IB Physics
Wave Properties (Part I)
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Science Department
Grade 12
Test
IB PHYSICS HL
Wave Properties (Part I)
IB Physics
Wave Properties (Part I)
Section A: Multiple Choice Questions (1 mark each)
1. The displacement d of a particle in a wave varies with distance x along a wave and with time t
as shown below
Which expression gives the speed of the wave?
A.
𝑙
4𝜏
B.
𝑙
2𝜏
C.
𝑙
𝜏
D.
2𝑙
𝜏
(1)
2. A mass on the end of a horizontal spring is displaced from its equilibrium position by a
distance A and released. Its subsequent oscillations have total energy E and time period T.
An identical mass is attached to an identical spring. The maximum displacement is 2A.
Assuming this spring obeys Hooke’s law, which of he following gives the correct time
period and total energy?
(1)
IB Physics
Wave Properties (Part I)
3. The graph shows how the displacement varies with time for an object undergoing simple
harmonic motion.
Which graph shows how the object’s acceleration a varies with time t?
(1)
4. A pendulum swings back and forth in a circular arc between X and Y.
The pendulum bob is
A. always in equilibrium.
B. only in equilibrium at X and Y.
C. in equilibrium as it passes through the central position.
D. never in equilibrium.
(1)
IB Physics
Wave Properties (Part I)
5. Microwave ovens cause the water molecules in food to resonate. The molecules have a
natural frequency of vibration f. In order to heat the food most effectively, the frequency of
the microwave should have a value
A. less than f.
B. equal to f.
C. greater than f.
D. as large as possible.
(1)
6. A pulse is sent down a string fixed at one end.
Which one of the following diagrams best represents the reflected pulse?
A.
B.
C.
D.
(1)
7. A transverse wave travels from left to right. The graph below shows how, at a particular
instant of time, the displacement of particles in the medium varies with position. Which
arrow represents the direction of the velocity of the particle marked P?
IB Physics
Wave Properties (Part I)
8. On which one of the following graphs is the wavelength λ and the amplitude a of a
wave correctly represented?

A.
Displacement
0
0
Distance along
wave
a

B.
Displacement
0
0
Distance along
wave
a

C.
Displacement
0
0
Distance along
wave
a

D.
Displacement
0
0
a
Distance along
wave
(1)
IB Physics
Wave Properties (Part I)
9. Which of the following diagrams best shows the path of a ray of monochromatic light
through a glass prism in air?
B.
A.
glass
air
glass
air
D.
C.
glass
air
glass
air
(1)
10. Waves of frequency f travel with speed c in air and enter a medium M of refractive
index 1.5. Which of the following correctly gives the frequency and speed of the waves
in the medium M?
frequency
speed
A.
f
c
1 .5
B.
f
1.5c
C.
1.5f
c
D.
f
1 .5
c
(1)
IB Physics
Wave Properties (Part I)
Section B: Answer all questions
1.
Simple harmonic motion and the greenhouse effect
(a)
A body is displaced from equilibrium. State the two conditions necessary for
the body to execute simple harmonic motion.
1. .........................................................................................................................
.........................................................................................................................
2. .........................................................................................................................
.........................................................................................................................
(2)
(b)
In a simple model of a methane molecule, a hydrogen atom and the carbon
atom can be regarded as two masses attached by a spring. A hydrogen atom is
much less massive than the carbon atom such that any displacement of the
carbon atom may be ignored.
The graph below shows the variation with time t of the displacement x from
its equilibrium position of a hydrogen atom in a molecule of methane.
The mass of hydrogen atom is 1.7  10–27 kg. Use data from the graph above
(i)
to determine its amplitude of oscillation.
(1)
(ii)
to show that the frequency of its oscillation is 9.1  1013 Hz.
(2)
IB Physics
(iii)
Wave Properties (Part I)
to show that the maximum kinetic energy of the hydrogen atom is 6.2  10–18 J.
(2)
(c)
Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of
oscillation f is given by the expression
f
1
2
k
,
mp
where k is the force per unit displacement between a hydrogen atom and the carbon
atom and mp is the mass of a proton.
(i)
Show that the value of k is approximately 560 N m–1.
(1)
(ii)
Estimate, using your answer to (c)(i), the maximum acceleration of the
hydrogen atom.
(2)
(d)
Methane is classified as a greenhouse gas.
(i)
Describe what is meant by a greenhouse gas.
(2)
IB Physics
(ii)
Wave Properties (Part I)
Electromagnetic radiation of frequency 9.1  1013 Hz is in the infrared region
of the electromagnetic spectrum. Suggest, based on the information given in
(b)(ii), why methane is classified as a greenhouse gas.
(2)
(Total 14 marks)
2.
Waves on a string
A travelling wave is created on a string. The graph below shows the variation with time t of
the displacement y of a particular point on the string.
Graph 1 y / mm
2.0
1.0
t / ms
0.0
0.0
0.1
0.2
0.3
0.4
0.5
–1.0
–2.0
The variation with distance x of the displacement y of the string at t = 0 is shown below.
Graph 2 y / mm
2.0
1.0
x / cm
0.0
0.0
0.1
0.2
0.3
0.4
0.5
–1.0
–2.0
(a)
Use information from the graphs to calculate, for this wave,
(i)
the wavelength;
(1)
(ii)
the frequency;
(2)
(iii)
the speed of the wave.
(1)
Wave Properties (Part I)
IB Physics
(b)
The wave is moving from left to right and has period T.
(i)
On graph 1, draw a labelled line to indicate the amplitude of the wave.
(1)
(ii)
T
On graph 2, draw the displacement of the string at t  .
4
(2)
(c)
One end of the string is attached to a wall. A student creates a single pulse in
the string that travels to the right as shown in the diagram below.
string
(i)
pulse
wall
In the space below, draw a diagram to show the shape and size of the
pulse after it has been reflected from the wall.
(2)
(ii)
By reference to Newton’s third law, explain the nature of the reflected
pulse that you have drawn in (c)(i) above.
(2)
(Total 11 marks)
IB Physics
3.
Wave Properties (Part I)
This question is about waves and wave properties.
(a)
By making reference to waves, distinguish between a ray and a wavefront.
(3)
The diagram below shows three wavefronts incident on a boundary between medium
I and medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is
incomplete.
A
C
E
F
medium I
medium R
B
(b)
(i)
D
On the diagram above, draw a line to complete the wavefront EF.
(1)
(ii)
Explain in which medium, I or R, the wave has the higher speed.
(3)
IB Physics
(iii)
Wave Properties (Part I)
By taking appropriate measurements from the diagram, determine the
ratio of the speeds of the wave travelling from medium I to medium R.
(2)
(Total 9 marks)