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
Want to see more full solutions like this?
Chapter 17 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- At t = 0, a transverse pulse in a wire is described by the function y=6.00x2+3.00 where xand y are in meters. If the pulse is traveling in the positive x direction with a speed of 4.50 m/s, write the function y(x, t) that describes this pulse.arrow_forwardA pipe is observed to have a fundamental frequency of 345 Hz. Assume the pipe is filled with air (v = 343 m/s). What is the length of the pipe if the pipe is a. closed at one end and b. open at both ends?arrow_forwardTwo sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [Hint: Use the trig identity sinu+sinv=2sin(u+v2)cos(uv2)arrow_forward
- a turning fork of frequency f=480 Hz has its first resonance when the water level is s distance 0.175 m below the open end of a tube, and its second resonance when the war level is 0.543 m below the open end, what is the speed of sound in this case? a. 360 m/s b. 340 m/s c. 345 m/s d. 353 m/sarrow_forwardA person is playing a small flute 10.75 cm long, open at one end and closed at the other, near a taut string having a fundamental frequency of 600.0 Hz. If the speed of sound is 344.0 m/s, for which harmonics of the flute will the string resonate? In each case, which harmonic of the string is in resonance?arrow_forwardA person wears a hearing aid that uniformly increases the sound intensity level to all audible frequencies by 35 dB. The hearing aid picks up the initial frequency of 4.5 kHz at an intensity of 4.55X10^-11 W/m^2. What is the intensity delivered to the ear drum?arrow_forward
- A 2.29-m long organ pipe acts as a closed-end resonator that produces several different harmonic frequencies in the audible range from 20 Hz to 20,000 Hz. Assuming a speed of sound of 343 m/s, determine the 5th highest frequency that the pipe can produce.arrow_forwardAlthough the vocal tract is quite complicated, we can make a simple model of it as an open-closed tube extending from the opening of the mouth to the diaphragm, the large muscle separating the abdomen and the chest cavity. What is the length of this tube if its fundamental frequency equals a typical speech frequency of 230 Hz? Assume a sound speed of 350 m/s.arrow_forwardThe fundamental frequency of an organ pipe, open at both ends, is 276.4 Hz. What should the length of this organ pipe be? Speed of sound in air at T = 20.0°C is 343 m/sarrow_forward
- What is the first overtone frequency for an organ pipe 2.00 m in length, closed at one end? The speed of sound in air is 344 m/s. 86 Hz 172 Hz 129 Hz 258 Hzarrow_forwardSuppose that the sound level of conservation is initially at an angry 70 dB and then drops to a soothing 52 dB. Assuming that the frequency of the sound is 510 Hz, determine the (a) initial and (b) final sound intensities and the (c) initial and (d) final sound wave amplitudes. Assume the speed of sound is 344 m/s and the air density is 1.21 kg/m3.arrow_forwardFor a 171Hz plane traveling wave in air with a sound pressure level of 40 dB re 20 pPa, find (a)the acoustic pressure amplitude, (b) the intensity, (c)the acoustic particle speed amplitude, (d) the acoustic density amplitude, (e) the particle displacement amplitudearrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University