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7.43.) Suppose that two parabolic reflecting surfaces face one another (with foci on a common axis). Any sound emitted at one focus will be reflected off the parabolas and concentrated at the other focus. The figure shows that paths of two typical sound waves. Using the definition of a parabola, "A parabola is the set of points P(x, y) in the plane that are equidistant from a fixed line L, called the directrix, and affixed point F, called the focus." show that all waves will travel the same distance. [Note: This result is important for the following reason: If the sound waves traveled paths of different lengths, then the waves would arrive at the second focus at different times. The result would be interference rather than clear sound.] Directrix Directrix Path of sound wave Focus Focus Common axis FIGURE 7.1.19 Parabolic reflecting surfaces in Problem 63

7.43.) Suppose that two parabolic reflecting surfaces face one another (with foci on a common axis). Any sound emitted at one focus will be reflected off the parabolas and concentrated at the other focus. The figure shows that paths of two typical sound waves. Using the definition of a parabola, "A parabola is the set of points P(x, y) in the plane that are equidistant from a fixed line L, called the directrix, and affixed point F, called the focus." show that all waves will travel the same distance. [Note: This result is important for the following reason: If the sound waves traveled paths of different lengths, then the waves would arrive at the second focus at different times. The result would be interference rather than clear sound.] Directrix Directrix Path of sound wave Focus Focus Common axis FIGURE 7.1.19 Parabolic reflecting surfaces in Problem 63

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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7.43.) Suppose that two parabolic reflecting surfaces face one another (with foci on a common axis). Any sound emitted at one focus will be reflected off the parabolas and concentrated at the other focus. The figure shows that paths of two typical sound waves. Using the definition of a parabola, "A parabola is the set of points P(x, y) in the plane that are equidistant from a fixed line L, called the directrix, and affixed point F, called the focus." show that all waves will travel the same distance. [Note: This result is important for the following reason: If the sound waves traveled paths of different lengths, then the waves would arrive at the second focus at different times. The result would be interference rather than clear sound.] Directrix Directrix Path of sound wave Focus Focus Common axis FIGURE 7.1.19 Parabolic reflecting surfaces in Problem 63
Transcribed Image Text:7.43.) Suppose that two parabolic reflecting surfaces face one another (with foci on a common axis). Any sound emitted at one focus will be reflected off the parabolas and concentrated at the other focus. The figure shows that paths of two typical sound waves. Using the definition of a parabola, "A parabola is the set of points P(x, y) in the plane that are equidistant from a fixed line L, called the directrix, and affixed point F, called the focus." show that all waves will travel the same distance. [Note: This result is important for the following reason: If the sound waves traveled paths of different lengths, then the waves would arrive at the second focus at different times. The result would be interference rather than clear sound.] Directrix Directrix Path of sound wave Focus Focus Common axis FIGURE 7.1.19 Parabolic reflecting surfaces in Problem 63
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