3B SCIENTIFIC
Instruction sheet
05/09 ELWE/ALF
®
PHYSICS
Acoustics Kit U8440012
1. Description
This set of apparatus makes it possible to impart an
extensive and well-rounded overview on the topic
of acoustics. The set can be used for conducting
numerous experiments.
Sample experiments:
1. String tones
2. Pure acoustic tones
3. Vibrating air columns
4. Open air column
5. Whistle
6. Vibrating rods
7. Infrasound
8. Ultrasound
9. Tuning fork with plotter pen
10. Progressive waves
11. Doppler effect
12. Chladni figures
13. Chimes
14. Standing waves
15. Overtones
16. Measurement of wavelength
17. Soundboard
18. Resonator box
19. Spherical cavity resonator
20. Stringed instruments and the laws they obey
21. Scales on stringed instruments
22. Measurement of string tension
23. Relation between pitch and string tension
24. Wind instruments and the laws they obey
25. C major scale and its intervals
26. Harmony and dissonance
27. G major triad
28. Four-part G major chord
29. Major scales in an arbitrary key
30. Introduction of semitones
The set is supplied in a plastic tray with a foam
insert that facilitates safe storage of the individual
components.
1
2. Contents
1 Trays with foam inserts for acoustics kit
2 Monochord
3 Bridge for monochord
4 Metallophone
5 Chladni plate
6 Tuning fork, 1700 Hz
7 Tuning fork, 440 Hz
8 Tuning fork with plotter pen, 21 Hz
9 Spring balance
10 Retaining clip
11 Table clamp
12 Helmholtz resonators
70 mm dia.
52 mm dia.v
40 mm dia.
34 mm dia.
13 Glass tube for open air column
14 Kundt’s tube
15 Glass tube for closed air column
16 Rod for Chladni plate/bell dome
17 Galton whistle
18 Plotter pen with holder
19 Lycopodium powder
20 Plastic block for clamp
21 Rubber top
22 Bell dome
23 Reed pipe
24 Whistle
25 Steel string
26 Nylon string
27 Resonance rope
28 Plunger
2
3. Technical data
Dimensions: 530 x 375 x 155 mm3 approx.
Weight: 4.5 kg approx.
4. Sample experiments
1. String tones
• Pluck the monochord string hard when it is
moderately taut.
• Subsequently increase the tension on the string
by turning the peg to the right. Pluck the string
again.
At first, a low tone is heard. As the string is tightened the tone gets higher.
Reasons: vibrating strings generate acoustic tones
by inducing alternating compression and rarefaction of the surrounding air. The greater the tension
in the string, the faster the vibrations are and the
higher the tone.
2. Pure acoustic tones
• Hit the 440 Hz tuning fork hard with the metal-
lophone beater.
A pure acoustic tone of a very specific, unchanging
pitch can be heard. This tone dies away very slowly.
Reasons: a tuning fork consists of a U-shaped steel
piece which merges into the stem at its vertex. As
the tuning fork only vibrates in one oscillation
mode (with both prongs either both moving apart
or both moving towards one another), it produces a
pure tone of an unchanging pitch. Owing to its
property of producing a constant pitch, tuning
forks are used for tuning musical instruments.
3. Vibrating air columns
• Attach the glass tube for demonstrating a
closed air column by means of the table clamp,
plastic block and retaining clip.
• Insert the tuning plunger into the glass tube.
• Hit the 440 Hz tuning fork hard with the metal-
lophone beater. By pulling out the plunger to a
greater or lesser degree it is possible to alter
the length of the closed air column.
There is only one plunger position at which the air
column resonates strongly. At any other position
there is no sound. Resonance can be detected by
the increase in sound volume.
Reasons: a closed air column starts resonating
when its length corresponds to one quarter of the
excitation wavelength. The tuning fork vibrates
with a frequency of 440 vibrations per second.
Applying the following equation:
Wavekength =
⋅
⋅
scm
/34000
pagationSpeedofpro
Frequency
sfreqExciting
/440
cm
⋅=
2.77
the wavelength of the tone produced is 77.2 cm.
One quarter of this wavelength is therefore
19.3 cm.
The distance between the plunger and the opening
at the end of the tube is 19.3 cm when resonance
occurs.
4. Open air column
• Conduct the same experiment with an open air
column (14).
The open air column, which is exactly double the
length of the closed air column, starts resonating
when the tuning fork is brought into its vicinity, as
can be heard by means of the increased volume.
Reasons: an open air column starts resonating
when its length is half that of the wavelength or
multiples of that length. Antinodes are formed at
the ends of the open air column and a node at the
middle.
5. Whistle
• Blow the whistle and change its length by
gradually drawing out the plunger.
Depending on the length of the whistle, its note
gets higher or lower but the character or timbre of
the note remains the same.
Reasons: blowing a uniform air stream into the
opening of a whistle causes the air trapped in the
pipe to vibrate and eddies then occur at regular
intervals air the air passes over the blade. The
resulting tone depends on the length of the air
column. In the case of a closed air column, the
length of the whistle (measured from the edge of
the blade to the base of the whistle) corresponds to
a quarter wavelength of the base tone. A node is
formed at the blade of the whistle and an antinode
is formed at the end of the pipe
6. Vibrating bars
• Use the striking hammer supplied to strike
several bars of the metallophone. When the
metal bars are struck, they produce a distinct,
melodious note, each of which has a similar
timbre. The shorter the length of the bar, the
higher the tone.
Reasons: elastic rods form systems capable of oscillating if they are resting upon a point where a node
is formed (about 22% of the total length between
the two ends).
3
7. Infrasound
• Without the plotter pen attached, make the
tuning fork (21 Hz) vibrate by pressing its
prongs together and suddenly releasing them.
The tuning fork produces slow vibrations that can
be perceived by the naked eye. When held close to
the ear, a very deep (barely audible) tone can be
heard.
Reasons: the prongs of the tuning fork vibrate in
opposite directions and give rise to compressions
and rarefactions in the surrounding air. When this
reaches the ear, it makes the eardrum vibrate. A
tone is thus perceived.
The tuning fork vibrates at approximately 20 vibrations per second. The lowest note that can be perceived by human hearing has a frequency of approximately 16 vibrations per second. Vibrations
below 16 Hz are not audible to the human ear. The
sound produced by these vibrations is called infrasound. (Latin: infra = below).
8. Ultrasound
• Blow the Galton whistle.
No sound can be heard, simply a hiss.
Reasons: owing to its short length, the Galton whis-
tle produces very high tones which are not audible
to the human ear. This phenomenon is called ultrasound. (Latin: ultra = above).
9. Tuning fork with plotter pen
• Attach the pen (8) to the prongs of the tuning
fork (21 Hz).
• Make the tuning fork vibrate by pressing the
prongs together and move a sheet of paper as
uniformly as possible under the pen so that the
motion is plotted onto it. Make sure that the
surface on which the paper rests is not too soft.
The pen traces a wavy line of a constant wavelength but decreasing amplitude on the paper.
Reasons: sound is produced by harmonic oscillations of solids, liquids or gases. The locus of the
oscillating particles of the body in relation to the
time traces a sine curve. When struck once, vibrating bodies exhibit a “damped” oscillation (continuous decrease in amplitude). If the supply of energy
is uninterrupted (constant sound of a car horn,
constant blowing of an organ pipe), the result is an
undamped oscillation of constant amplitude (loudness or volume).
10. Progressive waves
• Make a simple knot in the resonance rope and
attach it by the loop to the handle of a door.
• Make the wire moderately taut and jerk it
suddenly to the side.
From the centre of motion (the hand), a wave is
produced which runs along the wire with an increasing velocity, gets reflected at the fixed end
and returns to the point of origin.
Reasons: every solid, liquid and gas produces vibrations when disturbed suddenly. These vibrations
spread through a medium with a definite propagation velocity.
11. Doppler effect
• Strike the light-metal tuning fork (1700 Hz)
hard with the metallophone beater. Hold it
still for a short while and then rapidly move it
to and fro through the air.
In a state of rest, the tuning fork produces a clear
tone of uniform pitch. In a state of motion, the
pitch constantly changes. If the tuning fork is
moved towards the ear, the pitch rises, and if it is
moved away from the ear, the pitch decreases.
Reasons: when the distance between the source of
sound and the ear is decreasing, the time interval
between two compressions also decreases as a
second compression has to travel a shorter distance
to reach the ear compared to the first. The ear
registers a higher frequency. The tone thus gets
higher. When the source of sound is moved away
from the ear, the intervals between compressions
and rarefactions get longer. The tone thus becomes
deeper.
12. Chladni figures
• Use the table clamp and plastic block to attach
the Chladni plate to the workbench. Scatter
some bird sand or a similar material onto the
plate. Allow it to spread in a thin layer so as to
cover a third of the plate.
• With one hand, bow the plate exactly half way
between two corners with a good violin bow,
simultaneously touching one other corner
lightly with the finger of your other hand.
• Bow several strokes across the plate, preferably
quite forcefully so that the vibrations of the
plate are vigorous and well audible.
When the plate is being bowed, a very distinct
acoustic tone can be heard. At certain points, the
grains of sand experience lively resonance and
begin to bounce up and down on the surface of the
plate, accumulating in unusual figures on the surface.
Reasons: “standing waves” are formed on the plate.
When bowed, the plate does not vibrate uniformly
across its surface. At certain points (antinodes), the
plate begins to vibrate, whereas it is in a state of
complete rest at other points (nodes). By touching
the plate at one corner, the point is forced into
being a node.
4
13. Chimes
Hz
⋅
• Secure the bell dome to the bench with its
open end facing upwards using the table
clamp and plastic block.
• Strike the edge of the bell at different points
with a hammer. (Alternatively, the edges can
also be bowed with a violin bow.)
The pitch depends on the point at which the bell
has been struck. It is easily possible to obtain differences of a whole tone. If the bell is struck at
definite points, both tones are excited and the
result is a familiar “beating” (periodic increase and
decrease in volume at varying speeds).
Reasons: bells are curved vibrating plates. The
overtones are mostly not in harmony with the
fundamental tone. Bells too exhibit specific vibrating regions while they are chiming
14. Standing waves
• Make a simple knot in the resonance wire and
attach it by the loop to the handle of a door.
• Make the wire moderately taut and gently
move it round in circles.
• Now make the wire tighter and spin it faster.
When moved gently, nodes arise at both ends of
the wire and an antinode is created in the middle
of the wire. When moved faster, three nodes and
two antinodes are formed, and when moved even
faster, four nodes and three antinodes are formed.
Reasons: owing to the reflection at the door handle, standing waves are formed. Due to persistence
of vision, the original and reflected waves appear
to be simultaneous. In its fundamental mode, the
whole of the wire vibrates in one length, thus describing one half-wave. One antinode is observed in
the middle of the wire with nodes at both ends. In
the case of a first harmonic (octave), the wire vibrates describes the form of a complete wave (two
antinodes and three nodes); for the second harmonic, there are three antinodes and 4 nodes; and
so on.
15. Overtones
• First blow the whistle gently, then blow it very
hard.
Initially, a fundamental tone is heard. When the
whistle is blown hard, a much higher tone can be
heard.
Reasons: since the whistle is closed at one end
standing waves are always formed with a node at
the base and an antinode at the blade opening.
This is the case when the length of the whistle is
exactly 1/4 of the wavelength. It is also the case if
the distance of the opening from the base is 3/4,
5/4, 7/4, etc. of the wavelength.
Apart from the fundamental tone, all the possible
odd overtones or harmonics from the harmonic
series are produced at varying degrees of intensity.
The fact that every musical instrument has a very
characteristic timbre can be attributed solely to the
presence of individual harmonics of this kind appearing to a greater or lesser degree.
16. Measurement of wavelength
• Seal off the end of the 45-cm glass tube (21)
with the rubber cap and, holding the tube at
an angle, put a small quantity of lycopodium
powder into the tube using a teaspoon. Carefully spread a moderate quantity of the powder
uniformly to form a fine yellow strip in the
tube.
• Attach the glass tube by means of the retaining
clip, table clamp and plastic block.
• Strike the tuning fork (1700 Hz) hard on the
handle of the hammer and hold one prong directly alongside the opening of the tube. If
necessary, repeat this acoustic excitation several times.
At the antinodes, the lycopodium powder begins to
resonate strongly, whereas it is absolutely static at
the nodes. The powder particles fall to the base of
the tube and form periodic clusters that repeat 4½
times along the axis of the tube.
Reasons: the light-metal tuning fork has a frequency of 1700 vibrations per second. According to
the following equation:
Wavelength =
sm
⋅
/340
1700
Speed
Frequenncy
m
⋅=
2.0
The corresponding wavelength is 20 cm. Thus, 4½
half-waves or 2 full waves and one quarter wave can
“fit” in a 45-cm-long tube, as demonstrated in the
experiment. At the opening of the tube, there is
always an antinode and there is always a node at
the base of the tube.
17. Soundboard
• Hit the tuning fork that produces the note
a’ = 440 Hertz hard using the metallophone
beater and push the stem down onto the table
top.
Simply by holding it on the table, the barely audible tone produced by the tuning fork is amplified
to such an extent that it is now clearly heard
throughout the room.
Reasons: owing to the rising and falling vibrations
in the shaft of the tuning fork, the surface of the
table begins to resonate. Since the effective table
surface is much larger than the tuning fork, the
loudness of the tone is considerably intensified.
5
18. Resonator box
• Strike the A tuning fork (440 Hz) nice and hard
and place its stem on the resonator box of the
monochord.
There is a significant amplification of the tone.
Reasons: as explained in experiment 17.
19. Spherical cavity resonator
• One by one, bring the narrow tip of each of the
Helmholtz resonators close to your ear.
You hear a tone which gets deeper as the diameter
of the resonator becomes greater.
Reasons: every hollow space, regardless of its
shape, e.g. pipes, hollow spheres, has a very specific resonant frequency which is almost lacking
overtones. This harmonic can be produced by
blowing air across the opening of the hollow space
or simply by tapping the hollow space with your
knuckles. However, natural resonance is also created if the surrounding noise possesses tones which
match the harmonic of the resonator. In this way,
the spherical cavity resonator can be used to identify individual components of a mixed sound. If the
room is absolutely quiet, the resonator remains
silent.
20. String instruments and the laws they obey
• Insert the bridge vertically below the string of
the monochord so that its right edge exactly
coincides with the number 20 on the scale and
the 40-cm string is divided into two equal sections of 20 cm each.
• By tightening the peg, tune half the length of
the string to match the A tuning fork (440 Hz)
(standard pitch).
• By plucking, or preferably by bowing the
string, compare the pitch for string lengths of
40 cm, 20 cm, 10 cm and 5 cm.
For a string length of 20 cm, the note matches the
standard concert pitch A' = 440 Hz. For a string
length of 40 cm, the pitch is one octave lower at
A = 220 Hz. For length 10 cm, the pitch is one
octave higher A’’ = 880 Hz. Finally, when the length
of the string is 5 cm, the pitch is two octaves higher
A’’’ = 1760 Hz.
Reasons: when the string is twice as long, the pitch
is lowered by one octave. When string length is half
the length it is one octave higher and when the
length of the string is reduced to a quarter, the
note rises to the second octave. The frequency of a
string vibration is inversely proportional to the
string's length.
21. Scales on stringed instruments
• By moving the bridge, play the musical scale
that is tuneful to the human ear. In each case,
calculate the ratio of the vibrating section of
the string to the total length of the string
(40 cm).
Tone String length Ratio of the string
length to the total
length of the string
C 40 cm 1
D 35.55 cm 8/9
E 32 cm 4/5
F 30 cm 3/4
G 26.66 cm 2/3
A 24 cm 3/5
B 21.33 cm 8/15
C’ 20 cm 1/2
Reasons: under consistent conditions (e.g. string
length, string thickness, etc.), the sound is an octave higher when the string length is halved. In the
case of the other tones on the musical scale, the
relation between the vibrating section of the
string’s length and its total length also forms simple ratios. The smaller the ratio, the more pleasing
the harmony (octave 1:2, fifth C/G 2:3, etc.).
22. Measurement of string tension
• Attach the spring balance onto the monochord
and insert the end of the nylon string into the
eye of the spring balance.
• Pull the peg and, using the A' tuning
fork (440 Hz), tune the string to standard pitch.
• Use the spring balance to determine the ten-
sion of the string.
The string tension in the case of a nylon string is
5.5 kg.
23. Relation between pitch and string tension
One of the results of experiment 22 was that in order
to obtain a standard pitch, the tension on the nylon
string needs to be 5.5 kg. How much tension should
be applied in order to obtain a pitch that is one
octave lower (A = 200 Hz)?
• Loosen the peg till you hear the pitch of A.
• To make sure this is right, place the bridge
under the string at 20 cm on the scale (i.e. half
the total length of the string) and tune this
half-of the string to standard pitch. Removing
the bridge, the whole string will vibrate at half
the frequency.
The string tension has been reduced to 1.4 kg.
Reasons: the frequency of the string is proportional
to the square root of the tension. If the tensile
force on the string is higher by a multiple of 4, 9,
16, etc., the frequency is increased two-fold, three-
6
fold, four-fold, etc. As measured earlier, 1/4 of 5.5
is 1.4 (rounded up).
24. Wind instruments and the laws they obey
• Blow the whistle. You can change the effective
length of the whistle by moving the plunger.
When the length is short, the whistle produces a
high tone and when it is longer, it produces a lower
tone.
Reasons: when a weak air current passes through
the whistle, standing waves are produced. In this
case, the length of the whistle corresponds to a
quarter wave length. When a strong air current
passes through the whistle, overtones are produced
whose frequency is an odd multiple of the fundamental tone.
In the case of an open whistle, the first harmonic is
twice the frequency of that for a closed whistle.
25. C major scale and its intervals
• To determine the intervals, the higher fre-
quency is divided by the lower frequency.
For the interval D/C = 1188/1056, the common
divisor is 132. We thus get ratios of 9/8, 10/9,
16/15, 9/8, 10/9, 9/8 and 16/15.
Reasons: the intervals between the individual tones
of a musical scale are not equal. Intervals can be
distinguished into the major tone (9/8), minor tone
(10/9) and half-tone (16/15).
26. Harmony and dissonance
• Play all possible combinations on the reed
pipe.
Pleasing harmonies (consonances) are produced at
the octave, the fifth note, the fourth, the major
third and minor third. Discordant notes (dissonances) emerge between the second and seventh
notes. The combination of tones produced by two
neighbouring tones is also called dissonance.
27. G major triad
• Simultaneously blow notes G, B and D on the
reed pipe.
A highly melodious combination is heard. This
combination of notes is termed the G major triad.
Reasons: consonance is produced if several notes
produce a melodious combination of pairs. The G
major triad is formed as a combination of the major third and the minor third. The frequencies of
the notes G, Band D have a very simple ratio to one
another, viz. 4:5:6.
In order to derive this ratio, the fundamental frequencies specified on the reed pipe should each be
divided by 6.
(To obtain a physically correct frequency, the fundamental frequencies printed on the pipe need to
be multiplied by 33).
It is also possible for the tuning of the reed pipe
and metallophone to differ audibly due to manufacturing processes.
28. Four-part G major chord
• Add to the G major triad the G’ octave as well.
To achieve this, simultaneously play G, B, D
and G’.
The result is a full and melodious “four-part G
major chord”.
Reasons: a four-part major chord features the fol-
lowing consonances:
Octave 1:2
Fifth 2:3
Major third 4:5
Minor third 5:6
29. Major scales in an arbitrary key
• First play the C major scale on the metallo-
phone. Begin with C. Subsequently play a simi-
lar scale starting from G.
A C major scale from C’ to C’’ sounds pleasantly
consonant. If you try to play a similar scale starting
at G’, though, there is a definite dissonance at F’’.
The note is a semitone too low.
Reasons: according to experiment 25, the following
intervals must be exhibited in every scale:
9/8, 10/9 16/15, 9/8, 10/9, 9/8, 16/15
For the sequence of notes G’…G’’, however, the
following intervals are specified on the base plate
of the metallophone:
10/9, 9/8, 16/15
, 9/8, 10/9, 16/15, 9/8
The underlined intervals are correct, the others are
incorrect in this sense.
The intervals 9/8 and 10/9 are so close to one another that it is extremely difficult to distinguish
between them. Hence, the divergence from the
ideal between G’ and B’ is irrelevant. However, the
“imperfection’ between E’’ and F’’ is easily noticeable. In this case, an interval of 16/15 occurs instead of 9/8. The F’ note is therefore a semitone too
deep.
30. Producing half-tones
• On the reed pipe, play the scale from G’ to G’’
making sure that the A’ note of the reed pipe is
genuinely tuned to standard pitch. Use the
tuning fork to compare the pitch.
A G major scale on the reed pipe is pleasantly con-
sonant.
Reasons: instead of the F’ note, a completely new
note, F#, is introduced. The interval between F’
7
and F#’ is 9/8 and the interval between F#’’ and G’
is 16/15. This is achieved by taking the frequency of
the F note and increasing it by multiplying it by
25/24.
The new notes produced by sharpening the tones
are called C#, D#, F#, G# and A#. (E# and B# are
equivalent to F and C respectively).
This sharpening is denoted in musical notation by
a sharp sign appearing on the clave before the
note.
Flat notes, which are a semitone lower than the
conventional notes are produced by multiplying
the latter by 24/25. These notes are denoted in
musical notation by a flat sign preceding the note
on the clave. The new flat notes are called Db, Eb,
Gb, Ab and Bb.
In the tempered scale used on a piano, the notes
C# and Db, D# and Eb, F# and Gb etc. respectively
are played using the same key, since in each case
they are close enough to being identical.
Elwe Didactic GmbH Steinfelsstr. 6 08248 Klingenthal Germany www.elwedidactic.com
3B Scientific GmbH • Rudorffweg 8 • 21031 Hamburg • Germany • www.3bscientific.com
Subject to technical amendments
© Copyright 2009 3B Scientific GmbH
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