The most soaring vocal melody is in Johann Sebastian Bach’s Mass in B minor. A portion of the score for the Credo section, number 9, bars 25 to 33, appears in Figure P17.23. The repeating syllable O in the phrase “resurrection moratorium” (the resurrection of the dead) is seamlessly passed from basses to tenors to altos to first sopranos, like a baton in a relay. Each voice carries the melody up in a run of an octave or more. Together they carry it from D below middle C to A above a tenor’s high C. In concert pitch, these notes are now assigned frequencies of 146.8 Hz and 880.0 Hz.
(a) Find the wavelengths of the initial and final notes.
(b) Assume that the choir sings the melody with a uniform sound level of 75.0 dB. Find the pressure amplitudes of the initial and final notes.
(c) Find the displacement amplitudes of the initial and final notes.
(d) What If? In Bach’s time, before the invention of the tuning fork, frequencies were assigned to notes as a matter of immediate local convenience. Assume that the rising melody was sung starting from 134.3 Hz and ending at 804.9 Hz. How would the answers to parts (a) through (c) change?