3B Scientific Acoustics Kit - Manual (Page 6)

6
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 spe-
cific 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 cre-
ated if the surrounding noise possesses tones which
match the harmonic of the resonator. In this way,
the spherical cavity resonator can be used to iden-
tify 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 sec-
tions 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 oc-
tave 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 sim-
ple 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 stan-
dard 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-