The most soaring vocal melody is in Johann Sebastian Bach’s...

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 “resurrectionem mortuorum” (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?

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 “resurrectionem mortuorum” (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?

Key Concepts

Historical Tuning Variations

This concept addresses how frequency assignments in musical tuning have varied historically, affecting numerical values for frequencies of musical notes. Understanding historical tuning practices helps explain changes in computed wavelengths, pressure amplitudes, and displacement amplitudes when different reference frequencies are used.

Displacement Amplitude in Acoustic Waves

This concept details the relationship between the pressure amplitude and the displacement amplitude of particles in a medium due to sound waves. The displacement amplitude is calculated taking into account the density of the medium, the speed of sound, and the angular frequency, showing how particle motion amplitude relates to the pressure fluctuations of the wave.

Sound Pressure Level and Pressure Amplitude

This concept pertains to the measurement of sound, where the sound pressure level (often measured in decibels, dB) relates to the pressure amplitude of the sound wave. The decibel scale is logarithmic, and the pressure amplitude can be derived from the sound pressure level using reference values and the appropriate logarithmic conversion formulas.

Frequency and Wavelength Relationship

This concept involves the direct relationship between the speed of sound, frequency, and wavelength, generally expressed by the formula ? = v/f, where ? is the wavelength, v is the speed of sound, and f is the frequency of the note. It is fundamental to understanding how variations in frequency affect the length of a wave in a medium.

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