Exam Review: Topic 04 – Waves
Practice Test: 29 marks (37 minutes)
Additional Problem: 31 marks (45 minutes)
1.
Reagan IB Physics
A transverse wave travels from left to
right. The diagram on the right 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?
(Total 1 mark)
2.
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?
(Total 1 mark)
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Exam Review: Topic 04 – Waves
3.
Reagan IB Physics
Which of the following is a value of wavelength that is found in the visible region of the
electromagnetic spectrum?
A.
4 × 10–5 m
C.
4 × 10–9 m
B.
4 × 10–7 m
D.
4 × 10–11 m
(Total 1 mark)
4.
The shock absorbers of a car, in good working condition, ensure that the vertical oscillations of
the car are
A.
undamped.
B.
lightly damped.
C.
moderately damped.
D.
critically damped.
(Total 1 mark)
5.
The graphs show how the acceleration a of four different particles varies with their
displacement x.
Which of the particles is executing simple harmonic motion?
(Total 1 mark)
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Exam Review: Topic 04 – Waves
6.
Reagan IB Physics
The diagram on the right is a
snapshot of wave fronts of
circular waves emitted by a point
source S at the surface of water.
The source vibrates at a frequency
f = 10.0 Hz.
The speed of the wave front is
A.
0.15 cm s–1.
B.
1.5 cm s–1.
C.
15 cm s–1.
D.
30 cm s–1.
(Total 1 mark)
7.
Two coherent point sources S1 and S2 emit spherical waves.
Which of the following best describes the intensity of the waves at P and Q?
P
Q
A.
maximum
minimum
B.
minimum
maximum
C.
maximum
maximum
D.
minimum
minimum
(Total 1 mark)
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Exam Review: Topic 04 – Waves
8.
Reagan IB Physics
An object at the end of a spring oscillates vertically with simple harmonic motion. The graph
shows the variation with time t of the displacement x. The amplitude is x0 and the period of
oscillation is T.
Which of the following is the correct expression for the displacement x?
A.
 x 0 cos
B.
x 0 cos
2
t
T
2
t
T
C.
 x 0 sin
D.
x 0 sin
2
t
T
2
t
T
(Total 1 mark)
9.
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 the following gives the correct time period
and total energy?
New time period
New energy
A.
T
4E
B.
T
2E
C.
2T
4E
D.
2T
2E
(Total 1 mark)
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Exam Review: Topic 04 – Waves
10.
Reagan IB Physics
What is the best estimate for the refractive index of a medium in which light travels at a speed
of 2.7 × 108 m s–1?
A.
0.9
B.
1.0
C.
1.1
D.
2.7
(Total 1 mark)
11.
Plane wavefronts are incident on a boundary between two media labelled 1 and 2 in the
diagram.
The diagram of the wavefronts is drawn to scale.
The ratio of the refractive index of medium 2 to that of medium 1 is
A.
0.50.
B.
0.67.
C.
1.5.
D.
2.0.
(Total 1 mark)
12.
An orchestra playing on boat X can be heard by tourists
on boat Y, which is situated out of sight of boat X around
a headland.
The sound from X can be heard on Y due to
A.
refraction.
B.
reflection.
C.
diffraction.
D.
transmission.
(Total 1 mark)
5/12
Exam Review: Topic 04 – Waves
13.
Reagan IB Physics
Which of the following correctly describes the change, if any, in the speed, wavelength and
frequency of a light wave as it passes from air into glass?
Speed
Wavelength
Frequency
A.
decreases
decreases
unchanged
B.
decreases
unchanged
decreases
C.
unchanged
increases
decreases
D.
increases
increases
unchanged
(Total 1 mark)
14.
A sound wave of frequency 660 Hz passes through air. The variation of particle displacement
with distance along the wave at one instant of time is shown below.
0.5
displacement / mm
00
1.0
2.0
distance / m
–0.5
(a)
State whether this wave is an example of a longitudinal or a transverse wave.
.....................................................................................................................................
(1)
(b)
Using data from the above graph, deduce for this sound wave,
(i)
the wavelength.
...........................................................................................................................
(1)
(ii)
the amplitude.
...........................................................................................................................
(1)
(iii) the speed.
...........................................................................................................................
...........................................................................................................................
(2)
(Total 5 marks)
6/12
Exam Review: Topic 04 – Waves
15.
Reagan IB Physics
Travelling waves
(a)
Graph 1 below shows the variation with time t of the displacement d of a travelling
(progressive) wave. Graph 2 shows the variation with distance x along the same wave of
its displacement d.
4
Graph 1
d / mm
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
t/s
0.0
0.4
0.8
1.2
1.6
2.0
2.4
x / cm
–2
–4
4
Graph 2
d / mm
2
0
–2
–4
(i)
State what is meant by a travelling wave.
.........................................................................................................................
.........................................................................................................................
(1)
(ii)
Use the graphs to determine the amplitude, wavelength, frequency and speed of the
wave.
Amplitude:
.................................................................................................
(1)
Wavelength: .................................................................................................
(1)
Frequency:
.................................................................................................
.................................................................................................
(1)
Speed:
.................................................................................................
.................................................................................................
(1)
7/12
Exam Review: Topic 04 – Waves
Reagan IB Physics
Refraction of waves
(b)
The diagram below shows plane wavefronts incident on a boundary between two media
A and B.
medium A
medium B
The ratio
refractive index of medium B
is 1.4.
refractive index of medium A
The angle between an incident wavefront and the normal to the boundary is 50.
(i)
Calculate the angle between a refracted wavefront and the normal to the boundary.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(ii)
On the diagram above, construct three wavefronts to show the refraction of the
wave at the boundary.
(3)
(Total 11 marks)
Additional problems
16.
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)
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Exam Review: Topic 04 – Waves
(b)
Reagan IB Physics
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  10 Hz.
13
.........................................................................................................................
(2)
(iii)
to show that the maximum kinetic energy of the hydrogen atom is 6.2  10–18 J.
.........................................................................................................................
.........................................................................................................................
(2)
(c)
On the grid below, sketch a graph to show the variation with time t of the speed v of the
hydrogen atom for one period of oscillation starting at t = 0. (There is no need to add
values to the speed axis.)
(3)
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Exam Review: Topic 04 – Waves
(d)
Reagan IB Physics
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 (d)(i), the maximum acceleration of the hydrogen
atom.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(e)
Methane is classified as a greenhouse gas.
(i)
Describe what is meant by a greenhouse gas.
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
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 17 marks)
17.
This question is about waves.
(a)
With reference to the direction of energy transfer through a medium, distinguish between
a transverse wave and a longitudinal wave.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
10/12
Exam Review: Topic 04 – Waves
(b)
Reagan IB Physics
A wave is travelling along the surface of some shallow water in the x-direction. The
graph shows the variation with time t of the displacement d of a particle of water.
d / mm 10
8
6
4
2
0
0
0.05
0.1
0.15
0.2
0.25
–2
0.3
t/s
–4
–6
–8
–10
Use the graph to determine for the wave
(i)
the frequency,
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
the amplitude.
...........................................................................................................................
(1)
(c)
The speed of the wave in (b) is 15 cm s–1. Deduce that the wavelength of this wave is
2.0 cm.
.....................................................................................................................................
.....................................................................................................................................
(2)
(d)
The graph in (b) shows the displacement of a particle at the position x = 0.
On the axes below, draw a graph to show the variation with distance x along the water
surface of the displacement d of the water surface at time t = 0.070 s.
11/12
Exam Review: Topic 04 – Waves
Reagan IB Physics
d / mm 10
8
6
4
2
0
0
1
2
3
4
x/cm
–2
–4
–6
–8
–10
(3)
(e)
The wave encounters a shelf that divides the water into two separate depths. The water to
the right of the shelf is deeper than that to the left of the shelf.
wave fronts
shelf
direction of
travel of wave
30 
shallow water
deep water
The angle between the wavefronts in the shallow water and the shelf is 30°. The speed of
the wave in the shallow water is 15 cm s–1 and in the deeper water is 20 cm s–1. For the
wave in the deeper water, determine the angle between the normal to the wavefronts and
the shelf.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 14 marks)
12/12
Exam Review: Topic 04 – Waves
Reagan IB Physics
Mark scheme
1.
C
4.
D
7.
A
10.
C
13.
A
2.
D
5.
B
8.
A
11.
B
3.
B
6.
C
9.
A
12.
C
14.
(a)
longitudinal;
1
(b)
(i)
wavelength = 0.5 m;
1
(ii)
amplitude = 0.5 mm;
1
(iii)
correct substitution into speed = frequency × wavelength;
to give v = 660 × 0.5 = 330 m s–1;
2 max
[5]
15.
Wave phenomena
(a)
(i)
wave that transfers energy;
1
(ii)
amplitude
= 4.0mm;
1
wavelength = 2.4cm;
1
frequency
=
1
;
0.3
= 3.3Hz;
= 3.3  2.4;
speed
= 8.0cms1;
(b)
(i)
1
1
angle of incidence = 40;
sin r 
sin 40
1.4
r = 27;
angle = 63;
3
Award [1 max] for angle of incidence = 50, r = 33.
(ii)
construction: wavefronts equally spaced;
separation less in medium B;
angle in medium B correct  by eye;
3
[11]
13/12
Exam Review: Topic 04 – Waves
Reagan IB Physics
Additional problems
16.
Simple harmonic motion and the greenhouse effect
(a)
(b)
the force acting / accelerating (on the body) is directed towards equilibrium
(position);
and is proportional to its / the bodies displacement from equilibrium;
(i)
1.5  1010 m;
(ii)
T = 1.1  1012 s;
2
1


1
;
f  
12 
1
.
1

10


= 9.1  1013 Hz
(iii)
2
ω = (2f) = 5.7  1014 (rad s1);
Emax =
 mω x 
1
2
2
2
0
1
2
1.7 10 27  1.5 10 20  5.7  10 28 ;
2
2
= 6.2  1018 J
(c)
(d)
negative sine;
starting at zero;
with same frequency as displacement; (allow  2mm square)
(i)
(i)
(ii)
1
use of F = kx and F = ma;
560 1.5 10 10
 5.0 1019 ms  2 ;
to give a 
 27
1.7 10
(e)
3
k = (42f2mp) = 40  83  1026  1.7  1027;
 560 Nm1
(ii)
2
infra red radiation radiated from Earth will be absorbed by
greenhouse gases;
and so increase the temperature of the atmosphere / Earth;
2
2
the natural frequency of oscillation (of a methane molecule)
is equal to 9.1  1013 Hz;
because of resonance the molecule will readily absorb radiation
of this frequency;
2
[17]
14/12
Exam Review: Topic 04 – Waves
17.
(a)
Longitudinal
the particles (of the medium) vibrate in the same direction as the
direction of energy transfer;
(b)
(i)
(ii)
(c)
(d)
(e)
Reagan IB Physics
Transverse
the particles (of the medium) vibrate at right angles;
to the direction of energy transfer;
=
3
time period = 0.13 s;
1
1 

f  
 = 7.7(0.3) Hz;
T 0.13 

Award full marks for bald correct answer.
2
8 mm;
1
v
;
f
15
;
7 .7
 = 1.95 cm  2.0 cm
2
start at (–1.2 → –2.0) on y-axis;
sine curve of amplitude 8 mm;
wavelength 2 cm;
3
sin  1 v1

sin  2 v 2
v
sin  2  2 sin  1 ;
v1
20
=
sin30 to give 2 = 42°;
15
angle = 48°;
3
use of
[14]
15/12