Wave Behaviour — Free IB Physics HL Practice Questions

1FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A tuning fork of frequency 256 Hz is held above a resonance tube partially filled with water. The first resonance is heard when the air column length is 0.33 m. What is the speed of sound in air?

Solutions

2FoundationMCQStanding waves and resonance1 markPaper 1~2 min

Two waves, each of amplitude

3.0 \text{ cm}

, travel in opposite directions along a string and superpose to form a standing wave. What is the amplitude of oscillation at antinode?

Solutions

3FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A pipe open at both ends resonates at a fundamental frequency of

200 \text{ Hz}

. What is the frequency of the second harmonic of this pipe?

Solutions

4FoundationMCQStanding waves and resonance1 markPaper 1~2 min

A standing wave is formed on a string. The standing wave has a frequency of

60 \text{ Hz}

and a wavelength of

1.0 \text{ m}

. What is the speed of the travelling waves that superpose to form this standing wave?

Solutions

5FoundationMCQTypes of waves: Transverse and longitudinal1 markPaper 1~2 min

In a longitudinal wave, a compression travels through a medium. Which statement correctly describes the motion of the medium's particles relative to the direction of energy transfer?

Solutions

6FoundationMCQTypes of waves: Transverse and longitudinal1 markPaper 1~2 min

A slinky spring is pushed and pulled repeatedly along its length. Which statement correctly describes the wave produced and the motion of the coils?

Solutions

7FoundationMCQTypes of waves: Transverse and longitudinal1 markPaper 1~2 min

A wave travels horizontally through a medium. Which statement correctly distinguishes a transverse wave from a longitudinal wave in terms of particle motion?

Solutions

8FoundationMCQTypes of waves: Transverse and longitudinal1 markPaper 1~2 min

A student holds one end of a horizontal rope and moves it repeatedly up and down, sending a wave along the rope toward a fixed wall. Which statement correctly describes the motion of the rope particles relative to the direction of wave travel?

Solutions

9FoundationMCQDisplacement, velocity, and acceleration in SHM1 markPaper 1~2 min

A particle undergoes simple harmonic motion with angular frequency

\omega

. Which expression correctly relates the acceleration

a

of the particle to its displacement

x

from the equilibrium position?

Solutions

10FoundationMCQDisplacement, velocity, and acceleration in SHM1 markPaper 1~2 min

A particle oscillates in simple harmonic motion with amplitude

A

and angular frequency

\omega

. Which expression gives the speed of the particle as it passes through the equilibrium position?

Solutions

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

A particle undergoes simple harmonic motion with angular frequency

\omega

and amplitude

A

. At the instant the particle reaches maximum displacement, what is the magnitude of its acceleration?

Solutions

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

A particle undergoes simple harmonic motion with displacement

x = A\cos(\omega t)

. What is the phase difference between the velocity and the displacement of the particle?

Solutions

13FoundationSAQ-SReflection, refraction, diffraction, and interference5 marksPaper 2~8 min

Two coherent sources of microwaves are placed

d = 3.0 \text{ cm}

apart and emit waves of wavelength

\lambda = 1.5 \text{ cm}

. A detector is moved along a line far from the sources, perpendicular to the line joining them.

(a)

State the condition on path difference for constructive interference to occur at a point on the detector line, and explain why this condition produces constructive interference. [2 marks]

(b)

Calculate the angle

\theta

from the central maximum to the first-order maximum. *Useful relation:

d \sin\theta = m\lambda

* [3 marks]

Solutions

14MasterySAQ-SDoppler effect5 marksPaper 2~8 min

A student investigates the Doppler effect using a sound source that rotates in a horizontal circle of radius

0.50\,\text{m}

at a constant angular speed. A microphone is placed at a large distance from the circle. The source emits sound of frequency

440\,\text{Hz}

. The speed of sound in air is

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

. The maximum observed frequency recorded by the microphone is

462\,\text{Hz}

.

(a)

State why the observed frequency varies as the source rotates. [1 mark]

(b)

Calculate the linear speed of the sound source. [2 marks]

(c)

Calculate the minimum frequency observed by the microphone and determine the angular speed of the source. [2 marks]

Solutions

15ChallengeSAQ-LReflection, refraction, diffraction, and interference7 marksPaper 2~11 min

A physics student investigates the diffraction of water waves in a ripple tank. A straight wavefront of wavelength

\lambda = 2.4\,\text{cm}

approaches a narrow gap of width

b = 3.0\,\text{cm}

between two barriers. The wave speed is

v = 12\,\text{cm}\,\text{s}^{-1}

.

(a)

Calculate the angle from the straight-through direction to the first diffraction minimum. [2 marks]

(b)

Explain the effect on the diffraction pattern when the gap width is increased to

6.0\,\text{cm}

, keeping the wave frequency unchanged. [2 marks]

(c)

The student adjusts the wave frequency until the first minimum occurs at

\theta = 30°

with the same

3.0\,\text{cm}

gap. (i) Determine the new wavelength and the new wave speed. [2]
(ii) The wave speed in a ripple tank depends on water depth. The student claims that to achieve the new wave speed, only the frequency needs to be changed, not the water depth. Evaluate this claim. [1 mark]

Solutions

16FoundationSAQ-SReflection, refraction, diffraction, and interference5 marksPaper 2~8 min

Data

\text{width of central maximum} = \frac{2\lambda D}{b}

A student observes a single-slit diffraction pattern using red light of wavelength 700 nm. The slit width is 0.050 mm and the screen is placed 1.5 m from the slit.

(a)

State two ways in which the central maximum differs from the secondary maxima. [2 marks]

(b)

Calculate the width of the central maximum on the screen. [3 marks]

Solutions

17FoundationSAQ-SReflection, refraction, diffraction, and interference7 marksPaper 2~11 min

A ripple tank is used to study refraction of water waves. In deep water, the wavelength is

4.0 \text{ cm}

and the wave speed is

20 \text{ cm s}^{-1}

. When the waves enter shallow water at an angle of incidence of

40°

, the wavelength becomes

3.0 \text{ cm}

.

(a)

State what happens to (i) the frequency and
(ii) the wave speed as the waves move from deep to shallow water. [2 marks]

(b)

Calculate the frequency of the waves. [1 mark]

(c)

Calculate the wave speed in shallow water. [2 marks]

(d)

The waves cross the boundary at an angle of incidence of

40°

. Determine the angle of refraction as the waves enter the shallow water. [2 marks]

Solutions

18MasterySAQ-SStanding waves and resonance5 marksPaper 2~8 min

A stretched string of length

L = 1.2\,\text{m}

is fixed at both ends and driven by a vibrator. A standing wave with

3

antinodes is observed at a driving frequency of

f = 150\,\text{Hz}

.

(a)

State the condition the driving frequency required to produce a standing wave in the string. [1 mark]

(b)

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

(c)

The tension in the string is now increased while the driving frequency remains at

150\,\text{Hz}

. The standing wave pattern disappears. Explain why the pattern disappears and deduce the next higher frequency at which a standing wave could be re-established by adjusting only the driving frequency, given that the new wave speed on the string is

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

. [2 marks]

Solutions

19FoundationSAQ-LWave equations7 marksPaper 2~11 min

A wave pulse travelling along a string is described by

y(x,t) = \frac{0.50}{(x - 2t)^2 + 1}

where

x

and

y

are in metres and

t

is in seconds.

(a)

State the speed and direction of propagation of this pulse. [2 marks]

(b)

The table below shows values of

y

calculated at

t = 0

and at

t = 1.0\ \text{s}

.

x

/ m —

y

at

t = 0

/ m —

y

at

t = 1.0\ \text{s}

/ m 0.0 — 0.50 — 0.10 1.0 — 0.25 — 0.50 2.0 — 0.10 — 0.25 3.0 — 0.050 — 0.10 Determine the displacement of the peak of the pulse between

t = 0

and

t = 1.0\ \text{s}

, and show that this is consistent with your answer to (a). [2 marks]

(c)

State one advantage of using a pulse function, rather than a sinusoidal wave function, to model wave motion on a string. [1 mark]

(d)

Explain one limitation of the pulse model

y(x,t) = \dfrac{0.50}{(x - 2t)^2 + 1}

when applied to real wave behaviour on a string. [2 marks]

Solutions

20MasterySAQ-STypes of waves: Transverse and longitudinal5 marksPaper 2~8 min

A loudspeaker produces a sound wave that travels through air toward a microphone placed 1.7 m away. The sound wave has a frequency of 200 Hz and a wavelength of 1.7 m.

(a)

State the type of wave that sound is. [1 mark]

(b)

Describe how energy is transferred from the loudspeaker to the microphone. Refer to the motion of the air particles and the pattern of pressure variation produced. [2 marks]

(c)

State one difference between the direction of particle oscillation in this sound wave and in a transverse wave travelling along a stretched string. [1 mark]

(d)

Justify why a sound wave cannot propagate as a transverse wave through air. [1 mark]

Solutions

21ChallengeSAQ-LWave equations7 marksPaper 2~11 min

A student investigates transverse waves on a stretched string of linear mass density

\mu = 0.0025\,\text{kg m}^{-1}

under tension

T = 3.6\,\text{N}

. The displacement of the string is described by:

y(x,t) = 0.020\sin(15x - 120t)

where

y

and

x

are in metres and

t

is in seconds.

(a)

Determine the wave speed from the wave function. [1 mark]

(b)

Calculate the wave speed predicted by the string properties and state whether this consistent with your answer to (a). [2 marks]

(c)

Calculate the maximum transverse acceleration of a point on the string. [2 marks]

(d)

Show by substitution into the one-dimensional wave equation

\dfrac{\partial^2 y}{\partial x^2} = \dfrac{1}{v^2}\dfrac{\partial^2 y}{\partial t^2}

that the given function is a valid solution, and state the value of

v

that emerges. [2 marks]

Solutions

22FoundationSAQ-SProperties of waves (amplitude, frequency, wavelength, speed)5 marksPaper 2~8 min

A seismic P-wave travels through the Earth at a speed of

8.0 \text{ km s}^{-1}

and has a frequency of

2.0 \text{ Hz}

.

(a)

State the relationship between wave intensity

I

and wave amplitude

A

. [1 mark]

(b)

A second seismic wave of the same frequency has an amplitude three times greater than the first wave. Determine the ratio

\dfrac{I_2}{I_1}

of their intensities. [2 marks]

(c)

Calculate the wavelength of the seismic P-wave. Give your answer in metres. Useful relationships:

v = f\lambda

,

1 \text{ km} = 1000 \text{ m}

[2 marks]

Solutions

23FoundationSAQ-SProperties of waves (amplitude, frequency, wavelength, speed)5 marksPaper 2~8 min

A light wave in vacuum has a wavelength of 500 nm and travels at

3.0 \times 10^8 \text{ m s}^{-1}

.

(a)

Calculate the frequency of the light wave. [2 marks]

(b)

The light enters a glass block in which its speed is

2.0 \times 10^8 \text{ m s}^{-1}

. Determine the wavelength of the light inside the glass. [2 marks]

(c)

Deduce whether the frequency of the light changes as it enters the glass. [1 mark]

Solutions

24MasterySAQ-STypes of waves: Transverse and longitudinal5 marksPaper 2~8 min

A student generates a continuous wave in a long slinky spring by moving one end repeatedly up and down with a period of

T = 0.50\ \text{s}

. The distance between two consecutive crests is measured as

\lambda = 0.40\ \text{m}

.

(a)

State the type of wave produced by this motion. [1 mark]

(b)

Describe the motion of a single coil in the spring as the wave passes through it. Refer to both the direction of oscillation and the period of oscillation. [2 marks]

(c)

The student changes the motion so that the end of the spring is pushed and pulled repeatedly along the spring's length, keeping the same period

T = 0.50\ \text{s}

. Analyse how the wave now produced differs from the original wave. In your answer, compare the motion of the coils and deduce whether the wave speed changes, given that the wavelength is observed to remain

0.40\ \text{m}

. [2 marks]

Solutions

25FoundationSAQ-LPendulum and spring systems11 marksPaper 2~17 min

A spring-mass system oscillates with a period of 0.60 s when a 0.25 kg mass is attached. Separately, a simple pendulum of length 1.50 m is set into motion with small amplitude on Earth.

T = 2\pi\sqrt{\frac{m}{k}}, \quad T = 2\pi\sqrt{\frac{L}{g}}, \quad g = 9.81 \text{ m s}^{-2}

(a)

Determine the spring constant

k

of the spring. [2 marks]

(b)

Determine the period of the pendulum on Earth. [2 marks]

(c)

The pendulum is taken to a planet where the gravitational field strength is half that of Earth. Determine the new period of the pendulum on this planet. [2 marks]

(d)

Explain why the period of the spring-mass system would remain unchanged on the planet in (c). [2] (e) A spacecraft undergoes variable acceleration during flight. Evaluate which system — the spring-mass oscillator or the pendulum — would be more reliable for timekeeping aboard the spacecraft. [3 marks]

Solutions

26MasterySAQ-SDisplacement, velocity, and acceleration in SHM5 marksPaper 2~8 min

A loudspeaker cone oscillates with simple harmonic motion. The cone has an amplitude of

2.5\,\text{mm}

and a frequency of

120\,\text{Hz}

. At time

t = 0

, the cone is at its maximum positive displacement.

(a)

State the acceleration of the cone at the instant it passes through the equilibrium position. [1 mark]

(b)

Calculate the magnitude of the maximum acceleration of the cone. [2 marks]

(c)

The cone passes through the equilibrium position with maximum speed. Using energy conservation, explain why the speed is maximum at this point and not any other displacement. [2 marks]

Solutions

27ChallengeSAQ-LPendulum and spring systems7 marksPaper 2~11 min

A pendulum consists of a small metal bob of mass

m = 0.200 \text{ kg}

attached to a light string of length

L = 1.50 \text{ m}

. It is displaced by a small angle and released from rest. The pendulum is inside an elevator accelerating upward at

a = 2.00 \text{ m s}^{-2}

.

(a)

Determine the effective gravitational acceleration

g_{\text{eff}}

experienced by the pendulum bob in the accelerating elevator. [1 mark]

(b)

Determine the period of the pendulum in the accelerating elevator. [2 marks]

(c)

The bob is detached from the string and attached instead to a vertical spring of spring constant

k = 50.0 \text{ N m}^{-1}

. Calculate the period of oscillation of this spring–mass system inside the same accelerating elevator. [1 mark]

(d)

Explain why the period of the spring–mass system is unaffected by the elevator's acceleration, whereas the period of the pendulum is affected. Hence deduce which system would function as a more reliable clock in a non-inertial reference frame, and justify your answer. [3 marks]

Solutions

28FoundationSAQ-SDisplacement, velocity, and acceleration in SHM4 marksPaper 2~6 min

A mass-spring system oscillates with simple harmonic motion. The displacement of the mass from its equilibrium position is given by

x = 0.032\cos(4.5t)

, where

x

is in metres and

t

is in seconds.

(a)

State two characteristics of the acceleration of a mass undergoing simple harmonic motion. [2 marks]

(b)

Calculate the magnitude of the maximum acceleration of the mass. [2 marks]

Solutions

29FoundationSAQ-SDisplacement, velocity, and acceleration in SHM5 marksPaper 2~8 min

Data

v = \pm \omega \sqrt{A^2 - x^2}

,

\quad \omega = \dfrac{2\pi}{T}

A particle executes simple harmonic motion (SHM) with amplitude

A = 0.12 \text{ m}

and period

T = 2.0 \text{ s}

.

(a)

State how the speed of the particle changes as it moves from the equilibrium position to maximum displacement. [1 mark]

(b)

Calculate the maximum speed of the particle. [2 marks]

(c)

Determine the speed of the particle when its displacement from equilibrium is

x = 0.060 \text{ m}

. [2 marks]

Solutions

30MasterySAQ-SDisplacement, velocity, and acceleration in SHM5 marksPaper 2~8 min

A mass of

0.50\,\text{kg}

is attached to a spring and oscillates vertically with simple harmonic motion. The graph below shows how the displacement

x

of the mass from its equilibrium position varies with time

t

.

(a)

State the amplitude and period of the oscillation. [1 mark]

(b)

Calculate the maximum speed of the mass. [2 marks]

(c)

The mass is released from rest at

t = 0

. Discuss how both the net force on the mass and its kinetic energy change during the first quarter-period (

t = 0

to

t = 0.15\,\text{s}

). [2 marks]

Solutions

Wave Behaviour — Free Physics HL Practice Questions