Wave Behaviour — Free IB Physics SL Practice Questions

1FoundationMCQProperties of waves (amplitude, frequency, wavelength, speed)1 markPaper 1~2 min

An oscilloscope has its time base set to

5.0 \text{ ms div}^{-1}

. One complete cycle of a wave spans exactly 4 divisions on the horizontal axis. What is the frequency of the wave?

Solutions

2FoundationMCQProperties of waves (amplitude, frequency, wavelength, speed)1 markPaper 1~2 min

An oscilloscope displays a sound wave with a time base set to

2 \text{ ms per division}

. The trace shows exactly 2 complete cycles spanning 10 divisions. What is the frequency of the sound wave?

Solutions

3FoundationMCQProperties of waves (amplitude, frequency, wavelength, speed)1 markPaper 1~2 min

A displacement–time graph of a wave shows exactly one complete cycle occurring over

0.20 \text{ s}

. What is the frequency of the wave?

Solutions

4FoundationMCQProperties of waves (amplitude, frequency, wavelength, speed)1 markPaper 1~2 min

A transverse wave has a wavelength of

2.0\text{ m}

and a vertical distance from crest to trough of

0.40\text{ m}

. What is the amplitude of the wave?

Solutions

5FoundationMCQProperties of waves (amplitude, frequency, wavelength, speed)1 markPaper 1~2 min

A snapshot graph shows the displacement of a transverse wave at a fixed instant. The distance between two consecutive crests is

4.0 \text{ cm}

and the maximum displacement from the equilibrium position is

1.5 \text{ cm}

. What is the amplitude of this wave?

Solutions

6FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A string is fixed at both ends and vibrates in its third harmonic. How many nodes and antinodes are present in this standing wave?

Solutions

7FoundationMCQStanding waves and resonance1 markPaper 1~2 min

The distance between two consecutive antinodes of a standing wave on a stretched string is

0.40 \text{ m}

. What is the wavelength of the travelling waves that produce this standing wave?

Solutions

8FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A pipe of length

L

is closed at one end and open at the other. A standing wave is established at the fundamental frequency. The fundamental wavelength is

\lambda = 4L

. Which row correctly identifies the displacement boundary conditions at each end?

Solutions

9FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A string of length

1.2\text{ m}

is fixed at both ends and vibrates in its second harmonic. What is the distance between a node and its nearest antinode?

Solutions

10FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A string is fixed at both ends and vibrates in a standing wave pattern that has 5 nodes, including both fixed ends. Which harmonic is this?

Solutions

11FoundationMCQDisplacement, velocity, and acceleration in SHM1 markPaper 1~2 min

A particle undergoes simple harmonic motion. The graph of acceleration

a

against displacement

x

is a straight line passing through the origin, described by

a = -\omega^2 x

, where

\omega = 4.0 \text{ rad s}^{-1}

. What is the gradient of this graph?

Solutions

12FoundationMCQDisplacement, velocity, and acceleration in SHM1 markPaper 1~2 min

A particle undergoes simple harmonic motion with displacement

x = A\cos(\omega t)

. Which graph correctly shows the variation of acceleration

a

with time

t

?

Solutions

13FoundationMCQEnergy in SHM1 markPaper 1~2 min

The graph shows potential energy

E_p

versus displacement

x

for a particle undergoing simple harmonic motion. The curve is parabolic, symmetric about

x = 0

, and reaches a maximum value of

8.0\text{ J}

at the amplitude. What is the total mechanical energy of the system?

Solutions

14FoundationMCQPendulum and spring systems1 markPaper 1~2 min

A mass on a spring undergoes simple harmonic motion with amplitude

0.10 \text{ m}

and period

2.0 \text{ s}

. What is the maximum speed of the mass?

Solutions

15FoundationMCQDisplacement, velocity, and acceleration in SHM1 markPaper 1~2 min

An object oscillates such that its acceleration

a

and displacement

x

from equilibrium satisfy

a = -\omega^2 x

, where

\omega

is a positive constant. Which statement correctly describes the condition this equation imposes on the motion?

Solutions

16MasterySAQ-STypes of waves: Transverse and longitudinal5 marksPaper 2~8 min

An earthquake generates P-waves and S-waves simultaneously at the epicentre. P-waves travel through the Earth's interior at

v_\text{P} = 5.0 \text{ km s}^{-1}

. S-waves travel at

v_\text{S} = 3.0 \text{ km s}^{-1}

. A seismometer detects the P-wave arrival 4.0 s before the S-wave arrival.

(a)

State the difference in the direction of particle oscillation between P-waves and S-waves. [1 mark]

(b)

S-waves cannot travel through the liquid outer core of the Earth. (i) State the physical property that liquids lack which prevents S-wave propagation. [1]
(ii) Explain, using your answer to (b)(i), why S-waves cannot propagate through the liquid outer core. [1 mark]

(c)

Determine the distance from the earthquake epicentre to the seismometer. [2 marks]

Solutions

17MasterySAQ-STypes of waves: Transverse and longitudinal5 marksPaper 2~8 min

A student sets up a slinky spring to demonstrate wave motion. She holds one end and sends a single pulse along the slinky. The displacement of a coil in the slinky is perpendicular to the direction of energy transfer.

(a)

State the name of the type of wave being demonstrated. [1 mark]

(b)

Describe the motion of a single coil in the slinky as the pulse passes through it. [2 marks]

(c)

The student changes the motion so that the displacement of a coil is parallel to the direction of energy transfer. State how the direction of coil oscillation in this new wave differs from that in (b). [1 mark]

(d)

Identify one visible feature of the coil pattern in this new wave that was absent in the original transverse pulse. [1 mark]

Solutions

18ChallengeSAQ-LWave equations7 marksPaper 2~11 min

A marine biologist uses a piezoelectric transducer to generate ultrasound waves for studying sediment layers on the ocean floor. The transducer emits a continuous sinusoidal wave of frequency

50\,\text{kHz}

into seawater. The wave travels through a sand layer before reflecting off a rock bed. The speed of sound in seawater is

1500\,\text{m s}^{-1}

and in the sand layer is

1800\,\text{m s}^{-1}

. The density of seawater is

1025\,\text{kg m}^{-3}

and the density of sand is

2000\,\text{kg m}^{-3}

.

(a)

Calculate the wavelength of the ultrasound wave in the seawater. [1 mark]

(b)

Explain why the wave speed changes when the ultrasound enters the sand layer. [2 marks]

(c)

Calculate the wavelength of the ultrasound in the sand layer. [1 mark]

(d)

The wave reflects at the sand–rock interface, introducing a phase change of

\pi\,\text{rad}

. The reflected wave travels back through the sand interferes with the incident wave at the sand–seawater interface. State the phase condition required for destructive interference at the sand–seawater interface, and hence determine the minimum thickness of sand that produces this destructive interference. [3 marks]

Solutions

19FoundationSAQ-LWave equations7 marksPaper 2~11 min

A wave is generated in a ripple tank. The displacement of the water surface is given by

y(x,t) = 0.0050 \sin(12x - 8t)

where

x

is in metres,

t

is in seconds, and the amplitude is in metres. For deep-water waves, the wave speed is given by

v_{\text{deep}} = \sqrt{\dfrac{g\lambda}{2\pi}}

, where

g = 9.81 \text{ m s}^{-2}

.

(a)

(i) Determine the wavelength and frequency of the wave. [2]
(ii) Determine the wave speed. [1]
(iii) Determine the maximum speed of a water particle in the medium. [1 mark]

(b)

Calculate the theoretical deep-water wave speed for this wavelength. Hence evaluate whether this wave behaves as a deep-water wave. [2 marks]

(c)

The wave generator frequency is doubled while the water depth remains unchanged. The new wavelength is

0.262 \text{ m}

. Using the deep-water formula, calculate the theoretical deep-water speed for the new wavelength. Evaluate whether doubling the frequency makes the wave more or less consistent with deep-water behaviour, justifying your answer by comparing both wave speeds with their respective deep-water predictions. [1 mark]

Solutions

20MasterySAQ-STypes of waves: Transverse and longitudinal7 marksPaper 2~11 min

A student flicks one end of a stretched rope to produce a single pulse that travels toward a fixed wall 2.5 m away. The pulse reflects and returns to the student's hand. The total time for the pulse to travel to the wall and back is 0.80 s.

(a)

State the type of wave produced in the rope. [1 mark]

(b)

Calculate the speed of the pulse in the rope. [2 marks]

(c)

Describe the motion of a small segment of the rope as the pulse passes through it. [2 marks]

(d)

The student replaces the fixed end with a free end by looping the rope over a frictionless peg. Analyse how the reflected pulse from the free end differs from the reflected pulse at the fixed end, and justify this difference by referring to the boundary condition at each end. [2 marks]

Solutions

21FoundationSAQ-SReflection, refraction, diffraction, and interference5 marksPaper 2~8 min

Data

\dfrac{\sin \theta_1}{\sin \theta_2} = \dfrac{v_1}{v_2}

,

\quad v = f\lambda

A water wave passes from deep water into shallow water at an angle. The wave speed in deep water is

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

and in shallow water is

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

. The angle of incidence in deep water is

40°

.

(a)

State what happens to the frequency of the wave as it enters shallow water. [1 mark]

(b)

Explain what happens to the wavelength of the wave as it enters shallow water. [2 marks]

(c)

Calculate the angle of refraction in the shallow water. [2 marks]

Solutions

22MasterySAQ-SReflection, refraction, diffraction, and interference5 marksPaper 2~8 min

A student investigates the diffraction of water waves in a ripple tank. Plane waves of wavelength

\lambda = 2.0\,\text{cm}

approach a barrier with a single narrow gap of width

b = 1.5\,\text{cm}

. The student observes the pattern of waves beyond the gap. -

(a)

State the wave phenomenon observed when waves pass through the gap. - [1 mark]

(b)

Calculate the ratio

\dfrac{\lambda}{b}

and use it to determine whether significant diffraction will be observed. - [2 marks]

(c)

The student reduces the wavelength to

\lambda = 0.8\,\text{cm}

while keeping the gap width unchanged. Explain how the diffraction pattern changes. [2 marks]

Solutions

23ChallengeSAQ-LReflection, refraction, diffraction, and interference7 marksPaper 2~11 min

A marine biologist uses a boat-mounted sonar system to map the seafloor. The system emits a short pulse of sound at a frequency of

50\,\text{kHz}

directly downwards. The pulse reflects off the flat seafloor and returns to the boat

0.12\,\text{s}

later. The speed of sound in seawater is

1500\,\text{m s}^{-1}

.

(a)

Calculate the depth of the seafloor. The boat moves to a second region where the water depth remains

90\,\text{m}

. Here, a layer of sediment of thickness

4.5\,\text{m}

lies on top of a harder rock layer. The speed of sound in the sediment is

1700\,\text{m s}^{-1}

. [2 marks]

(b)

Calculate the time interval between the arrival of the echo from the top of the sediment layer and the echo from the rock layer at the boat. [3 marks]

(c)

Explain why the amplitude of the echo returning from the rock layer is significantly smaller than the amplitude of the echo returning from the top of the sediment layer. [2 marks]

Solutions

24FoundationSAQ-SReflection, refraction, diffraction, and interference7 marksPaper 2~11 min

A student shines a laser through a single narrow slit onto a screen, producing a diffraction pattern. The slit width is

b = 0.10 \text{ mm}

, the wavelength of the laser light is

\lambda = 650 \text{ nm}

, and the distance from the slit to the screen is

D = 2.0 \text{ m}

. The condition for single-slit diffraction minima is

b \sin\theta = m\lambda

, where

m

is a non-zero integer.

(a)

Describe how the diffraction pattern on the screen changes when the slit width is increased. [2 marks]

(b)

Calculate the angular position

\theta

of the first minimum from the central maximum. [2 marks]

(c)

The student replaces the laser with one of wavelength

\lambda = 450 \text{ nm}

, keeping all other conditions the same. Determine the width of the central maximum on the screen for this new wavelength, and explain whether the central maximum is wider or narrower than for the original laser. [3 marks]

Solutions

25MasterySAQ-SReflection, refraction, diffraction, and interference5 marksPaper 2~8 min

An engineer tests the acoustic design of a concert hall. A loudspeaker emitting a single pure tone of frequency

440\,\text{Hz}

is placed at one end of the hall. A microphone detects the sound. The speed of sound in air is

340\,\text{m s}^{-1}

.

(a)

State the wave phenomenon that allows sound to be detected around a corner, not in the direct line of sight of the loudspeaker. [1 mark]

(b)

Calculate the wavelength of the sound wave. [2 marks]

(c)

The engineer replaces the loudspeaker with one emitting a frequency of

8800\,\text{Hz}

. The doorway through which the sound must pass to reach the microphone has a width of

0.039\,\text{m}

. Evaluate whether significant diffraction of this higher-frequency sound will occur through the doorway. [2 marks]

Solutions

26MasterySAQ-SPendulum and spring systems6 marksPaper 2~9 min

Data

g = 9.81 \text{ m s}^{-2}, \quad E_{\text{k}} = \tfrac{1}{2}mv^2, \quad E_{\text{el}} = \tfrac{1}{2}kx^2, \quad T = 2\pi\sqrt{\dfrac{l}{g}}

A mass of 0.50 kg is attached to a spring of spring constant 20 N m⁻¹ on a frictionless horizontal surface. The mass is displaced 0.12 m from its equilibrium position and released from rest. A simple pendulum, also with a bob of mass 0.50 kg, oscillates on a string of length 1.2 m with small amplitude.

(a)

State the forms of energy exchanged during one complete oscillation of each system. (i) Mass–spring system. [1]
(ii) Pendulum system. [1 mark]

(b)

Calculate the maximum speed of the mass in the mass–spring system. [2 marks]

(c)

Evaluate the effect on the period of the pendulum when the string length is halved to 0.60 m and the bob mass is doubled to 1.0 kg. [2 marks]

Solutions

27MasterySAQ-SPendulum and spring systems6 marksPaper 2~9 min

A student investigates the oscillation of a pendulum and a mass–spring system. The pendulum consists of a bob of mass

0.25 \text{ kg}

suspended from a light string of length

0.80 \text{ m}

. The mass–spring system consists of the same

0.25 \text{ kg}

mass attached to a spring of spring constant

12 \text{ N m}^{-1}

. Both systems undergo small-amplitude oscillations.

g = 9.81 \text{ m s}^{-2}, \quad T_{\text{pendulum}} = 2\pi \sqrt{\frac{l}{g}}, \quad T_{\text{spring}} = 2\pi \sqrt{\frac{m}{k}}

(a)

State two conditions required for a system to undergo simple harmonic motion. [2 marks]

(b)

Calculate the period of oscillation of the pendulum. [1 mark]

(c)

Calculate the period of the mass–spring system. [1 mark]

(d)

The student claims that changing the mass to

0.50 \text{ kg}

would make the two periods equal. Evaluate this claim by considering how each period depends on mass. [2 marks]

Solutions

28ChallengeSAQ-LPendulum and spring systems9 marksPaper 2~14 min

A student investigates the relationship between the period of oscillation and the mass for a spring–mass system. The spring has a small but non-negligible mass. The student measures the period

T

for different hanging masses

m

and plots a graph of

T^2

against

m

. The data yields a straight line with gradient

4.0 \pm 0.1 \ \text{s}^2 \ \text{kg}^{-1}

and y-intercept

0.05 \pm 0.02 \ \text{s}^2

.

(a)

Determine the spring constant

k

of the spring, including its absolute uncertainty. [3 marks]

(b)

Explain the physical significance of the non-zero y-intercept in this experiment. [2 marks]

(c)

The student forms a simple pendulum of length

L = 1.00 \pm 0.01 \ \text{m}

using the same set of masses. Determine the period of this pendulum and compare it with the period of the spring–mass system when

m = 0.50 \ \text{kg}

. [2 marks]

(d)

Evaluate which system — spring–mass or simple pendulum — is more suitable for precise timekeeping in a laboratory where temperature varies significantly. [2 marks]

Solutions

29FoundationSAQ-LPendulum and spring systems9 marksPaper 2~14 min

Data

T = 2\pi\sqrt{\frac{L}{g}}, \quad T = 2\pi\sqrt{\frac{m}{k}}

A precision pendulum clock is designed to keep accurate time on Earth. The pendulum has a length of 0.994 m and advances one second per complete oscillation, giving a period of 2.00 s.

(a)

Determine the design value of

g

used in the clock's calibration. [2 marks]

(b)

The clock is transported to the top of a mountain where

g

decreases by 0.50%. Determine the new period of the pendulum at this location. [2 marks]

(c)

An alternative timekeeper uses a spring–mass system with mass 0.50 kg, designed to have the same 2.00 s period as the pendulum on Earth. Determine the required spring constant

k

. [2 marks]

(d)

Evaluate which timekeeper maintains more accurate timekeeping at the mountain location. Support your answer with a quantitative calculation of the timing error accumulated over one hour. [3 marks]

Solutions

30MasterySAQ-SPendulum and spring systems5 marksPaper 2~8 min

A simple pendulum of length

L = 1.20

m is displaced by a small angle and released from rest. A displacement–time graph of the motion shows two complete oscillations beginning at maximum positive displacement. The maximum displacement of the bob from equilibrium is not labelled on the graph axis; the scale must be read directly.

(a)

State the amplitude of oscillation as read from the graph. [1 mark]

(b)

Calculate the period of the pendulum using

g = 9.81

m s

^{-2}

. [2 marks]

(c)

The pendulum is then released from a much larger angle so that the small-angle approximation no longer holds. - (i) Explain how the shape of the displacement–time graph would differ from that observed at small angles. [1] -
(ii) Deduce whether the period of oscillation would be greater than, equal to, or less than the value calculated in (b). [1 mark]

Solutions

Wave Behaviour — Free Physics SL Practice Questions