Question about Musical Construction
Subject Arts
Arts
Source Originais Teachy
Originais Teachy
Topic Musical Construction
Musical Construction
Difficulty Hard
Hard
(Originais Teachy 2024) - Question Hard of Arts
While studying the interconnection between art and mathematics, a group of 8th-grade students decided to create a musical instrument that could illustrate geometry concepts and numerical sequences. Inspired by the sound generated by a string instrument, the students built a 'Geometric Monochord', a structure with a single string stretched by a system of pulleys and adjustable weights. By varying the tension and the mass of the weights placed on the string, they noticed sound variations that were linked to mathematical proportions. However, the group wants to deepen the experience and relate the frequencies produced by the lengths of the string to mathematical sequences and series concepts, specifically the Fibonacci Sequence. Considering a monochord with a length of 1 meter, whose fundamental frequency is 220Hz when the string is free of additional weights, and knowing that the vibration frequency is inversely proportional to the length of the vibrating part of the string, what would be the resulting frequency of the string when a weight of 50g is placed exactly 1/3 of the length of the string from one of the fixed ends?a.
330Hz
Answer sheet:
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