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INSTRUCTIONAL OBJECTIVES Students will • Understand the relationship between sound intensity and distance • Investigate factors which cause noise in turbine engines NATIONAL MATHEMATICS STANDARDS Algebra • Understand patterns, relations, and functions – Understand and perform transformations such as arithmetically combining, composing, and inverting com- monly used functions, using technology to perform such operations on more-complicated symbolic expressions – Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions • Represent and analyze mathematical situations and structures using algebraic symbols – Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations – Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases – Use symbolic algebra to represent and explain mathematical relationships Problem Solving • Solve problems that arise in mathematics and in other contexts • Apply and adapt a variety of appropriate strategies to solve problems INTRODUCTION One of the major concerns with aircraft noise is the level of sound experienced in relationship to distance from the airport. As sound moves out from a source, the compression waves are transferred from air molecule to air molecule. One way to quantify this is to look at a measure called “sound intensity.” The intensity is the rate of the energy transfer through a unit area of the plane wave. The rate of energy transfer is power, so it follows that intensity I is a measure of the power of the sound P per unit area, A: I = DE Dt A = PA Since the SI unit for power is the watt, then the units of intensity I are watts/area, or W/m2. If it is assumed that the sound wave propagates evenly over a spherical area, then the surface area of a sphere is used to write: I=P 4πr2 This shows that as the distance r increases, the intensity of the sound decreases. Sound intensity level (SIL) is a related measure with the units decibels. It is the logarithmic measure of the sound intensity as compared to the intensity of the softest sound a person can hear, designated Iref (the reference intensity). The value of Iref is 1.00310–12 W, or 0 dB. SIL=10.0log I 10I ref Pushing the Envelope: A NASA Guide to Engines Noise 67 PHYSICS AND MATHPDF Image | NASA Guide to Engines
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