Team Number: Ch078
Team Number: Ch078
School Name: Santa Fe High School
Area of Science: Room Acustics
Project Title: A Computational To Sonar Point Determination
A Computational To Sonar Point Determination Team members: Alessandra Peluso Vanessa DiLoreto Matthew Smith Thuso Simon Date of submission: 4-03-02 Instructor: Anita Gerlach Project Statement Our project will calculate the foci of sound waves in a three-dimensional environment. This science is useful for planning for buildings, theaters, classrooms, and even satellites. Algebra and trigonometry will be used to determine the foci. The variables used will be the primary materials used to create the environment, their sound absorptive qualities, and the dimensions of the environment. Computers will be used to carry out the input of data and calculations. Computers may also be used for visualization. Background The subject of foci points comes up often when building a theater. The most expensive seats in a theater are where the highest quality of sound is heard, which is where the foci points of the theater are. Foci points are used in the construction of speakers, and in the placing of speakers, in such a way that the sound quality will be the highest, in places such as cars, and theaters. A focus point is where the sound waves meet when reflected, in a room. Math models help describe where these points will be in certain rooms. The size and shape of a certain room determines where these foci points will be. There are also several other factors that have an affect on the sound waves, and where and when they will travel. Sound waves will be partially absorbed into different materials, at different rates. While almost all of a sound wave reflected off of a concrete wall would be deflected, some would be refracted, which means it is absorbed, and can reflect in a different direction than the rest of the wave that was not absorbed. If however, a sound wave is directed at a thick carpet, or heavy upholstery, curtains, etc., the sound will be absorbed at a different rate. These different rates of absorption cause interesting effects on the sound wave. It can be reflected the same direction, only a short time later, causing reverberation. This means that the sound wave was absorbed in the material, and could not escape for a while. The slowed down sound wave creates an echo in the room, because the sound waves that were not absorbed have reached the focus point a short time earlier than the absorbed sound wave. This delay is not very noticeable, but the lower quality of sound is very noticeable. Other factors that cause reverberation time are objects that deflect the sound so that it has a longer distance to travel to the focus point. Thus, the sound wave will again arrive at a later time, creating a slight delay, taking away from the quality of the noise that is projected. Materials Programming -Computers -UNIX programming Presentation - Microsoft power point Background information - Internet -Books Method Our project did not require us to perform experiments in the field. Our form of acquiring information was to do extensive research in the field. A large portion of this project was the search for pertinent information to the subject of acoustics. We gained knowledge in the many areas of acoustics. We learned about sound waves and how they react to different substances. The research also covered how acoustics are used in the real world, the world we live in today. We then had to study parabolas, to get a basic understanding of how sound waves are deflected, and what foci points pertain to. We learned a lot through our physic's and algebra classes. For our project, we originally had several different math models. All of these models helped determine different aspects of acoustics in a certain room. Some equations assisted us in finding the reverberation time, while others defined the perfect shape of a room, to achieve maximum quality of sound over the most widespread area. Due to time restrictions, we had to limit the amount of detail we could put into studying acoustics. We chose a few math models to help us get a better understanding of acoustics. We first started with a very basic formula, 4RCC = U, to determine the focus point of a parabolic room, where R is the focus point. This equation is very basic, and it cannot be applied to the real world in any way, because to create a never-ending parabolic room is at this point in time, impossible. We next attempted to calculate the reverberation time of a room, using Sabine's equation for reverberation time: RT=. 161V/A. This equation was much more difficult for us to use, because it involved several separate variables. V stands for the volume of a room, and A stands for the absorption coefficient of the material of the room. We attempted to create two separate computer programs to assist us with our observations. The first computer program used our math model that figured out the focus point in a parabolic room. This program used the input of the height and size of the parabolic room, and could find the exact spot of the focus point in the room. This program was very simple, using our very basic equation. We obtained data from this, but as the equation and the program were very basic, the answer was also very basic. Next, we attempted to form a much more complicated computer program. We attempted to use our equation for reverberation time. This program was more difficult, because it used the input of several different factors. It required the height, and widths of the room. It also required the input of the absorption coefficients of whatever material the room was made of. This was very hard to do, because we had to create a menu for the user to choose which material to use. Then we had to make this choice represent the specific number value of whatever material was chosen. This number was then to be plugged back into the original equation. Though we attempted to complete this program several different ways, we were unsuccessful in creating a working program that could accurately find the reverberation time of a room. Observations Our limitations were as follows. All of the resources needed to perform experiments were unattainable due to lack of funds. We did not find any similar studies or experiments that pertained to our project at all. We had no way of testing the information and data we collected. We could not test the validity of our data, the answers we obtained with our program, although we do feel we have been honest to the equation and feel that our answers are correct. We were unable to find, or gain access to any similar studies with which to compare; however we do feel that we held up our original goals with what our program was to perform. Conclusion We feel our project partially does what we intended. It gives the foci points to a parabolic room. This however, is not very useful in real life, because a parabolic room is hard to come by. The data we received shows the accurate spot where the sound waves would hypothetically travel in this parabolic room. This also takes for granted the absorption of sound waves, meaning the walls were completely solid, which is also, not possible in real life. Our attempt at creating a program to determine the reverberation time of sound based on the materials that the room was composed of failed. If we had been successful in creating this program, the results could have been applied to real life. It would aid an architect in building an arena by giving an approximation of where the foci points are located, and where sound absorbing materials could be placed, to dampen echoes. Bibliography 1. "Acoustics Calculations" www.homepage.ihug.com.au.?audio?audio?gadgets.html November 9, 2001 2. "Room Acoustic" www.web.iol.lz/etos/irooms.htm November 9, 2001 3. "Noisenet Acoustics" www.noisenet.org/Noise_Room%20Acoustics_Reverb.htm November 9, 2001 4. "Wave Refraction" www.kttering.edu/drussel/Demons/refract/refract.html November 9, 2001 5. "Netroedge Room Simulation" www.netroedge.com/phil/RoomSim November 13, 2001 6. Faughn, Jerry and Serway, Raymond Physics
Team Members
Anita Gerlach
Makoena Simon