Background and Possible Experimental Methods for IYPT Problems 6, 1, 7, 13, and 5
DC
6. Singing Glass
When rubbing the rim of a glass containing a liquid a note can be heard. The same happens if the glass is immersed in a liquid. How does the pitch of the note vary depending on different parameters?
Ideas:
The most difficult part of this experiment will be obtaining lots of glasses of similar size. The pitch of the note is equivalent to the frequency of the sound wave emitted from the glass, caused by vibration from rubbing the glass with a finger. We will need to determine frequencies, and doing it by ear will not be a good option. A microphone could be attached close to the vibrating glass and run to an oscilloscope, where the waveform can be visualized and the frequency accurately determined.
A glass is similar to a tuning fork. When the end of a tuning fork is struck to set up a vibration (just as the rim of a glass is rubbed to set the glass vibrating), a note is heard. Connecting the tuning fork to a wooden box (resonator) amplifies the note. The same can be done by attaching the base of a glass to a wooden box if needed, so the frequency differences between different glasses can be more easily heard.
We know that the smaller an object is, the higher its frequency of vibration. The larger it is, the lower the pitch will be. The shape of the object is also important, because sound waves generated by one part of the object (the rim) will be reflected by other parts of the object (the inside of the glass and the base). Brass instruments with different shapes (trumpet and French horn, for example) produce notes with different pitches (trumpet has higher pitch, French horn lower) because of the shape of the cavities between which sound waves are reflected. Therefore, the depth of a glass, the circumference of the rim, the height of the glass, the thickness of the glass, and whether the glass is cylindrical or bowl-shaped will all be variables that determine the glass's frequency of vibration.
Change one of the variables; keep the rest constant to determine how each of the variables affects the resultant pitch. We will have to obtain different glasses for this, and I suggest that we use cylindrical glasses (similar in shape to cafeteria cups, but smoother and with a smooth base) because they are easier to obtain than wine glasses, which are bowl-shaped. I have three such cylindrical glasses at home that I'll be able to bring in if nobody knows of a good place where we can get good glasses. Mr. Roser on Chemistry Floor blows glass; somebody may want to go down there to ask him if he has any glasses we can use. We need glasses that have the following properties:
Variables for cylindrical glasses:
Constants:
Depth
radius, thickness, height
Rim circumference/radius
depth, thickness, height
Thickness
depth, radius, height
Height
depth, radius, thickness
We want at least two glasses for each variable; for example, we will want to have at least two glasses with different depths so we can see how the depth changes the frequency of vibration. This makes at least 8 glasses that we will have to obtain. I suggest having three glasses for each variable; three is always a good number when doing experiment trials. That comes to 12 glasses. That doesn't sound too bad; the only difficult part will be obtaining the glasses.
- Rotation
A long rod, partially and vertically immersed in a liquid, rotates about its axis. For some liquids this causes an upward motion of the liquid on the rod and for others, a downward motion. Explain this phenomenon and determine the essential parameters on which it depends.
Ideas:
This problem appears to operate around the same principles that govern whether or not a liquid will form an upward-directed meniscus, or a downward-directed one when left to reach equilibrium in a graduated cylinder. One of these principles is surface tension, which arises due to attractive intermolecular forces. These attractive intermolecular forces, along with friction with the container walls and the rod, are definitely what's responsible for the observed motion of the liquid. This was determined by analyzing our experimental setup-if the same torque is exerted on the liquid by the rod, the container is kept the same so that its coefficient of friction is constant, and only the liquid changes, then the properties of the liquid must be what's causing the observed effects.
Fluid dynamics will be essential in determining the parameters that govern the liquid's observed motion. When a rod is made to rotate in the center of a cylindrical basin as shown in the diagram of this problem, it exerts a torque on the surrounding liquid. The liquid is dragged along with the rotating rod, and near the container walls, the liquid's velocity must decrease because at any surface, the velocity of the liquid must be zero. This goes the same for the surface of the rod, and because liquid velocity is zero at the rod's surface, these zero-velocity molecules drag others along as the rod rotates, and a flow pattern is set up in the liquid.
Viscosity of the liquid (a measure of the attractive intermolecular forces present between liquid molecules) will play a major role in the type of flow pattern that results. If needed, small opaque solid particles can be thrown in so that the flow pattern can be visualized more easily. Using liquids with different viscosities, experiments can be done to determine an area of viscosity for which the upward motion of the liquid about the rod begins to change to a downward motion. Density of the liquid will also be a major variable. To do viscosity experiments, the density of the solution must be kept constant, and this can probably be done by making different solutions of liquids. This is a good job for someone with a good chemistry background. To do density experiments, viscosity will have to be kept constant, and again, different solutions can be made.
- Heated Needle
A needle is hanging on a thin wire. When approached by a magnet, the needle will be attracted. When heated, the needle will return to its original position. After a while the needle is attracted again. Investigate this phenomenon, describe the characteristics, and determine the relevant parameters.
Ideas:
Heating destroys magnetism, in much the same way as superconductivity is destroyed by magnetic fields (this was something interesting that I put together during recent reading). The mechanism for magnetic field creation by a magnet is the alignment of atomic domains within a magnet. These domains consist of small dipole-like regions, and when they are aligned, a magnetic field is produced. The intensity of the magnetic field is dependent upon the number of domains, how well they are aligned, and how strong each domain is. In reality, domains are never perfectly aligned, for the same reason that the needle in this problem ceases to be attracted by a heated magnet.
All atoms exhibit motion. This motion was first seen in pollen grains and then in molecules, and it was termed Brownian motion after the person who first discovered it in pollen. It is nothing but the random motion of atoms. This random motion is caused by thermal energy. Gas molecules gain kinetic energy when the temperature of the gas rises, and this happens for atoms also. Only at absolute zero (which can never be attained) will atoms come to rest. Since room temperature is far from absolute zero, we can be assured that atoms in our magnetic domains are in constant random motion, and can never become perfectly aligned.
When a magnet is heated, the temperature of the magnet rises, which causes atoms in the magnet to gain kinetic energy. They move more, and consequently, the magnetic domains become increasingly disaligned. Since the strength of the magnetic field produced by a magnet is proportional to the degree of alignment of the magnet's domains, the magnetic field strength decreases. Therefore, the needle will be attracted with less force than before. When the magnet becomes heated to such a degree that its domains are spread in random directions, no magnetic field is produced, and the needle no longer is attracted and swings back to its original position.
- Gas Flow
Measure the speed distribution of the gas flow in and around the flame of a candle. What conclusions can be drawn from the measurements?
Ideas:
This could be another video project, unless if anyone knows of a way to determine the speed distribution using the different colors of the flame. Basically, the gas flow is the same as that of a fluid being pushed past a stationary sphere. The fluid starts in front of the sphere, moves along the sides, and leaves a wake behind the sphere as it passes. The gas within the flame of a candle should move in much the same way.
On the outside of the flame, convection currents are set up that are flattened by air pressure due to gravity. The currents are due to the temperature difference between the flame and the surrounding air. The rising gas from the flame sets the currents into motion, and the temperature difference keeps currents in the form of vortices going. Vortices that form are similar to the convection cells that form in the Earth's upper atmosphere as a result of unequal heating by the Sun.
Since it is difficult to distinguish the different colors in a flame (also, a flame is constantly changing shape), markers of some sort are needed to trace the pattern of the changing flame. Solid particles (similar to the small, visible wood embers that float upward in the gas flow of a campfire) thrown into the flame in such a way as to not disturb the flame is what will help us measure the speed distribution. These particles need to be dark so they will be visible against the flame. Using video, we can trace the movement of particles in each frame, and from position data taken in each frame, we can compute the average velocity of each particle from frame to frame. A pattern should result; particles near the outside of the flame should move with different speeds than particles near the center of the flame, and perhaps more patterns may result due to the effect of the convection currents around the flame.
I've heard a bit about particle-image velocimetry; there are programs available that will allow the position of a particle to be tracked over time, and for a product, a graph showing average velocity vectors of particles is made. Duke's physics department has one such program, written by a graduate student. The only problem with that program is that the program treats light spots on a frame to be particles, and not dark spots. The program would have to be modified for the purpose of locating the dark particles in our flame.
- Dropped Paper
If a rectangular piece of paper is dropped from a height of a couple of meters, it will rotate around its long axis whilst sliding down at a certain angle. What parameters does the angle depend on?
Ideas:
I've got a report from the Internet that explains the parameters that the angle depends on, but the experiment to find these parameters was done with a strip in water, not a strip in air. Therefore, results may be different, although the principles used to investigate this problem are likely the same. Water and air are both fluids, so fluid dynamics will be essential in explaining the parameters.
Besides reading this report, more research should be done on the Froude number and how to calculate it. This number will be essential to explaining the parameters that govern the paper strip's movement through air.
The first step of this experiment is to obtain a rectangular piece of paper. The paper should be stiff so that slight bends in the paper won't have to contribute to our analysis by introducing more variables. The paper needs to be massed and measured. It also needs to be quite flat so that we can treat the paper as being two-dimensional, ideally. If the fluid dynamics we will be using requires three-dimensional objects, then we can determine the depth of the paper strip later.
We will have to pick a drop height (say, 3-5 meters), and drop the strip from that height for each trial. This is definitely going to have to be a video project, so a drop height should be chosen that allows us to see both the angle at which the strip falls, the initial and final heights of the strip, and ideally, the strip itself in good resolution. The initial and final heights should also be quite close together to minimize parallax error, but should be far enough apart so that the full motion of the paper strip can be observed.
A few initial drops need to be done to determine where we're going to go with this experiment; we need to get a feel for how different strips fall. Variables for our strips will be mass, length, and width (thickness might be another variable, but we'll probably not choose to consider it now since it involves three dimensions). Length and width were both made variables because the strip will be dropped from the same orientation each time, and whether the paper is longer in length (horizontal measurement) or width (vertical measurement) when it falls vertically will make a difference in the strip's motion. Change one variable and keep the others constant, and see how the strip falls. This must be done to see how we will set up the video.
As shown on the report, there were several patterns for how the strip falls. Although this experiment was done in water, we have certainly seen the same types of patterns when paper falls through air. Therefore, a strip of paper does not always rotate about its long axis while sliding down at a certain angle, as this problem suggests. There are limits to how long the strip of paper can be made, how wide the strip can be, and how massive it can be for it to still exhibit the same kind of motion given in this problem. These limits, likely including the Froude number, will help us determine equations for strip motion.