^{1,a)}and Kendez Parker

^{1}

### Abstract

A weather balloon filled with carbon dioxide gas is used as a positive spherical acoustic lens. High frequency but audible sound from a circular loudspeaker ensonifies the balloon and produces increased sound pressure levels in a region along the principal axis according to a ray acousticsmodel. This enhancement was measured experimentally and was found to agree with theory. The possibility that interference from reflected sound off walls or the floor could mask or mimic the expected focusing was countered by calculating and measuring within a “shadow zone” in which only direct rays or rays refracted by the balloon exist by the method of Fresnel volumes. The experiment described in this paper would be a suitable learning experience for junior high and high school students showing how rays and Snell’s law apply to sound as well as light and giving them a measurable predicted focal region for enhanced sound pressure levels.

Thanks are due to Georgia Southern University physics major Andy Bean for help in initial measurements undertaken prior to the beginning of this investigation. Also thanks are due to James P. Braselton of the Department of Mathematical Sciences at Georgia Southern University for help in the development of the mathematica program used to produce the ray diagram of Fig. 2. And finally special thanks are due to Jim LoBue of the Georgia Southern University Chemistry Department for filling the experimental weather balloons on multiple occasions with carbon dioxide gas.

I. INTRODUCTION

II. THEORY

III. EXPERIMENT

IV. CONCLUSIONS

### Key Topics

- Sound pressure
- 13.0
- Acoustical measurements
- 11.0
- Acoustics
- 11.0
- Loudspeakers
- 11.0
- Acoustic waves
- 10.0

##### G09B

## Figures

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}.

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.

(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.

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 2.4*r* 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.

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 2.4*r* 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.

(Color online) Experimental setup showing Brüel & Kjær Type 2230 Precision Integrating Sound Level Meter in “close” position.

## Tables

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 2.4*r* 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).

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 2.4*r* 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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