# AiS Challenge Team Interim

Team Number: 078

School Name: Santa Fe High School

Area of Science: Acoustics

Project Title: A Computational Approach to Sonar Focal Point Determinations

Problem Definition:
Creating a math Model for the behavior of acoustic sound waves with various materials, such as wooden chairs, drywall, curtains, carpets, etc. is very important in today's theaters. To achieve the highest quality sound possible, a math model needs to be created to find where and when different sound waves will go, and how much they will be absorbed. Very high quality sound was achieved in the theaters of ancient Rome, but we have yet to find out how they could have calculated enough to have such wonderful acoustics. Modern theaters spend millions of dollars to achieve good sound, and they don't always succeed.

Problem Solution:
We will create a computer program using our math model. This program will take into account the several variables, such as the shape of the room, size of the room, and objects in the room, as well as the composition of everything in the room, including seats, and walls that affect the acoustics of a room. This program will be used to find where the sound goes to when it is projected from one spot in the room.

Progress to Date:
We have started on constructing a computer program that will calculate all that we need to find out. We have found several equations that will be factored into this program. We also have information on the many variables that come into play when speaking of acoustics. We have found the absorption qualities of several different substances that will also play a role in developing this program. We have found a lot of information on the subject. Some of the information we have found that will help us to succeed with this project will now be discussed. If a sound Wave collides with a wall in a perfectly elastic collision, then the wave will reflect with the same power it had before the collision. This will cause echoes, which take the overall quality of the sound down. This is due to the same sound traveling in different waves in different directions and some colliding with objects and some going directly to the listener. The sound waves will eventually reach the listener at different times, and the listener will not receive a high quality sound. If a sound wave collides with an object and has a perfectly inelastic collision, the sound wave will be absorbed, and there will be no reflection. This is not good also, because if all of the sound waves projected are absorbed, the listener will receive very little sound. Different materials have different absorption rates. We will attempt to achieve the perfect balance between the two opposite types of collisions.

Expected Results:
We expect, once completed, to be able to calculate where the sound waves will travel to, and how long it will take them to get there with our computer program. It will need the input of several factors such as the size of the room, and the composition of it, meaning what materials everything in it is made of. Once completed with calculating this for an empty room, we will attempt to enter new variables into the equations, such as furniture, that will change how sound travels from a room. This program will hopefully also be able to calculate where in the room the highest quality of sound can be heard, when the sound is projected from various places around this room.

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