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

150 7. Pipes, Waveguides, and Resonators(c) What will be the amount of acoustic wattage that emanates out throughthe open end of the pipe?5. A 70 dB (re 20 μPa) 1 kHz signal is incident normally to a boundary betweenthe air and another medium having a characteristic impedance of 780 Pa s/m.(a) Determine the effective root-mean-square pressure amplitude of the reflectedwaves.(b) Determine the effective root-mean-square pressure of the transmittedwaves.(c) How far from the boundary is the location where pressure amplitude in thepattern of standing waves equals the pressure amplitude of the incidentwave?6. The speed of sound in water is 1480 m/s. Consider a series of 2960-Hz planewaves in water normally incident to a concrete wall. It can be assumed thatall of the sound energy is completely absorbed by the wall. The pattern ofstanding waves results in a peak pressure amplitude of 30 Pa at the wall and apressure amplitude of 10 Pa at the nearest pressure node at a distance of 50 cmfrom the wall.(a) What is the ratio of the intensity of the reflected wave to that of the incidentwave?(b) Find the specific acoustic impedance of the wall.7. An acoustic signal consisting of 400-Hz plane wave is normally incident to anacoustical tile surface having a complex impedance of 1500 – i3000.(a) Find the standing wave ratio in the resultant pattern of standing waves.(b) Determine the locations of the first four nodes.8. A loudspeaker is fitted to one end of an air-filled pipe of 12 cm radius togenerate plane waves inside the pipe. The far end of the pipe is closed off by arigid cap. A 5-kHz signal is fed into the loudspeaker. The measured standingwave ratio of pressure at one location in the pipe is 7. At another location insidethe pipe 50 cm downstream of the pipe, the measured standing wave ratio is9. Derive an equation that includes these ratios and the distance betweenthem which can be used to establish the absorption constant for the signalbeing propagated inside the pipe. To simplify matters, assume that absorptioncoefficient α ≪ 1.9. Prove analytically (assuming ka ≪ 1) that the frequencies of the resonance andthose near antiresonance of the forced-open tube with damping correspond tothe frequencies of maximum and minimum power dissipation, respectively.10. Determine the lowest normal mode frequency of a fluid-filled cubic cavity (oflength L to a side) that consists of five rigid walls and one pressure releaseside. Plot the pressure distribution associated with that node.11. Given a rigid-walled rectangular room with dimensions 6.50 m × 5.65 m ×3 m, calculate the first 10 eigenfunctions. Assume the sound propagation speedc = 344 m/s.12. A concrete water sluice measures measure 25 m wide and 8 m deep. It iscompletely filled with water. Find the cutoff frequency of the lower mode ofpropagation, assuming the concrete to be totally rigid.