A ray model of sound focusing with a balloon lens: An experiment for high school students
An acoustical ray incident from a fluid medium with speed of sound c 1 is refracted at the interface with a second fluid medium with speed of sound c 2.
(Color online) To-scale experimental ray diagram where the radius of the balloon is taken to be 1 m. Note that focusing is very strong at about 2.4 times the radius on the acoustical axis.
Side view: reflection off the floor. The diagram is to scale. The position of the loudspeaker, balloon, and sound meter are denoted by L, B, and M, respectively. The center of the balloon is 4.00 m from the loudspeaker. The radius of the balloon is r = 23.5 cm, while the wavelength used is λ = 3.445 cm. Also see Fig. 5.
Top view: reflections off the walls. The diagram is to scale. The position of the loudspeaker, balloon, and the various meter positions are denoted by L, B, c, f, r, l, respectively, where c stands for close position, f stands for focal region, r stands for right, and l stands for left. The loudspeaker, balloon, close, and focal region positions are all centered between the walls. The balloon center is placed 4.00 m from the loudspeaker. The close position is placed 10 cm plus the radius of the balloon (r = 23.5 cm, also wavelength is λ = 3.445 cm) from the center of the balloon. The focal region is placed 2.4r from the center of the balloon where r is the radius of the balloon. The right and left positions are located 50 cm to the right and left perpendicular to the acoustical axis of the focal region position in the horizontal plane. Also see Fig. 5.
(Color online) Experimental setup showing Brüel & Kjær Type 2230 Precision Integrating Sound Level Meter in “close” position.
Sound pressure levels with and without the balloon: Close position is on the acoustical axis 10.0 cm from the balloon surface; focal region is on axis 2.4r from the balloon center (where r is the radius of the balloon [r = 23.5 cm], and the balloon center is 4.00 m from the loudspeaker); right and left are in the focal plane but displaced horizontally 50 cm to the right and left, respectively (see Fig. 4).
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