String Bean Physics

This is actually the Physics of string beans, onions, chicken, and their specific sauce from Panda Express. As I let the feeling of freedom from the arrival of Christmas Break, I got dinner with my mom at Panda Express on Saturday night. As I held my three item plate in its bag, I discovered that I couldn't keep the little container holding the string bean chicken from falling over and spilling sauce all over the bag, so I decided to hold it. After a few minutes of holding the rather warm container of food, I thought to myself, "Hey! Physics! Heat!" The small container of food, which was kept hot in its tray was transfering some of this heat to my hand. To start at the beginning of the process: something, probably electricity, heated water in large metal trays, providing the water with heat. This heat is then easily transfered to the metal trays above it, raising its temperature rapidly to a high temperature because metal has a low specific heat, requiring relatively little energy to raise its temperature. This heat is then flows to the food in the metal trays, which was put into a small paper container and given to me. The heat from this food then flowed to my hand, making my hand feel hot. After a while, the food didn't feel so hot anymore. This meant that the system consisting of my hand and the food container was reaching equilibrium, where both the food temperature and my hand's temperature would be the same. However, I'm pretty sure that it didn't, which is a good thing because the food was very hot to begin with, so it probably would have burned my hand, plus the food wouldn't have been very hot anymore :-( . I'm not sure whether this was an isobaric or isochoric process, or neither. I don't think my fingers expanded, but perhaps they did, and I don't think that the pressure inside by fingers increased either, but I don't know. Maybe it did. Scary.....

Physics in Low Brass!

Now, while you might possibly be thinking that low brass instruments usually only serve as metronomes for the rest of the band with very few chances at the melody, that's not entirely true. Although we do find ourselves playing only eighth-notes on down beats more often than the flutes, clarinets, and trumpets do, we often have glory parts of our own (for a good example, listen to "Overture to Colas Breugnon." Go sixteenth-notes!). Or if you want to hear something really different, come to "Merry TubaChristmas," featuring euphoniums(/baritones/me!) and tubas only! I went to a rehearsal for this on Saturday, so along with our awesome lab on Friday, I feel like analyzing the Physics involved in this glorious section of the band.

Now among the various low brass intruments, there are pleny of examples of physics in closed tubes, as our intruments are made of metal tubes and our lips close one end as well as provide sound vibrations. All of these instruments work using the same physics concepts as well. Although the trombone uses a slide instead of valves, as the tuba and baritone do, all three of these instruments legnthen their curly "tube" to create different pitches(however, tuning them to the correct pitches is another story :-) ). Since these instruments are "closed tubes," the harmonics can be calculated using the equation Fn=(2n-1)F1, or (2n-1)(v/2L). For my particular instrument playing the f below middle c, first harmonic present is about 190 Hz, with the other harmonics being twice and three times that. As the valves are pressed, or the slide is lowered, the tube gets longer, increasing L and therefore decreasing the fundamental frequency and all subsequent frequencies, lowering the pitch. But, as we learned in class, these instruments will only let one's lips vibrate at a certain frequency (which explains a lot, especially why I have lots of difficulty "lipping up" my rather flat e flat). When the lip position is tightened to vibrate at the next "open" frequency, the lips vibrate faster, thus resulting in a faster frequency of sound waves and a higher pitch. And over the weekend at TubaChristmas rehersal (an hour and a half of glorious baritone and tuba sound!), I discovered once again that having my lips constantly vibrate at a high frequency is not only difficult to maintain, it hurts! I'm not sure how much it had to do with the frequency and how much had to do with muscle fatigue, but about an hour in I didn't want to play the first part anymore. :-)

Although I'm a devoted baritone player, I have tried trombone as well. Yet in both my attempts to find the correct pitches and listening to our outstanding Band 4 trombonists, I've found that even though the tube of a trombone seems much shorter than the winding ones of a baritone, they have relatively the same sound, as does the small-tubed "valve trombone" I play during Marching Band (except baritones sound prettier. Sorry trombonists, I love my instrument). I wonder if the diameter of the tubes has anything to do with it, because we use the same mouthpieces and our music is interchangable, except for the sound. An interesting question to look into. :-)

By the way, that's me with my baritone in its case and my uncle's trombone, plus the mouthpiece I use for both in my right hand. Isn't my shirt cool? :-)

More Musical Physics!

Talk about a busy musical weekend! Although I know that those in Youth Symphony had it even worse, I had Select Band tryouts early Sunday morning which took at least two and a half hours, and then a Christmas Concert in the evening, plus the Football game on Friday evening (Go Raiders!) and lots of practicing for my tryout. And I didn't realize until a few hours before the concert that I was using Physics with every note I played! Almost every note I play involves at least one of the four valves on my instrument, which consist of a metal rod with holes in it, a metal tube, oil to allow the valve to move, and a spring to return the valve to its unpressed position. When I press the valve, the spring force (-Kx, where x is the distance compressed from the spring's equilibrium point) is equal to the force my finger applies on the top of the valve. Thus the valve has a net force of zero, an acceleration of zero, and in this case a velocity of zero as well since it has reached the bottom of the tube. But when I am not using that valve, the spring force (for I seriously doubt that the spring is ever allowed to reach equilibrium while the valve is in its tube, otherwise the valve may not stay up and play correctly) is equal to the normal force of the valve on the cap keeping it in its tube. This senario is pictured above, with a very bad attempt to draw a spring, even though it was at least my fourth attempt. Since the oil attempts to keep the kinetic friction to a minimum, I wonder what the velocity of the valve is. However, I would need to take a few measurements, such as the greatest and least compression from equilibrium, and experiment to find the force constant of the spring. Perhaps I should do that. It could help answer some questions about why I have difficulty playing fast pieces. But I bet it won't; the instrument is not to blame for my slow fingers. :-)

Happy Halloween, Charlie Brown!

I know it's supposed to be something about "The Great Pumpkin," but I'm officially in Christmas mode now that Thanksgiving has past. I've taken out my Hallmark Christmas singing snowman/dog and snowman at piano people, and marched in the Waikiki Christmas Parade (which was pretty fun, although it started raining and got pretty cold afterward). But this weekend, I noticed a lot of Physics. First of all, the explaination of the title of my entry. For my birthday (which was only a few days before Halloween), my aunt and uncle gave me a bobble-head figure of Charlie Brown trick-or-treating as part of my present (sorry he's sideways, I forgot that I took the picture longways). As I was pondering harmonic motion, I realized, "Hey! Charlie Brown!" Being the type of bobble-head that he is, Charlie Brown's head bounces on a spring. I thought, "If I were to push down on his head, the spring force should accelerate his head back up past the equilibrium point, until it comes to a stop, then accelerates back down in harmonic motion." However, when I actually tried it, the spring was too rigid to allow any noticable displacement along the y axis once it returned to equilibrium. However, if it had been less rigid, the spring should have forced Charlie Brown's head up and past the equilibrium point, then once it reached its amplitude height, it should have accelerated down at the same acceleration as it went up until it passed the equilibrium point and gradually stopped, repeating this process indefinetely (of course, assuming that there is no air resistance or gravity).

However, this wasn't the only Physics I noticed this weekend, and I'm so excited that I must tell everything!!! :-) While I was at the Varsity football game this Saturday, I got myself a shave ice at half-time. As I got to the very bottom where all that was left was melted ice and strawberry syrup, I tried to get my straw (with the spoon side down) all the way to the bottom to get all the liquid, I thought to myself, "Oh no, because I crushed the straw and now there's only a small triangular shaped opening on the bottom, I'm not going to be able to suck out the liquid as fast or as easily." But I was! I suddenly remembered my fluid dynamics Physics chapter, where we learned that V1A1=V2A2, and that pressure decreases as v increases. So the liquid in my straw must be moving much faster at the bottom entering the straw since the area was less, and the pressure must be less as well! Yeah! Physics epiphany! However, this also meant that I was able to drink my remaining shave ice faster, so I soon found myself with none left. Oh well. It was good.

The Physics of Music

Does that sound wierd? Normally you hear about the Mathematics of music, but not Physics. Well, this weekend, I discovered how Physics is truly involved in music, or more specifically, in taking care of and playing my instrument.

I play the baritone (pictured above). If you don't know what that is, it's basically a small tuba (another name for it is "tenor tuba") with a beautiful, mellow sound. I love it :-). However, my valves have been sticking recently, so my dad and I tried to figure out why. This involved taking out the valve, examining the wear patterns, cleaning the tube as well as the valve, and finding out that the bottom of the valve was probably sticking to the spring. After discovering this and cleaning the sticking valves, we put them back in, a simple process which involves valve oil (also pictured above. My valve oil container has a very small opening for the drops of oil to come out of, even smaller than what the top lookes like in the picture. But this bottle alone demonstrates a very important fluid principle. As I squeeze the bottle, the pressure my fingers applied is transfered to the walls is transfered throughouth the fluid. The pressure then pushed the fluid out of the bottle in accordance with the fluid equation of continuity.

However, my valve oil bottle is not the only part of my playing that displays the fluid equation of continuity. My instrument does as well. As I blow into my instrument via the small tube coming off the large bell, the air moves through the different tubes of my instrument, all of which are different sizes. I blow air into the small area tube at a fast rate, and as it travels through the instrument, the diameter of the tube gets larger, until the air comes out of the very large bell at the top. The diameter of the mouthpiece tube is 0.016m, and the diameter of the largest part of the tube that the air probably still completely occupies is about .12m. Thus, by the fluid equation of continuity, which states that V1A1=V2A2, the equation would state that 0.01149(Vbell)=2.01e-4(Vmouthpiece), or that the velocity of the air coming out of the bell is only 1.75% that of the velocity at which it goes in. That sure explains why the air coming out of the bell is barely noticable. Well, now that I know what the increasing diameter of the tube does to the air, I wonder what it does for the sound? Oh well, got to wait a little longer to find that out.

Waiting for Manapua

Have you ever been to Island Manapua around lunchtime? It's packed! Their manapua are the best, and everyone knows it. Good for business, but bad for me because it results in my having to wait a long time in line before getting my lunch/snack, depending how early it is. Well, on Saturday, I found myself in this position, waiting in a long line to get my steamed pork manapua and rice cake. I was just inside the store and right up against the closed door. As I stood there, I began to get tired, so I decided to lean on the door. As I slowly leaned against the door and wondered whether it would swing open and send me falling backwards out the door, I realized "Hey! Static Friction! Torque! Physics!" It was an enlightening moment. There were forces al around me: my weight (mg down!), the friction of the floor on my shoes as well as the friction of the handle of the door (where I was leaning) on my back, keeping me from falling straight down. There were also the normal forces of the floor and handle on me. I have included an approximate Free Body Diagram above. But not only do these forces act on me, I am also applying a torque onto the handle bar, and thus to the door. The torque I applied would be equal to the normal force times the distance I was from the line of hinges on the edge of the door. There was even static friction between the hinges inside themselves, as well as static friction at the other sides of the door with the door posts. It was static friction and torque that allowed me to take a break by leaning on that door. The friction caused the door to stay in place, and my small distance from the hinges kept me from attaining so much torque that I would fall backwards out of the store. That would not have been fun. :-)

Moving Benches

Unfortunately, this week was not quite as Physics filled as last week was, without The Lion King and all. However, I did go to the Homecoming Game with the Marching Band where we were melting in the hot sun along with the rest of the fans, and I took the SAT where one of my extra pencils kept kept getting pushed off the side of my desk as my left elbow (I'm a leftie) brushed over it (Projectile Motion! Vyo=0, Vx, H=height of desk, X=distance from edge of desk/original position: -H=-4.9T^2, X=VxT). But that's not the example I'm about to discuss.

The moment of rotational Physics that I experienced this week (or the first good one that I thought of) was moving benches out on the soccer field during Marching Band on Wednesday. On Tuesday, Mr. Hotoke had thought of the idea that I could stand on a bench to conduct so that everyone could see me better, and so for that day and Wednesday, we had to move the benches about four feet from their original positions. As I started to move the bench on my own on Wednesday, I could only do it one end at a time because dragging didn't work, so I picked up one end and rotated it. Lifting the bench created an axis of rotation at the middle of the leg of the bench farthest from me. As I walked with the bench, my hands were applying a force perpendicular to the bench, as my body stayed in the same orientation (perpendicular) to the bench and I was moving parallel to my body. Therefore, since the force was perpendicular to r, the distance from the axis of rotation to my hands, the equation for the torque as a result of my hands is (tau)=rF. (Sorry, no values again. I was concentrating to hard on Band :-) ) This torque caused the bench's very quick angular acceleration from rest, later keeping it moving at near constant speed, then its deceleration as I set it back down. I then applied the same principles to the opposite side of the bench to place it parallel to its original position. Moving the bench back took the same motions, except in the opposite direction. Four examples of torque! Wow, and they only took about three seconds each. And the benches worked well; I could see everyone, probably everyone could see me as well as ever, and I didn't fall off, despite the fact that a light, movable bench on grass is not the most stable thing to stand on. A pretty good day. :-)