Sarah Springer
[Background] [Procedure] [Uncertainty] [Data]
[Analysis] [Wave Patterns] [Bibliography]
[Links]
[Research Page]
Wine Glass Acoustics
In the 1960’s Ben Franklin invented the first American made musical instrument, the glass harmonica (Miley, 2). Yet, “the underlying physics of the ‘armonica’ or the glass harmonica remains mysterious” (Bunce, 1). The glass harmonica works much the same way as rubbing a finger around a wine glass. The pitches are altered only by changing the amount of water in the glass or by grinding away glass from the bottom or the rim (Bunce, 1). Since we already know the relationship between the size of the bowl and the pitch, (otherwise constructing the glass harmonica would be nearly impossible) I am more concerned with the relationship between the pitch and the amount of water in the glass. This is what I will endeavor to discover.
When one rubs their finger around a
glass, the glass vibrates similarly to the string on a violin vibrates when it
is rubbed with a bow (Sabbeth, 7). As
the bow glides across the violin string, it pulls the string with it due to
friction. “As the string is displaced
to one side, the tension in it results in a restoring force tending to pull the
string back to its original position (Backus, 167). This, of course, happens several times a second and is what
causes the string to vibrate. If we were
to imagine the string is the glass and the bow is our finger, we might have
good idea why rubbing a glass produces a note.
Since I can not adjust the tension like I could the string of a violin,
I will add and subtract water to change the pitch.
Sound travels through water at
approximately 1,440 meters per second while it travels through glass at
approximately 4,500 meters per second (Giancoli, 309). Since the velocity of sound is much greater
through glass, a glass with no water in it is going to vibrate at a relatively
high frequency. As more water is added,
the vibration of the glass is going to slow down therefore producing a lower
note. I hypothesize the amount of water
needed to go from one note to the next, will be even intervals, directly proportional
to the pitch. [Table of Contents]
In order to test my hypothesis, I used a relatively simple set up that took very little time to prepare. Sugar, water, measuring cup (that shows ounces), two sizes of the same wine glass, a tuner, a pen, and paper are the only materials that I used. I started by putting a very small amount of water in the larger of the two wine glasses (about one ounce of water), because there needs to be some water in the glass for it to produce a tone. The finger that is going to rub the rim of the glass also needs to be wet in order for the glass to produce a tone. This can be easily taken care of by quickly dipping it in water before continuing. Next I turned the tuner on and placed it near the glass so it would pick up this pitch. I chose the closest pitch to what the tuner was currently picking up and adjusted the water level in the glass until that note was perfectly in tune (in my case a G#). I recorded this note and then measured the amount of water in the glass by pouring it into a measuring cup. I recorded this amount next to the note in both cups and ounces (the water amount is in two units purely for backup purposes so I could make sure I did not write down a value incorrectly).
Continuing on, I replaced the water in the glass and added additional water until the next pitch was perfectly in tune (in my case a G). I then recorded this note and the amount of water in the glass that it took to produce it. Note: the pitch gets lower as more water is added. I continued on like this until the glass was almost completely full and I had recorded nine or ten different pitches. I also used the same procedure with a smaller, but similarly shaped, glass. Since I am not endeavoring to discover the relationship between the size of the glass and the pitch, I used the smaller glass only to support any findings evident with the larger glass.
Later, after pondering the results of the experiment, I decided I wanted to try this procedure using something that had a different density than water. Since it was easily accessible, I used sugar water. I started with about two cups of water and heated it to almost a boil. I then added sugar until it no longer dissolved (was saturated) and used the sugar water in place of the plain water in the aforementioned procedure with the larger glass. [top]
Before I started this experiment I was worried that the speed at which I moved my finger around the top of the glass would have an impact on the pitch. This could have been a real unfortunate uncertainty since it would be extremely difficult to gage how fast I was moving my finger across the glass and even harder to keep it consistent. However, I tested this when I started to take data and the speed of my finger had no apparent affect on the pitch the glass produced. Also, water on the outside of the glass had no notable effect on the on the pitch of the glass. This was helpful because when making small adjustments to the amount of water in the glass, water would often spill and drip down the outside and it did not become imperative that I stop a wipe it off every time.
Some uncertainties
that did occur were in measuring the amounts of water in the wine glass. First it was rather difficult to pour the
water from the glass to the measuring cup.
Because of the way the wine glass was shaped, the water often ran down
the side of the glass instead of pouring directly into the measuring cup. After some practice at this I became quite
proficient, however, and consequently kept this uncertainty to a minimum. Second, once the liquid I was trying to
measure exceeded one cup, I had to resort to using two different measuring cups
because I did not have a larger one that was marked at each ounce. Yet I do not think the uncertainty margin is
very large here either since I was extremely careful to measure exactly one cup
into the first measuring container and the second container I used for
measuring was marked at every Tablespoon, more accurate that the first
one. Finally, other factors that could
have contributed to the uncertainty margin were the innumerable small sounds
that could have been present in my house when I was conducting the
experiment. For instance, the hum of
the heater the refrigerator lull, or a light bulb buzz could have all
contributed slightly to the pitch the tuner was picking up and consequently
caused it to read something slightly different from the true pitch of the
glass. Fortunately all of the
uncertainties that I have been able to think of thus far are relatively small. I therefore state that my measured values
could not have been off by more than a half of an ounce on either side as seen
below for the larger glass. [arriba] 
My raw data is as follows or there is a graph of it on the following page that will be referred to later.
