# AiS Challenge Team Interim Report

Team Number: 073

School Name: Santa Fe High School

Area of Science: Physics

Project Title:
Acoustical Analysis of Longitudinal Waveforms in Relation to Suitability of Non-Designated Areas for Musical Quality Sound Containment

Problem Definition

The students at Santa Fe High have great pride in their school, and this year especially have joined together to support their many sports teams. Many students have chosen to show their support by joining the marching band, which this year improved significantly and was invited to play at both the pre-game ceremony and halftime at the Cotton Bowl in Dallas, Texas. Unfortunately, with so much new interest in the band program, the current band room is not large enough for the demand put upon it. The school, therefore, needs to find another room to use for band practice.

Our team has undertaken the task of acoustically modeling one of the large arts rooms above the band room to determine if it would be suitable for use as such a musical environment.

Problem Solution

There are two main properties of sound we will be addressing in this project: 1) The reflection of sound waves off of surfaces in the room; and 2) Their interference, either constructive or destructive, when they come into contact with each other. Initially, we will use a simple square room without any obstructions inside as our modeling environment. From there, we will have three clear progressions in the development of our project:

• 1. Model the movement of one wave front as it reflects off of the walls of the modeling environment.
• 2. Add one or two more wave fronts to the simulation and determine to what degree they will come into contact with each other.
• 3. Add to all the waves the normal properties associated with sound (frequency, amplitude, and wavelength), thus determining to what extent there will occur constructive and destructive wave interaction in the modeling environment.

In order to solve this problem, we will use the mathematical formulas used to calculate the three main properties of sound (listed above), as well as the formulas used to determine the paths of reflection the sound waves will take when they hit the walls, floor, and ceiling of the room.

Progress Thus Far

When first defining our project, we thought to concentrate solely on the phenomenon of destructive wave interference of sound waves, completely disregarding the other aspects of acoustics (like wave reflection). However, as we progressed in defining the problem, we realized that trying to confine it to such a limited sphere would not only create an extremely unrealistic situation, but would also be difficult to model. Accordingly, we revised our direction slightly, as outlined above.

After meeting together and discussing the realities of the project, we now have a specific situation to model on computer, and have researched the mechanics of how to do it. We have recruited two mentors, one a mathematician and programmer, and the other a physicist who specializes in complexity science. Our meetings with provided valuable insight and is one of the main reasons we decided to change the focus of our project.

We have completed the majority of our background research, assisted greatly by Charles Schmid, Executive Director of the Acoustical Society of America, who kindly sent us a vast amount of information published by his organization. We have yet to go through everything he sent us, but it looks as if it is going to be extremely helpful.

Our next step will be to connect with our programming mentor, Roger Frye, to begin the actual programming of our computer model. Once this is completed we will begin to gather data and fill in the blanks in our puzzle.

Expected Results

Upon the completion of our project, we plan to have a working computer model of the way sound travels around a typical room. We will produce visual representations of this movement, and will also determine where the sound interferes constructively and destructively. All this will allow us to determine what modifications to the room might be needed to make it suitable for use as a band room.

Team Members

Team Mail