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Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation . If a tuning fork for the note above middle on an even-tempered scale has a frequency of approximately hertz (cycles per second), find . If the maximum displacement of the end of the tuning fork is millimeter, determine the equation that describes the movement of the tuning fork.
Source: David Lapp. Physics of Music and Musical Instruments. Medford, MA: Tufts University, 2003
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and determine the equation that describes the movement of the tuning fork.
Answer to Problem 54AYU
Explanation of Solution
Given:
The end of a tuning fork moves in simple harmonic motion described by the equation . The tuning fork for the note above middle on an even–tempered scale (E ) has a frequency of approximately hertz(cycles per second). The maximum displacement of the end of the tuning fork is millimeter.
Formula used:
Calculation:
The maximum displacement is the amplitude. Therefore . The frequency is given by
Therefore and the movement of the tuning fork is described by the equation
Chapter 8 Solutions
Precalculus
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