Math Problem Statement

The frequencies for the seven “white key” notes produced on the tempered scale of a piano (starting with middle C) are shown in Table 1.4. A computer analyzes the pressure displacement versus time for the wave produced by a tuning fork and gives its equation as y = 1.23 sin (2073.55x - 0.49) + 0.44. (a) Estimate the frequency of the note produced by the tuning fork. (b) Identify the note produced by the tuning fork.

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Wave Analysis
Harmonic Motion
Frequency Calculation

Formulas

General wave equation: y = A sin(kx - ωt + ϕ) + C
Frequency formula: f = ω / (2π)

Theorems

Simple Harmonic Motion Principles

Suitable Grade Level

Grades 10-12