THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

Problems for Chapter 8 169Kinsler, Lawrence E. Frey, Austin R., Coppens, Alan B., and Saunders, James V. 1982.Fundamentals of Acoustics, 3rd ed. New York: John Wiley & Sons, Chapters 9and 10.Munjai, M. L. 1987. Acoustics of Ducts and Mufflers. New York: John Wiley & Sons.Prasad, M. G. 1991. Characterization of acoustical sources in duct systems—progress andfuture trends. Proceedings of Noise-Con, Tarrytown, New York. Ames, Iowa: Instituteof Noise Control Engineering.Prasad, M. G. and Crocker, M. J. 1998. Acoustic modeling (ducted source systems).In: Crocker, Malcolm J., ed. Handbook of Acoustics. New York: John Wiley & Sons,Chapter 14.Problems for Chapter 8In the following problems, consider the fluid medium to be air at the standardconditions of 1 atmosphere and 20 ◦ C, unless otherwise stated.1. It is desired to make a Helmholtz resonator out of a sphere with a diameter 12cm for 350 Hz.(a) What should be the diameter of the hole in the sphere?(b) What should be the pressure amplitude of the incident acoustic plane waveat 350 Hz if it is to produce an excess internal pressure of 25 μbar?(c) If the hole is doubled in area, what will be the resonant frequency?(d) What will be the resonance frequency if two independent separate holes,each of the diameter found in part (a) are drilled in the sphere?2. Consider a loudspeaker system that is rigid-walled and back enclosed. Itsinside dimensions are 40 cm × 55 cm × 44 cm. The front panel of cabinetis 4 cm thick and it has a 22-cm diameter hole cut out to accommodate aloudspeaker.(a) What is the fundamental frequency of this cabinet considered as aHelmholtz resonator?(b) A direct-radiating loudspeaker having a cone of 22 cm diameter and 0.008kg mass and a suspension system of 1100 N/m stiffness is mounted inthe cabinet. Find the resonance frequency of the cone. It may be assumedthat the effective mass of the system is that of the cone and that of the airmoving in the opening of the cabinet. The effective stiffness is the sum ofthe stiffness of the cone and that of the cabinet.(c) What would be the resonant frequency of the loudspeaker if it were notmounted in the cabinet and it has no air loading?(d) Find the acoustic power emitted if the cone is driven with an amplitude of2.5 mm at the frequency established in part (b).(e) Under the conditions same as that of (d) what is the amplitude of the forceacting on one of the 55 cm × 44 cm panels?3. A rectangular room has internal dimensions of 3.0 m × 5.0 m × 2.6 m andwalls of 12 cm thickness. A door that opens into the room has dimensions of2.2 m × 0.8 m. Assume that the inertance of the door opening is equivalent ofa circular opening of equal area.