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Question

Difficulty: MediumExplicit Detail Retrieval

Passage:
In 1787, German physicist Ernst Chladni published Entdeckungen über die Theorie des Klanges ("Discoveries on the Theory of Sound"), detailing a methodology for visualizing acoustic vibrations. Chladni stroked the edge of glass or metal plates covered with fine sand using a violin bow. The resonant vibrations caused the sand to migrate away from regions of maximum displacement (antinodes) and accumulate along nodal lines, where the plate remained stationary. While earlier natural philosophers had observed standing waves in fluids, Chladni was the first to systematically map two-dimensional modal patterns across varied geometries, such as circular and square plates. Although his technique was initially dismissed as a mere parlor trick by contemporary Academicians, Napoleon Bonaparte later funded a prize competition in 1809 for a mathematical explanation of these patterns. This prize ultimately prompted mathematician Sophie Germain to formulate the first boundary-value differential equations describing thin-plate elasticity, laying the structural framework for modern acoustic engineering.

According to the passage, which of the following statements regarding Ernst Chladni's acoustic work is explicitly supported? Consider each of the three choices separately and select all that apply.

  1. Sand accumulated on regions of the vibrating plates where physical displacement was minimal or absent.Answer
  2. B
    Chladni was the first investigator to document standing wave phenomena in fluid environments.
  3. Napoleon Bonaparte sponsored a competition aimed at providing a mathematical explanation for Chladni's observed patterns.Answer

Answer

The statements confirming that sand accumulated on regions where displacement was minimal or absent and that Napoleon Bonaparte sponsored a competition for a mathematical explanation are both explicitly supported by the text.
The correct choices directly reflect explicit facts in the text: sand collected along nodal lines where the plate remained stationary (matching the statement that sand accumulated where displacement was minimal or absent), and Napoleon Bonaparte funded a 1809 prize competition seeking a mathematical explanation of the figures.

Step-by-Step Solution

1
Evaluate the choice regarding sand gathering on stationary portions of the plate.
The passage directly confirms that sand migrated away from antinodes to gather along nodal lines 'where the plate remained stationary.'
Direct textual retrieval verifies that sand accumulated in areas lacking physical movement.
2
Evaluate the choice regarding whether Chladni was the first to observe standing waves in fluids.
The passage notes that 'earlier natural philosophers had observed standing waves in fluids,' making Chladni's innovation the mapping of 2D patterns on plates rather than initial fluid observations.
Direct textual retrieval demonstrates that fluid standing waves were documented prior to Chladni.
3
Evaluate the choice regarding Napoleon Bonaparte's sponsorship of a math competition.
The text explicitly states that 'Napoleon Bonaparte later funded a prize competition in 1809 for a mathematical explanation of these patterns.'
Direct textual retrieval confirms Napoleon's sponsorship of the competition.

Key Concept

Explicit Detail Retrieval requires identifying statements directly stated in the text through accurate paraphrasing while avoiding misread modifiers, reversals, or false claims of historical priority.
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Explicit Detail Retrieval

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