In a Whispering Gallery, Any Sound at One Focus of an Ellipse

question 33

Short Answer

In a whispering gallery, any sound at one focus of an ellipse reflects off the ellipse directly to the other focus. The figure shows an elliptical whispering gallery, where x is the center of the ellipse. What is the distance that sound travels from focus $F_{1}$ to focus $F_{2} ?$

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Definitions:

Laissez Faire

An economic philosophy advocating minimal governmental intervention in the market and the private sector.

Capitalism

An economic system characterized by private or corporate ownership of goods and services, intended for profit.

Justice Theorist

An individual who studies or develops concepts related to justice, focusing on its application in society, law, or morality.

Society's Benefits

The advantages or positive outcomes that accrue to the general public or community from certain actions, policies, or programs.