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

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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 F1F_{1} to focus F2?F_{2} ?
 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} ?


Definitions:

Ebbinghaus

A psychologist known for his work on memory, specifically the discovery of the forgetting curve and the spacing effect.

Shereshevsky

Referring to Solomon Shereshevsky, a Russian journalist with a phenomenal memory, often studied in psychology for his extraordinary mnemonical capacities.

Ebbinghaus

Herman Ebbinghaus, a German psychologist known for his pioneering work on memory, especially the forgetting curve and the spacing effect.

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Data or knowledge that has been recently acquired or understood by an individual.

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