave type. Include the absolute uncertainty in each speed. [4]

b

Using all four distances, calculate a speed for each wave type at every distance. Analyse whether the two wave types travel at the same speed in this spring. [2]

c

Evaluate whether the experimental evidence supports the claim that transverse and longitudinal waves travel at the same speed in the same medium. In your answer, discuss the role of measurement uncertainties in reaching your conclusion. [2]

Solutions

28QuestionIdentifying Crest Trough Compression and RarefactionAssessment Practice

2 marks~3 minCriterion A

Ultrasound imaging is used in hospitals to examine soft tissues such as a developing fetus. The transducer emits high-frequency sound waves that travel through the body as alternating compressions and rarefactions.

a

Identify one reason why ultrasound waves can travel through soft tissue but are partially reflected at a boundary between two tissues of different densities. [1]

b

A radiographer notes that ultrasound cannot produce clear images of structures located behind bone. Explain one physical reason for this limitation, linking your answer to the wave behaviour of compressions and rarefactions at the tissue–bone boundary. [1]

Solutions

29QuestionIdentifying Crest Trough Compression and RarefactionAssessment Practice

6 marks~9 minCriterion D

A medical technician uses an ultrasound scanner to image a fetus during pregnancy. Ultrasound waves are longitudinal waves that travel through soft tissue at approximately 1540 m/s. They reflect at boundaries between tissues of different densities — for example, between soft tissue (

\rho \approx 1050\ \text{kg/m}^3

) and bone (

\rho \approx 1900\ \text{kg/m}^3

). The reflected waves are detected and used to construct the image.

a

Explain what compressions and rarefactions are in a longitudinal wave. [2]

b

Explain how a difference in tissue density at a boundary causes ultrasound waves to reflect. [2]

c

Evaluate the use of ultrasound reflection for prenatal imaging, considering safety, image quality, and the effect of tissue density differences. [2]

Solutions

30QuestionApplications Sonar Ultrasound and Musical InstrumentsAssessment Practice

3 marks~5 minCriterion A

An ultrasound pulse is emitted at

t = 0\ \mu\text{s}

and travels through layers of skin, fat, and muscle. The first reflected pulse returns at

t = 13\ \mu\text{s}

with an amplitude equal to

80\%

of the emitted pulse. The second reflected pulse returns at

t = 26\ \mu\text{s}

with an amplitude equal to

40\%

of the emitted pulse.

a

State one mechanism by which the ultrasound pulse loses energy as it travels through biological tissue. [1]

b

Explain how acoustic impedance mismatch at a tissue boundary determines the amplitude of a reflected pulse. [1]

c

Using the data provided, explain why the second reflected pulse has a smaller amplitude than the first. [1]

Solutions

31QuestionApplications Sonar Ultrasound and Musical InstrumentsAssessment Practice

6 marks~9 minCriterion C

An ultrasound transducer is placed 0.50 m from a flat reflective surface. It emits a pulse and records the time for the echo to return. The total distance travelled by the pulse is 1.0 m. Using

v = \dfrac{d}{t}

, predicted time delays are calculated for four materials.

Speed of sound — Air:

343\ \text{m/s}

, Water:

1482\ \text{m/s}

, Steel:

5960\ \text{m/s}

, Plastic:

2200\ \text{m/s}

Predicted time delay (ms) — Air: 2.92, Water: 0.675, Steel: 0.168, Plastic: 0.455

Experimental time delay (ms) — Air: 2.91, Water: 0.678, Steel: 0.195, Plastic: 0.460

a

Calculate the percentage error for each material using

\text{percentage error} = \left|\frac{\text{experimental} - \text{predicted}}{\text{predicted}}\right| \times 100\%

[2]

b

Deduce, with reference to your values from (a), whether the model

v = \dfrac{d}{t}

is valid for each material tested. [2]

c

Evaluate the physical reason why one material produces a significantly larger percentage error, and explain what this suggests about the limitation of the model

v = \dfrac{d}{t}

for that material. [2]

Solutions

32QuestionSpeed of Sound in Solids Liquids and GasesAssessment Practice

5 marks~8 minCriterion C

The kinetic-molecular model predicts the speed of sound in a medium using

v = \sqrt{\frac{B}{\rho}}

where

B

is the bulk modulus and

\rho

is the density. Measured and theoretical speeds of sound at 20°C are given below.

Medium	Measured speed (m/s)	Theoretical speed (m/s)
Air	343	330
Water	1482	1500
Steel	5960	6100

Percentage discrepancy is defined as

\text{Percentage discrepancy} = \frac{|\text{Measured} - \text{Theoretical}|}{\text{Theoretical}} \times 100

a

Calculate the percentage discrepancy for each medium. [3]

b

Deduce which state of matter the kinetic-molecular model describes most accurately, using your results from (a). [1]

c

Evaluate the overall validity of the kinetic-molecular model for predicting the speed of sound across all three states of matter. [1]

Solutions

33QuestionApplications Sonar Ultrasound and Musical InstrumentsAssessment Practice

4 marks~6 minCriterion B

The table below shows string lengths and fundamental frequencies for four orchestral string instruments.

Instrument	Violin	Viola	Cello	Double Bass
String length (m)	0.33	0.43	0.70	1.10
Fundamental frequency (Hz)	196	150	92	59

a

Deduce the fundamental frequency of a string instrument with a string length of 0.55 m. Support your answer with a calculation using the pattern in the data. [2]

b

Justify the relationship between string length and fundamental frequency using the wave equation

v = f\lambda

and the condition for a standing wave on a string fixed at both ends. [2]

Solutions

34QuestionApplications Sonar Ultrasound and Musical InstrumentsAssessment Practice

6 marks~9 minCriterion B

A student investigates how the tension in a guitar string affects the frequency of the sound it produces. A string of fixed length and thickness is stretched over a pulley; a hanging mass provides the tension. The following data are recorded:

Hanging mass (kg)	0.10	0.20	0.30	0.40	0.50
Frequency (Hz)	130	184	225	260	291

Use

g = 9.8 \text{ m s}^{-2}

.

a

Construct a graph of frequency (y-axis) against

\sqrt{m}

(x-axis), where

m

is the hanging mass. Describe the pattern shown. [2]

b

Deduce a general rule relating frequency

f

to tension

T

, where

T = mg

. Justify your rule using the graph. [2]

c

A guitar string snaps when its vibration frequency exceeds 350 Hz. Analyse whether the string will snap if the hanging mass is increased to 0.80 kg. [2]

Solutions

35QuestionApplications Sonar Ultrasound and Musical InstrumentsAssessment Practice

6 marks~9 minCriterion D

A medical technician uses ultrasound to examine two structures: a liver tumour approximately 12 cm below the skin and a thyroid nodule approximately 2 cm below the skin. Two probes are available: one at 3.5 MHz and one at 7.5 MHz. The speed of ultrasound in human tissue is

1540 \, \text{m/s}

.

a

Calculate the wavelength of the 3.5 MHz ultrasound in tissue. [1]

b

The 7.5 MHz probe produces a wavelength of

2.05 \times 10^{-4}

m in tissue. Deduce how this shorter wavelength affects the minimum size of structure that can be detected, and state one consequence for imaging deep tissue. [2]

c

Evaluate which probe is more appropriate for each examination. In your response, analyse the trade-off between resolution and penetration depth, and discuss how the assumption of uniform tissue density may limit the accuracy of either probe. [3]

Solutions

36QuestionLaws of ReflectionAssessment Practice

4 marks~6 minCriterion B

Two plane mirrors are arranged at exactly

90°

to each other. A ray of light strikes the first mirror at an angle of incidence of

30°

and then reflects onto the second mirror. Refer to the diagram showing the mirror arrangement and the ray path.

a

State the number of reflections the ray undergoes before exiting the mirror system. [1]

b

Calculate the angle of reflection at the second mirror. Show your working. [2]

c

Explain why a ray entering any

90°

mirror system always exits antiparallel to the incident ray, regardless of the initial angle of incidence. [1]

Solutions

37QuestionRefraction Through Glass Blocks and WaterAssessment Practice

8 marks~12 minCriterion D

Anti-reflective coatings on solar panels use thin-film interference to reduce reflection losses. A magnesium fluoride layer (

n = 1.38

) is deposited on a glass substrate (

n = 1.52

). Manufacturing requires rare materials — lanthanum and hafnium — sourced from limited locations, causing environmental disruption. After 25–30 years, separating coating layers from the glass substrate during recycling is difficult. A

300\,\text{W}

solar panel operates in a location receiving

4.5

peak sun hours per day.

Use

E = Pt

, where

E

is energy in kWh,

P

is power in kW, and

t

is time in hours.

a

Explain how the magnesium fluoride coating reduces reflection of light with wavelength

\lambda = 550\,\text{nm}

in air. State the condition for destructive interference in terms of coating thickness

t

, wavelength

\lambda

, and refractive index

n

. [2]

b

The coating increases the panel's power output by

3\%

. Calculate the additional electrical energy generated per year, assuming the panel operates for 365 days. Show your working clearly. [2]

c

Evaluate the trade-offs involved in using advanced anti-reflective coatings on solar panels. In your response, address at least two of the following: environmental cost of mining and manufacturing; benefits of increased renewable energy generation; challenges of recycling and disposal; unequal global distribution of critical materials. Also discuss one limitation of the thin-film interference model in predicting coating performance over the panel's lifetime. [4]

Solutions

38QuestionRay Diagrams and Image Formation BasicsAssessment Practice

3 marks~5 minCriterion C

A student investigates refraction as light passes from air into a glass block. The table shows the angle of incidence

i

and angle of refraction

r

for four trials.

Trial 1	$i = 20°$	$r = 13°$
Trial 2	$i = 30°$	$r = 19°$
Trial 3	$i = 45°$	$r = 28°$
Trial 4	$i = 60°$	$r = 35°$

Snell's law for light entering glass from air:

n = \dfrac{\sin i}{\sin r}

a

Using Trial 2, calculate the refractive index

n

of the glass. [1]

b

A second student uses Trial 4 to calculate

n

and obtains a different value. Deduce whether the two results are consistent with the glass having a single refractive index, and identify one source of experimental uncertainty that could account for any difference. [1]

c

Evaluate whether the glass could be used to achieve total internal reflection when light travels from the glass into air, given that the critical angle

\theta_c

is related to refractive index by

\sin \theta_c = \dfrac{1}{n}

. [1]

Solutions

39QuestionRay Diagrams and Image Formation BasicsAssessment Practice

5 marks~8 minCriterion A

A student investigates image formation by a converging lens of focal length

f = 10

cm. She places an object at distances

u

from the lens and records the image distance

v

.

u

(cm): 20.0, 15.0, 12.0, 10.0, 5.0

v

(cm): 20.0, 30.0, 60.0, undefined, −10.0

a

Describe the pattern relating

v

to

u

as

u

decreases from 20.0 cm to 5.0 cm. Include reference to the sign of

v

. [2]

b

Using the lens equation

\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}

, deduce the value of

v

when

u = 7.5

cm, and justify what the sign of your answer indicates about the image. [3]

Solutions

40QuestionPlane Concave and Convex MirrorsAssessment Practice

6 marks~9 minCriterion B

A student investigates a concave mirror of unknown focal length

f

, where

10 \text{ cm} < f < 15 \text{ cm}

, by placing an object at distances

u =

5, 10, 15, 20, 25, and 30 cm and recording the image formed at each position.

a

Predict the image characteristics (real/virtual, upright/inverted, magnified/diminished) at each of the six object distances. [2]

b

Using your predictions, deduce a general rule that relates the type of image produced to the object's position relative to

F

and

C

. [2]

c

Justify your rule in part (b) by discussing the behaviour of principal rays in a concave mirror ray diagram, including what happens when reflected rays diverge rather than converge. [2]

Solutions

Waves Sound and Light — Free MYP4 Physics Practice Questions