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Acoustics And Architecture by Paul. E Sabine

By Paul. E Sabine

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In Fig. maximum the displacement of the particles to the direction of propagation, is pictured at right angles of the the and excursions of the particles is envelope shown. Suppose now that the ideal perfectly reflecting barrier is replaced by one at which a part of the in11, cident energy is absorbed, so that the amplitude of the reflected wave is not A but kA, k being m Stationary wave absorbent ends. Fi<;. 12. than leSS a tube with unity. Referring to Eq. absorbent barrier ? (d+r) \(l - 18, = A[sin k) sin wt cos -2fc A cos At the write in the case of an - k sin art c sin intcrnodes, cos J 5) co(< L = we may ^ c (1 + co(* + -tA(l k) cos - is zero, *>* = c amplitude is A (1 k).

Accompanying these pressure changes are corresponding changes in the temperature. Viewing the progress of the plane wave through the air, we see all the foregoing changes advancing from particle to particle with a velocity equal to the square root of the In time, each set of ratio of the elasticity to the density. conditions is repeated at any point in the medium once in each cycle. In space, the conditions prevailing at any slight instant at a given point are duplicated at points distant from .

Represent the undisturbed condition of the air by 41 equally spaced particles. Let the distance from to 40 be the distance the disturbance travels during a complete vibration of a single particle. ; D h f R,o < 40 FIG. 6. Fia. 5a. Compreseional plane wave moving to the right. Fia. 56. Compressional plane wave reflected to the left. FIG. 6. Stationary wave resultant of Figs. 5a and 56. wave length of the wave motion and is denoted letter X. the Greek by The line A shows the positions of each of the particles the first particle, having made a at the instant that P called the > complete vibration, is in its equilibrium position and is According to the conception of the kinetic theory of gases, the molecules of a gas are in a state of thermal agitation, and the pressure which the gas Here for the purpose exerts is due to this random motion of its molecules.

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