A singing wine glass as an instrument for teaching acoustics.

A singing wine glass as an instrument for teaching
acoustics.
José Antonio Zárate Colín, Marisol, Rodríguez Arcos, Karina Ramos Musalem,
Estela Margarita Puente Leos and Marcos Ley Koo
Facultad de Ciencias, Universidad Nacional Autónoma de México.
Abstract
In this paper, we present the work done by a group of three undergraduate students majoring in
physics during their leisure time, in order to study the singing wine glass phenomenon. Here we
describes the tests performed to identify variables, and their measurement, that where used in
the experimental analysis. Although this is a simple experiment, considering it for teaching
sound waves can be a very illustrative experience.
Keywords
Laboratory activities. Informal physics teaching and learning. Wine glasses singing. Sound
waves.
TEACHING METHOD PROPOSAL
Throughout its history, physics has been based on experimental research. Thus, experimental
physics education is essential for a complete training of students majoring in physics, regardless
of their theoretical or as experimental interest.
Unfortunately, in México, most of the experimental physics courses at all educational levels,
follow very strict traditional formats, where the students initiative is of no concern; just guided
by the teacher, students construct their knowledge mechanically. Most of the times, courses
have the tendency to make students follow a series of instructions, as a recipe, which include
the list of material and equipment, the procedure, step by step, and even the results and
conclusions that should be obtained, as the goal of the experiment; so that students lost interest,
as well as the opportunity to develop capabilities and abilities, which are essential for their
professional lives, provided by a good experimental training.
This kind of method can limit the vision that students have on the experimental practice, leading
students to think that experimentation plays a minor role in science and prefer to become a
theoretical physicist. A rigid and restrictive experimental course can mean a barrier to develop
skills such as: critical thinking, problem solution orientation, hypothesis formulation, etc.
Having theses ideas in mind, we launch an effort, looking for alternative methods of
experimental teaching in the Physics department of the Facultad de Ciencias of the Universidad
Nacional Autónoma de México, and this proposal comes up.
The method here proposed is not strictly based in one pedagogical theory but it has ideas of the
constructivism learning theory which is based on observation and analysis Students construct
their own understanding and knowledge of phenomenon, through experiencing and taking into
account those experiences. If they encounter something new, they have to check against it with
previous ideas and experiences, maybe changing what they believe, or maybe discarding the
new information as irrelevant. In any case, they actively build their own knowledge, to do this,
they must ask questions, explore and evaluate what they know. Always guided by the teacher,
students construct their knowledge actively rather than just mechanically acquiring knowledge
from the teacher or the textbook. We considered also some proposal of interactive methods of
teaching (Etkina et al).
The method can be summarized in the following steps:
• reproduction of a system, a phenomenon already known, or propose a project on which
students want to focus their attention;
• observation and reflection set out hypothesis that explain what is observed in the phenomenon
being studied;
• design one or more experiments to test the proposed hypothesis;
• observation and reflection, once more, to confirm hypothesis;
• recognition of important variables to the experiment and suggestion on how to quantify them;
• analyze the results; and
• draw up a model, which allows prediction of results under conditions different to those under
which the experiment has been conducted.
• If necessary, to reconsider hypothesis and carry out complementary activities.
EXPERIMENTS CARRIED OUT AND RESULTS
This work is an example of the type of experiments designed and carried out by a group of three
undergraduate students (José Antonio Zárate Colín, Marisol, Rodríguez Arcos and Karina
Ramos Musalem), as students of physics of the Facultad de Ciencias of the Universidad
Nacional Autónoma de México,
The project arisen from a final project for an experimental course of third semester course
(Collective Phenomena) of the Physics Curriculum of the Facultad de Ciencias of the
Universidad Nacional Autónoma de México. Students had to choose the project and the only
condition was to choose a phenomenon, which aroused their interest and comprised the topics
(thermodynamics, fluid mechanics and waves) studied in the course during the semester. After a
bibliography search, they read some papers and choose (Chen, Rossing), the singing wine glass
phenomenon. For this project they carry out the experiment presented here as the two first
stages (dependence of the resonance frequency on the wine glass shape and dependence of the
resonance frequency on volume of liquid inside a wine glass). For these stages they worked
during a month in the laboratory class time.
After finishing the semester they were so interested on the subject that they asked the teachers
to continue with experimentation during their leisure time, for almost one year. They work in a
laboratory, which is not used for classes.
Vibration and waves are classical topics in all physics curricula. One of the more usual lecture
demonstration is to make a wine glass sing by rubbing its rim with a wet finger. Young people
are very familiar with the phenomenon and many street musicians can even be found giving
concerts with wineglasses containing water, but most of the students only observe and they
never analyze and quantify. In this work, we present the results of the study of the phenomenon
well known of a “Singing Wine Glass”; on which the group of students focused their attention.
A wine glass can be simple and complex at the same time: to produce sound is easy but to
understand the phenomenon and quantify it is different matter. As a topic for physics courses
can be not only an amusing event but also a very useful instrument of learning and can become
an excellent way towards experimentation.
The student’s work was done during the time they fulfilled their course requirements for the
B.Sc. degree, and it comprising different stages, in which some goals were reached via different
experiments the students carried out, and follow the method proposed. Most of the time they
worked alone but their teachers Marcos Ley Koo and Estela Margarita Puente Leos always
supervised them.
The study was divided into four main stages:
Dependence of the resonance frequency on the wine glass shape.
Students wondered about the variables on which depends the frequency of sound produced
while rubbing the rim of a wine glass. The first hypothesis was that the wine glass resonance
frequency depends on shape and the volume of liquid inside of it. So they observed and they
carried out hypotheses that explain what they observed.
Firstly, in order to analyze the dependence on shape they use four different shape wine glasses
(figure 1): a champagne glass, a Burgundis glass, a cocktail glass and a red wine glass.
Figure 1. Different shape wine glasses (from left to right): champagne glass, Burgundis glass,
cocktail glass and red wine glass
With the help of a laptop, a microphone, and the digital audio editing software Goldwave the
sound produce while rubbing with a wet finger the rim of each shape of the wine glasses was
recorded, analyzed and the natural vibration frequency for each shape obtained. The results
obtained allowed to conclude that the frequency depends on the shape. Resonance frequency is
greater when its shape is closer to that of a cylinder and smaller when is more spherical.
Dependence of the resonance frequency on volume of liquid inside a wine glass.
The wine glasses were filled with different amounts of water to obtain a relation between the
volume and the frequency for each type of wine glass when its rim is rubbed. Again with a
microphone, a laptop, and the software Goldwave the natural vibration frequency was obtained.
The results showed (figure 2) that frequency decreases as liquid filling volume increases, and
this behavior is independent of glass shape. No matter which shape is, frequency depends no
linearly on volume of liquid inside. As sound obtained while rubbing the rim of the glass,
depend on the resonant cavity and when the amount of liquid changes the resonant cavity
changes, frequency changes. This would be able to be confirmed using glasses of same form but
of different size.
Figure 2. Dependence of frequency on volume of liquid inside a wine glass
Dependence of the resonance frequency on the kind of liquid inside.
After finishing the experiment, students continued to design more experiments to test the
formulated new hypothesis. So, they asked themselves what would happen if instead of water
they used another liquid: Frequency changes?. On which characteristic of the liquid depends?
Once more, they observed and though about, in order to confirm the hypothesis.
Wine glasses were filled with different liquids; the characteristics studied were density,
viscosity and compressibility. With this goal in mind, students carried out three experiments so
they could study the dependence of the resonance frequency of the glass wine with respect to
different properties of the liquid that it contains.
Again, with a microphone and a laptop, the vibration frequency was measured for different
kinds of liquids. To observe the effect of changing density, students worked with one wine glass
filled with 200 ml of liquid. They use a mixture water-alcohol, and the proportion of water and
alcohol was changed, from 10 ml to 200 ml of alcohol, the total volume was always 200 ml.
With this process, liquid density was less than water. In a similar way, they work with a mixture
of corn syrup and water, so liquid density increased. With Goldwave software, students while
rubbed the rim of the wine glass, recorded during 30 s in order to obtain frequency.
Frequency does not change meaningfully within the density range evaluated. So, students
concluded that frequency does not depend on density, but this cannot affirm for densities ranges
out of those of experiment.
In order to observe if frequency depends on viscosity, students use liquids of different
viscosities: corn syrup, auto motor oil (SAE 40), glycerin, ketchup, peanut butter, liquid
chocolate, condensed milk, salad dressing, y shampoo. Frequency was measure for 200 ml of
each liquid. Viscosity was obtained with a Brookfield DV-II viscometer.
Data shows that frequency depends of viscosity, but, with the amount of data obtained, it was
not possible to predict its behavior.
To evaluate the hypothesis that frequency depends on isothermal compressibility, students did
not measure the compressibility but they qualitative changed it. They use a wine glass of 450 ml
of capacity and a mixture of water and gelatin. More gelatin less compressibility. With 300 ml
of mixture inside, they waited to thicken and measure frequency while rubbing the rim of the
wine glass. From data, frequency decreases with increased compressibility
Energy needed to break a wine glass.
During the experiments, students questioned if the frequency value obtained with the software
was the right one, due to the non-controlled way of making the wine glass to vibrate. They used
their finger to rub the rim of the wine glass, so they suppose that if the frequency obtained was
the fundamental frequency of the wine glass, then they could make it to vibrate until reach the
resonance and the wine glass would break. The obtained a mean frequency of 650 Hz.
They propose the following method: the fundamental frequency for different wine glasses
without liquid inside was found knowing the resonance frequency of the wine glasses, with the
help of a signal generator, a speaker and an amplifier, the wineglasses were excited at their
resonance frequency until they were broken. Electric power supplied to the speaker, as well as
the time needed to break the wine glass were measured in order to quantify the energy needed
to rupture.
Figure 3. Experimental set up use to vibrate wine glass until reach the resonance and breakup.
A high definition and a high speed cameras were used to record the standing waves formed in
the rim of the wineglasses. The resulting photographs and videos were analyzed with a Tracker
video analysis and modeling software and it was possible to obtain quantitative results.
Figure 4. Time needed to break the wine glass vs electric power supplied to the speaker
From data obtained, after a log-log plot, it was possible to quantify the energy needed to break
the wine glass, arriving to the equation:
P = 10 b t a
(1)
where t is the Time needed to break the wine glass and P is the electric power supplied to the
speaker, and,
€
a = (−5.7 ± 0.6) and b = (7.6 ± 1.6)
(2)
dE
From here we have, from the electric power supplied to the speaker, as P =
, integrating,
dt
€
€
we obtain for the energy (E) need to break the wine glass:
E=
10 b a +1
t
a +1
€
(3)
Students continued to have questions: from the relation between the time needed to break the
wine glass and electric power supplied to the speaker, they found a value for the electrical
energy used to break the wine€glass, but was this energy the same of the acoustical energy
transferred to the wine glass during the process?. So, finally, with the help of a decibel meter
they obtained the relation between the sound pressure obtained from the speaker and electric
power supplied to it. Frequency was fixed at 650 Hz, the mean resonance frequency of the wine
glasses.
Figure 5. Sound intensity obtained from the speaker vs electric power supplied to the speaker.
From figure 5, relation between sound intensity (Ia) obtained from the speaker and electrical
power supplied to the speaker (Pe) is a logarithmic relation:
I a = 14.3 log(Pe ) + 121.0
(4)
In acoustics (Kisnley et al, Heller), sound pressures and intensities are usually described using
logarithmic scales known as sound levels. This is because most of sound pressures and
€ to 10 W/m2. Logarithmic are consistent with the humans sensing of
intensities vary from 10-12
the relative loudness of two sounds by the ratios of their intensities. The decibel (dB) scale is
used in acoustics as a unit of sound levels,
Sound intensity is defined as the sound power per unit area. The intensity level (IL) of a sound
is defined by
"I %
IL = 10 log 10 $$ ''
# I0 &
(5)
where I0 is the reference intensity, which is the standard threshold of hearing intensity, IL is
expressed in decibels referenced to Io 10−12 watt/m2.
€
Since audible sound consists of pressure waves, one of the ways to quantify the sound is to state
the amount of pressure variation relative to atmospheric pressure caused by the sound. Because
of the great sensitivity of human hearing, the threshold of hearing corresponds to a pressure
variation less than a billionth of atmospheric pressure.
As the intensity and effective pressure of progressive plane and spherical waves is related by
I=p2/ρ0c, then the sound pressure level (SPL) can be expressed as the effective sound pressure
of a sound p relative to a reference value p0.
"p %
SPL = 20 log 10 $$ ''
# p0 &
(6)
SPL is measured in dB referenced to p0=20 micropascals in air. This reference pressure in air is
set at the typical threshold of perception of an average human.
€
Sound power level (SWL) or acoustic power level is a logarithmic measure of sound intensity
in comparison to a reference level of 10−12 watt (1 pW).
"P %
SWL = 10 log 10 $ a '
# P0 &
(7)
Sound Power Levels and Sound Pressure Levels are expressed in decibels, but they are not the
same decibels. The decibel is only used to compress a wide range of absolute values into a
manageable range. It is not €
an absolute unit, but is a ratio. Without a reference level, it means
nothing. The sound power level indicates the total acoustic energy that a machine, or piece of
equipment, radiates to its environment. The sound pressure level is a measure for the effect of
the energy of an acoustic source (or a collection of sources) and depends on the distance to the
source(s) and acoustic properties of the surroundings of the source
From equation (4), and taking into account equations (5) and (7), for the sound power Pa, we
have:
"P%
Pa = 14.3 log(Pe ) + 121.0 = 10 log 10 $ '
# P0 &
€
10 121.0€Pe
14.3
" P %10
= $$ ''
# P0 &
Then,
€
€
1.4
1.4
P = 10 12.1 Pe P0 = 10 0.1 Pe
as, P0 is 10−12 watt, we have a relation between the sound power P obtained from the speaker
and electrical power supplied to the speaker (Pe).
€
Students wonder about more questions about the singing wine glass phenomenon, but they must
continue with other projects and new experiments.
CONCLUSION
• The method used for experimental teaching motivated students to continue making
experiments even outside classroom and beyond the original course.
•Students learned to apply acquired knowledge, from different areas of physics, to propose an
experiment and carried it in different stages, in order to analyze the phenomenon they were
interested on.
•Students could confirm or reject the hypothesis they suggest at different stages of the
experiment.
•Students learned to perform critical analysis, which improved their ability to solve technical as
well as conceptual problems.
References
Chen Yoh-Yuh. (2005). Why does Water Change the Pitch of a Singing Wineglass that Way it does?.
American Journal of Physics. 73. 2-6.
Etkina Eugenia, Planinsi Gorazd, Vollmer Michael. (2013). A Simple Optics Experiment to Engage in
Scientifics Inquiry. American Journal Physics. 81. 2-9.
Kinsler, Laurence E., Frey, Austin R., Coppers, Alan, B. and Sanders, James V. (2000) Fundamental of
acoustics. 4th edition. John Wiley and Sons, Inc. USA
Heller, Erick J. (2013).. Why You Hear What You Hear. Princeton University. USA.
Rossing, Thomas D. (1990). Wine Glasses, Bell mode, and Lord Rayleigh. The Physics Teacher. 28. 2-5.
Affiliation and address information
José Antonio Zárate Colín, Marisol, Rodríguez Arcos, Karina Ramos Musalem, Estela Margarita Puente
Leos and Marcos Ley Koo
Laboratorio de Acústica,
Departamento de Física,
Facultad de Ciencias,
Universidad Nacional Autónoma de México,
Circuito Exterior, Ciudad Universitaria,
04510, México, D.F.
México
e-mail:[email protected]
e-mail: [email protected]
e-mail: [email protected]