Serway & Jewett — Superposition and Standing Waves: Problem 33

Suppose a flutist plays a 523-Hz C note with first harmonic displacement amplitude \(A_1 = 100 \text{ nm}\). From Figure 17.21b read, by proportion, the displacement amplitudes of harmonics 2 through 7. Take these as the values \(A_2\) through \(A_7\) in the Fourier analysis of the sound and assume \(B_1 = B_2 = \dots = B_7 = 0\). Construct a graph of the waveform of the sound. Your waveform will not look exactly like the flute waveform in Figure 17.20b because you simplify by ignoring cosine terms; nevertheless, it produces the same sensation to human hearing.