MORLEY SENIOR HIGH SCHOOL
YEAR 12
PHYSICS (STAGE 3)
SOUND WAVE CONCEPTS TEST
Student’s Name:
Tutorial Group:
Teacher’s Name:
Date:
_____________________________________________________________________________________

A wave is a disturbance travelling along or through a medium transmitting energy in succession to the
particles of the medium, i.e., a wave is the propagation of a disturbance. The medium does not travel
with the disturbance. Electromagnetic radiations, like light, require no medium for their transmission.

The characteristic of wave motion is that energy is transferred without a transfer of the matter, from
which the medium is made.

A sound wave is a longitudinal pressure wave that travels through an elastic medium, like air, as a
series of compressions (above normal air pressure) and rarefactions (below normal air pressure).
Graphical representation of a Sound wave in Air

A sound wave can be represented in space, at any given instant in time, in terms of (a) displacement,
and (b) pressure.
An analysis of the two Graphs
The displacement wave (a) is one quarter
of a wavelength (λ/4) out of phase with the
pressure wave (b).
Where the pressure is a maximum (a
compression) or a minimum (a rarefaction)
the displacement from equilibrium is zero.
Where the pressure variation is zero, the
displacement is a maximum or minimum.

The wavelength of a wave is the
distance between two successive crests or
between two successive troughs.

Particles at the centre of a compression and at the centre of a rarefaction both have zero displacement.
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
1

Displacement is measured in micrometres. [1 micrometre (1 μ) = 10 – 6 metre]

When a sound wave passes through air the pressure variation is ~ ± 0.01 % of atmospheric pressure.
1. What is the approximate wavelength of the pressure – distance wave given as graph (b)?
[2 marks]

A sound wave, as a longitudinal wave motion, occurs as a series of compressions and rarefactions.

A longitudinal wave is one in which the vibration of the particles is parallel to the direction of energy
flow, i.e., to the direction of wave travel.
The Displacement of particles in a Sound wave

To form a compression, the particles of the transmission medium to the left of the compression have
moved forward, and the particles to the right have moved backward.
DIRECTION OF WAVE TRAVEL
DIRECTION OF ENERGY FLOW
PARTICLE
-
VIBRATION BACKWARDS ( )
VIBRATION FORWARDS (+)
2.
Can you show with arrows, on the adjacent
sketch, the directions in which the air ‘particles’ are
displaced to form a compression, and a rarefaction?
[4 marks]
Wave Speed

The speed of a wave (v) is the speed at which energy E is transferred through a given medium.
Wave Speed (v) = Frequency (f)  Wavelength ()
Where v = speed of wave [metres per second (m s – 1)]
f = frequency of wave [cycles per second or Hertz (Hz)]
 = wavelength [metres (m)]
3. A 512 Hz sound wave travels at a speed of 331 m s – 1 through air, which is at pressure of 103.1 kPa
and a temperature of 0 0C; what is the wavelength  of the sound wave?
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
2
[2 marks]
 The speed of sound in gases depends somewhat on temperature as shown by this physics equation:
v ≈ (331 + 0.60 T) m s – 1; where T is the temperature in 0 C.
4. What is the speed of sound in air at 20 0 C?
[2 marks]

A loudspeaker is an electromagnetic device that converts electrical signals into sound waves.
5.
What causes the loudspeaker coil to
oscillate (move forwards and backwards)
inside the field of the permanent magnet?
[2 marks]
6. How does oscillation (or vibration) of the loudspeaker cone produce a series of compressions C and
rarefactions R, which travel to our eardrums, and cause them to vibrate?
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
3
[2 marks]
Travelling Waves and Standing Waves

A travelling wave is a wave which transfers energy from one part of a medium to another part of the
medium, e. g., a sound wave.

A standing wave results from the superposition of identical periodic waves travelling through the
same medium in opposite directions. In the region where two waves overlap, their resultant
displacement is the algebraic sum of their separate displacements (a crest is considered positive and a
trough negative).
Interference: Principle of Superposition

Interference is the interaction of two waves, or pulses, which travel simultaneously through the same
medium.

Principle of Superposition: In the region where two waves overlap, their resultant displacement is
the algebraic sum of their separate displacements (a crest is considered positive and a trough
negative).

Constructive interference is the interaction of two identical
waves which are in the same phase and results in the maximum
reinforcement of each wave by the other. An antinode is a point where
there is continuous constructive interference.
7.
Which sketch shows maximum reinforcement of each wave pulse
by the other? Draw a circle around the area of maximum reinforcement of
the two wave pulses.
[1 mark]

Destructive interference is the interaction of two identical waves
which are in opposite phase and results in the complete cancellation, i.e.,
annulment of each wave by the other. A node is a point where there is
continuous destructive interference.
8.
Which sketch shows complete cancellation of each wave pulse by
the other? Draw a circle around the area of complete cancellation of the
two wave pulses.
[1 mark]
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
4
Destructive and Constructive Interference of Light Waves

In considering the interference of
two waves, we use the term phase to
describe the relative position of their
crests.

For destructive interference,
where crests of one wave repeatedly
meet troughs of the other wave, the two
waves are out of phase by one half of a
wavelength (½ λ).

When the crests and troughs are
aligned, for constructive interference, the
two waves are in phase.
Destructive and Constructive Interference of Two Waves
Now study these three graphs showing two waves, and their sum, as a function of time at three locations.
Graph A
Graph B
Graph C

Constructive interference is the interaction of two identical waves which are in the same phase and
results in the maximum reinforcement of each wave by the other.

Destructive interference is the interaction of two identical waves which are in opposite phase and
results in the complete cancellation, i.e., annulment of each wave by the other.
9. Which graph shows constructive interference? Explain.
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
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[2 marks]
10. Which graph shows destructive interference? Explain.
[2 marks]
11. Which graph shows partially destructive interference? Explain.
[2 marks]
Standing Transverse Waves in a Stretched String

Standing or stationary waves result from the superposition of identical periodic waves travelling
through the same medium in opposite directions.
A standing transverse wave is established on a stretched string by vibrating the string up and down at a
frequency that coincides with the natural frequency of the stretched string. The natural frequency of a
stretched string depends on its mass per unit length, and on its tension.
The fundamental frequency of a stretched string is given by this physics equation:
f1 = √[T/(m / L)]
2L
Where T = string tension (N); m = string mass (kg); and L = strength length (m).
A study of the adjacent photograph of a standing wave on a stretched string
shows that the string appears to have segments which simply oscillate up
and down. The points where the stretched string remains still at all times are
called nodes N; and the points where the stretched string oscillates with
maximum amplitude are called antinodes A N.
Source of Image URL: <http://www1.union.edu/newmanj/lasers/Light%20as%20a%20Wave/standing%20wave2.JPG>
12. Why is the fundamental frequency of a thick guitar string lower than the fundamental frequency of a
thin string with the same tension and length?
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
6
[2 marks]
Longitudinal Standing Waves in Closed and Open Pipes

The sketches, given directly below, provide a diagrammatical and mathematical study of the physics
of longitudinal standing waves in closed and open pipes.
13.
B
y
anal
ysin
g
the
“pat
tern
of
the
mod
es of
vibration” for open pipes, can you sketch, in the above diagram on the right for open pipes, the
“missing mode of vibration” for the third (3 rd) harmonic?
[3 marks]
Location of Nodes and Antinodes

In closed pipes, a displacement node N always occurs at the closed end (because there the air is
unable to move); and a displacement antinode A N always occurs at the open end (because there the
air can move).

In open pipes, a displacement antinode A N occurs at both open ends since the air is free to move at
open ends. Also, there must be at least one displacement node occurring within an open pipe for a
standing wave to be established within that pipe.
14. Why can resonance in closed pipes only produce odd-numbered harmonics 1st, 3rd, 5th, 7th...?
[3 marks]
_____________________________________________________________________________________
[Total marks = 30]
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
Percent score =
7
P12: SOUND WAVE CONCEPTS TEST  M. J. McGarry (2010)
8