Concept explainers
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 l 46.8 Hz and 880.0 Hz. Find the wave lengths of (a) the initial note and (b) the final note. Assume the chorus sings the melody with a uniform sound level of 75.0 dB. Find the pressure amplitudes of (c) the initial note and (d) the final note. Find the displacement amplitudes of (e) the initial note and (f) the final note.
(a)
The wavelength of the initial note
Answer to Problem 17.29P
The wavelength of the initial note is
Explanation of Solution
Given info: The initial assigned frequency is
The velocity of air in sound is
Write the expression for the wavelength of the initial note.
Here,
Substitute
Conclusion:
Therefore the wavelength of the initial note is
(b)
The wavelength of the final note.
Answer to Problem 17.29P
The wavelength of the final note is
Explanation of Solution
Given info: The final assigned frequency is
The velocity of air in sound is
Write the expression for the wavelength of the final note.
Here,
Substitute
Conclusion:
Therefore, the wavelength of the final note is
(c)
The pressure amplitude of the initial note.
Answer to Problem 17.29P
The pressure amplitude of the initial note is
Explanation of Solution
Given info: The final assigned frequency is
The sound level of the melody is
Write the expression for the intensity level of the sound.
Here,
Substitute
Thus the intensity of the sound is
Write the expression for the maximum change in pressure.
Here,
Substitute
Conclusion:
Therefore, the pressure amplitude of the initial note is
(d)
The pressure amplitude of the final note.
Answer to Problem 17.29P
The pressure amplitude of the final note is
Explanation of Solution
Since the level of the sound from melody is same for both the initial and final note so the intensity of the sound for final note also remains same due to which the pressure amplitude for the final note is same as the pressure amplitude for the initial note.
From Part (c) of the question, the speed of the final note is,
Conclusion:
Therefore, the pressure amplitude of the final note is
(e)
The displacement amplitude of the initial note.
Answer to Problem 17.29P
The displacement amplitude of the initial note is
Explanation of Solution
Given info: The final assigned frequency is
The sound level of the melody is
Write the expression for the displacement amplitude of the of the initial note.
Substitute
Conclusion:
Therefore, the displacement amplitude of the initial note is
(f)
The displacement amplitude of the final note.
Answer to Problem 17.29P
The displacement amplitude of the final note is
Explanation of Solution
Given info: The final assigned frequency is
The sound level of the melody is
The expression for the displacement amplitude of the of the final note is,
Substitute
Conclusion:
Therefore, the displacement amplitude of the final note is
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Chapter 17 Solutions
Physics for Scientists and Engineers (AP Edition)
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