Problem 14: Ball on Membrane

“When dropping a metal ball on a rubber membrane stretched over a plastic cup, a sound can be heard. Explain the origin of this sound and explore how its characteristics
depend on relevant parameters.”

I. Phenomenon Demonstration

• BALL TRAMPOLINE – KANNADA – 13MB by Arvind Gupta https://youtu.be/NQJEt1VZK_E 
• The World’s Bounciest Surface. by The Action Lab https://youtu.be/mHumpKBD8qE
• The Bounciest Surface in the World! by The Gripsion https://www.youtube.com/watch?v=z0enFzMZi24

II. Books, Encyclopedia, Discussion and Forum Posts

• Wikipedia: Vibrations of a circular membrane https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane 
• Wikipedia: Hearing the shape of a drum https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum 
• Vibrations of Ideal Circular Membranes (e.g. Drums) and Circular Plates https://courses.physics.illinois.edu/phys406/sp2017/Lecture_Notes/P406POM_Lecture_Notes/P406POM_Lect4_Part2.pdf 
• Drum Head Modal Vibrations  https://courses.physics.illinois.edu/phys406/sp2017/Student_Projects/Spring09/Knud_Sorensen/K_Sorensen_Phys498POM_Spring09_Final_Report.pdf 
• Circular Drum Head Simulation https://www.compadre.org/osp/EJSS/4495/280.htm 
• Circular Membrane (drum head) Vibration by Dan Russell https://youtu.be/v4ELxKKT5Rw 
• Vibrations of a Soap Membrane. Bessel function example by LeoGalP https://youtu.be/fs56Ox86eZM 

III. Research Paper

• Russel, D. (2010). Basketballs as spherical acoustic cavities. American Journal of Physics 78, 549. https://doi.org/10.1119/1.3290176
• Eichwald, B., Argentina, M., Noblin, X., Celestini, F. (2010). Dynamics of a ball bouncing on a vibrated elastic membrane. Phys.Rev. E 82, 016203 https://doi.org/10.1103/PhysRevE.82.016203  
• Katz, J. (2008). Thump, ring: the sound of a bouncing ball. Eur. J. Phys. 31, 849. DOI:10.1088/0143-0807/31/4/014
• Gritter, L., Crompton, J., Yushanov, S. (2010). Analysis of Burning Candle. https://www.comsol.com/paper/download/62922/koppenhoefer2_paper.pdf