1. Jonathan Knabe
CHLADNI’S LAW – FINAL PROJECT

2. • Ernst Friedrich Chladni von Sachsen
– *1756 - †1827
• German physicist & musician
• “Father of Acoustics”
• Vibration of plate  violin bow
– Robert Hooke 1680
• Chladni’s Law
– F = C(m+2n)^P
HISTORY AND BACKGROUND

3. Circular Plate
U(x,y,t) = X(x)Y(y)T(t)
Rectangular Plate
THEORY AND HISTORY

4. Circular PlateRectangular Plate
THEORY AND HISTORY
http://en.wikipedia.org/wiki/Normal_mode#/media/File:Drum_vibration_mode12.gif

5. SETUP AND EXPERIMENTAL METHOD
Function
Generator
Mechanical
Driver
Plates & Salt

6. N (Circular
Nodes)
Freq.
(Trial 1)
Freq.
(Trial 2)
Freq.
(Trial 3)
Average STDEVA
1 105 107 103 105 ± 2
2 350 356 353 353 ± 3
3 884 888 881 884.3 ± 3.5
4 1678 1681 1693 1684 ± 8
5 2770 2765 2752 2762.3 ± 9.3
6 4070 4080 4060 4070 ± 10
RESULTS
Trial P C
Trial 1 2.0692 95.355
Trial 2 2.0573 97.304
Trial 3 2.0762 94.412
Average 2.06757 95.690
STDEVA ± 0.0095 ± 1.475

7. RESULTS
y = 95.692x2.0675
R² = 0.9968
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 1 2 3 4 5 6 7
FrequencyinHz
N (Circular Modes)
Frequency vs. N (Circular Nodes)

8. • P = 2.06757 ± 0.0096
– about 7 STDEVA from P = 2
– P is “roughly” 2 (Fletcher 2004)
• what does that mean?
• Best P = 2.0573 only 2.87% off
• No linear modes M, only N
– Mainly after 5000 Hz
• Square plate was hard to
predict
– Mathematica demonstration
DISCUSSION

9. INTERESTING RESULTS

10. • B-B-D-B-A-G-Gb
7 NATION ARMY – THE WHITE STRIPES
G3A6B4 D8
497Hz–494Hz 4685Hz–4698Hz 1740Hz-1760Hz 195Hz-196Hz

11. THANK YOU

12. 1. Rossing, Thomas D.; Fletcher, Neville H. (2004), Principles of Vibration and Sound, Springer, pp. 73–74, ISBN
9780387405568.
2. Fletcher, Neville Horner; Rossing, Thomas D. (1998), The Physics of Musical Instruments, Springer, p. 680, ISBN
9780387983745.
3. Wolfram Mathematica Demonstrations -http://demonstrations.wolfram.com/ChladniFigures/
4. Curtis, Mark; Parry, Adam (2003), Chladni Plates,
http://www.nhn.ou.edu/~johnson/Education/Juniorlab/Chladni/2001-ChladniPlates-CurtisParry.pdf
5. Elmore, William C.; Heald, Mark A. New York: Dover Publications, Chladni Plate Theory,
http://www.phy.davidson.edu/StuHome/derekk/Chladni/pages/theory.htm#rectp
6. Xiao, Wence; Supervisor: Madsen, Anders (2010), Chladni Pattern,
http://rudar.ruc.dk/bitstream/1800/5190/1/Chladni%20Pattern.pdf
7. Stöckmann H. J., 2007. ”Chladni meets Napoleon”. Eur. Phys. J. Special Topics 145, 15–23 https://www.uni-
marburg.de/fb13/forschungsgruppen/quantenchaos/dateien/paper/EPJST_2007_145_15_Stoeckmann.pdf
WORKS CITED AND BIBLIOGRAPHY

13. • https://bkpmedia.s3.amazonaws.com/photos/4011A_fro
nt_lrg.jpg
• http://www.tecnoedu.com/Pasco/img/SF9324.jpg
• http://www.pasco.com/images/products/wa/WA9607_3
30_32689.jpg
• http://upload.wikimedia.org/wikipedia/commons/thumb
/d/d1/Echladni.jpg/150px-Echladni.jpg
• http://upload.wikimedia.org/wikipedia/commons/thumb
/0/03/Bowing_chladni_plate.png/220px-
Bowing_chladni_plate.png
IMAGE SOURCES