The most soaring vocal melody is in Johann Sebastian Bach\'s Mass in B minor. In

Question

The most soaring vocal melody is in Johann Sebastian Bach's Mass in B minor. In one section, the basses, tenors, altos, and sopranos carry the melody from a low D to a high A. In concert pitch, these notes are now assigned frequencies of 146.8 Hz and 880.0 Hz. (Use 343 m/s as the speed of sound, and 1.20 kg/m3 as the density of air.)

(a) Find the wavelength of the initial note.

(b) Find the wavelength of the final note.

(c) Assume the choir sings the melody with a uniform sound level of 74.0 dB. Find the pressure amplitude of the initial note.

(d) Find the pressure amplitude of the final note.

(e) Find the displacement amplitude of the initial note.

(f) Find the displacement amplitude of the final note.

Explanation / Answer

v=f * wavelength

1. ) wavelength = velocity/frequency = 343/146.8 = 2.33 m

2.) wavelength of the final note = 343/880 = 0.389 m

Intensity in dB = 10 log (I / I0) = 20 log ( P/P0 ) .

Pressure amplitude = P0 * 10 ^ (dB/20) = 5011.87 * P0

Also, dB = 10 log (I / I0) = 20 log ( S/S0 ), where S is the displacement amplitude. Using these two formula one can get the pressure and displacement amplitudes.

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