PRELAB5: SOUND WAVES IN TUBES
INTRODUCTION
Sound is longitudinal mechanical vibrations that are transmitted as pressure wave through
mediums such as gases, liquids, solids, and plasmas. Sound cannot travel in vacuum.
Experimental measurements of the speed of sound in air were carried out successfully
between 1630 and 1680 by a number of investigators, prominently Mersenne. Newton (16421727) derived the relationship for wave velocity in solids, a cornerstone of physical acoustics
(Principia, 1687). Sound travels through air at a velocity of approximately 343 m/s (1050ft/s)
at 1 atm and 20˚C, or
v = 331.5 m/s + (0.6 m/s) T
(1)
where temperature T is in degrees Celsius.
Because its energy is spread over larger and larger area, the amplitude of a sound wave
decreases as it travels away from a source such as a vibrating speaker or tuning fork. These
waves also reflect from surfaces and in reflection lose amplitude through absorption. The
sound wave can be a pulse, or continuous perturbation. The wave can be decomposed into
sinusoidal components in time.
The eighteenth century saw major advances in acoustics at the hands of the great
mathematicians of that era, who applied the new techniques of the calculus to the elaboration
of wave propagation theory. In the nineteenth century the giants of acoustics were Helmholtz
in Germany, who consolidated the field of physiological acoustics, and Lord Rayleigh in
England, who combined the previous knowledge with his own copious contributions to the
field in his monumental work “The Theory of Sound.” Also in the 19th century, Wheatstone,
Ohm, and Henry developed the analog between electricity and acoustics.
The twentieth century saw a burgeoning of technological applications of the large body of
scientific knowledge that was by then in place. Wallace Clement Sabine (1868-1919)
produced a groundbreaking work on architectural acoustics, and many others followed.
Underwater acoustics was used for detecting submarines during World Wars. Sound
recording and the telephone globally transformed our society. Sound measurement and
analysis reached new levels of accuracy and sophistication through the use of electronics and
computers. Electronic instruments were introduced to musicians. The ultrasonic frequency
range enabled wholly new kinds of application in medicine and industry. New kinds of
transducers (generators and receivers of acoustic energy) were discovered and invented.
Sound Reflection
Sound wave will be reflected by a surface.
The reflection of sound obeys the law of
reflection, i.e. “Angle of incidence equals
angle of reflection.”
 r  i
PRELAB5: Sound waves in Tubes page 1
Wave reflected from a fixed end will be 180˚ out of phase with respect to the incident wave,
i.e. an incident wave with positive sign will produce a reflected wave with a negative sign.
On the other hand, the reflected wave from an open end will be in-phase with respect to the
incident wave, i.e. the reflected wave has the same sign as that of the incident wave. In this
lab, you will determine the sign of the reflected sound wave from open tube and closed tubes
respectively.
Standing wave
The reflected waves can interfere with incident waves, producing patterns of constructive and
destructive interference. This can lead to resonances called standing waves in rooms. It also
means that the sound intensity near a hard surface is enhanced because the reflected wave
adds to the incident wave, giving pressure amplitude that is twice as great in a thin “pressure
zone” near the surface. This is used in pressure zone microphones to increase sensitivity. The
doubling of pressure
gives a 6 decibel
increase in the signal
picked up by the
microphone.
Reflection of waves
in strings and air
columns are
essential to the
production of
resonant standing
waves in those
systems. For
example, the graph
below shows a standing wave of an open-closed tube.
The schematic standing wave (pressure) of open-open, closed-closed, or open-closed
systems are shown in the graph below.
Acoustic Lab 5: Sound waves in Tubes page 2
1. Open-open or closed-closed: the fundamental frequency is ݂ଵ ൌ
௩
ଶ௅
, and the higher
harmonics are f2=2f1, f3=3f1, ….
2. Open-closed: the fundamental frequency is ݂ଵ ൌ
௩
ସ௅
and higher harmonics are f2=3f1,
f3=5f1, ….
In human, standing wave plays an important role in speech of vowel sounds:
•
•
•
•
The vocal tract can be considered a single tube extending from the vocal folds to the lips,
with a side branch leading to the nasal cavity.
The length of the vocal tract is typically about 17 centimeters, though this can be varied
slightly by lowering or raising the larynx and by shaping the lips.
The pharynx connects the larynx (as well as the esophagus) with the oral cavity.
The oral cavity is the most important component of the vocal tract because its size and
shape can be varied by adjusting the relative positions of the palate, the tongue, the lips,
and the teeth.
The characteristic resonance produced by our vocal track is called Formant. A musical
instrument may have several formant regions dictated by the shape and resonance properties
of the instrument. The human voice also has formant regions determined by the size and
shape of the nasal, oral and pharyngeal cavities (i.e. the vocal tract), which permit the
production of different vowels and voiced consonants.
Formant regions are not directly related to the pitch of the fundamental frequency and may
remain more or less constant as the fundamental changes. If the fundamental is well below or
low in the formant range, the quality of the sound is rich, but if the fundamental is above the
formant regions the sound is thin and in the case of vowels may make them impossible to
produce accurately - the reason singers often seem to have poor diction on the high notes.
Acoustic Lab 5: Sound waves in Tubes page 3
Prelab Report 05
1. The result of open-open system (e.g. flute and other wind instruments) or closed-closed
tube of length L has standing waves where the wave length of the nth harmonic is shown
in the Table below. The corresponding frequency is listed in the third column, where v is
the speed of sound in the tube.
harmonics
1
2
3
…
n
wavelength
2L
L
2L/3
…
2L/n
frequency
f1=v/2L
2 f1
3 f1
…
n f1
Question: An open-open PVC pipe of length 60 cm. What is the fundamental resonance
frequency in the air at 1 atm and 20˚C? What is the frequency of the next higher harmonic?
2. On the other hand, an open-closed tube of length L has standing waves with only odd
harmonics shown in the Table below:
harmonics
1
3
5
…
2n+1
wavelength
4L
4L/3
4L/5
…
4L/(2n+1)
frequency
f1=v/4L
3 f1
5 f1
…
(2n+1) f1
Question: An open-closed PVC pipe of length 60 cm. What is the fundamental resonance
frequency in the air at 1 atm and 20˚C? What is the frequency of the next higher harmonic?
Acoustic Lab 5: Sound waves in Tubes page 4