1. BANJOS MUSIC 318 MINICOURSE ON PLUCKED STRING INSTRUMENTS How a Banjo Works J. Rae and T. Rossing, Proc. ISMA 2004. Banjos J. Rae (in Science of String Instruments ed. T. Rossing, Springer 2010) The structural dynamics of the American five-string banjo J. Dickey, JASA 114, 2958 (2003) Experimental investigation of an American five-string banjo L.Stephey and T. Moore, American Journal of Physics 124, 3276 (2008)

2. BANJOS BANJOS ARE MAINLY OF THREE TYPES: 4-STRING BANJO WITH RESONATOR: POPULAR IN RAGTIME AND DIXIELAND JAZZ; USUALLY PLAYED IN STRUMMING OR FLAT PICKING STYLE 5-STRING BANJO WITH RESONATOR: POPULAR IN BLUEGRASS MUSIC; USUALLY PLAYED WITH PICKS 5-STRING BANJO WITHOUT RESONATOR: USED IN OLD-TIME MUSIC; OFTEN PLAYED IN CLAW HAMMER STYLE (STRINGS ARE PICKED AND BRUSHED WITH THE FINGERS) THE BRIDGE RESTS ON A MYLAR MEMBRANE WHOSE TENSION CAN BE ADJUSTED WITH A HOOP AND BOLTS WITH THE RESONATOR IN PLACE, THE INSTRUMENT HAS AN ENCLOSED AIR CAVITY, AS FOUND IN GUITARS, VIOLINS, MANDOLINS, AND OTHER INSTRUMENTS. TUNING OF THE CAVITY IS POSSIBLE BY USE OF ADJUSTABLE SPACERS CALLED RAEJUSTERS WHICH CHANGE THE SPACING BETWEEN THE RESONATOR AND THE REST OF THE BANJO POT

3. BANJO BANJO WITH RESONATOR OFF AND ATTACHED

4. BANJO SOUND A 5-STRING BANJO IS USUALLY TUNED TO D,B,G,D,G (294, 248, 196, 147, AND 393 Hz, RESPECTIVELY). THE BRIGHT SOUND HAS MANY HARMONICS. SPECTRUM OF BANJO SOUND FOLLOWING A PLUCK OF THE OPEN 1 ST STRING

5. BANJO SOUND FRACTION OF TOTAL SOUND UP TO AND INCLUDING HARMONICS Hn

6. MODES OF VIBRATION THE COMPLEX VIBRATION OF A SYSTEM CAN BE CONVENIENTLY DESCRIBED IN TERMS OF NORMAL MODES OF VIBRATION. A NORMAL MODE IS CHARACTERISTIC OF THE VIBRATING OBJECT ITSELF AND IS NOT DEPENDENT ON HOW THE OBJECT IS EXCITED OR OBSERVED. FOR A MANDOLIN, A NORMAL MODE IS DETERMINED BY THE COUPLED MOTION OF ITS STRINGS, BRIDGE, HEAD, ENCLOSED AIR CAVITY, AND THE NECK/HEADSTOCK/FINGERBOARD ASSEMBLY. THE DEFLECTION OF AN OBJECT AT A PARTICULAR FREQUENCY IS CALLED AN OPERATING DEFLECTION SHAPE (ODS). AN ODS MAY RESULT FROM THE EXCITATION OF MORE THAN ONE NORMAL MODE. A CURVE FITTING PROGRAM MAY BE USED TO DETERMINE THE INDIVIDUAL NORMAL MODES FROM THE ODS.

7. HOLOGRAPHIC INTERFEROMETRY EXPERIMENTAL MODAL ANALYSIS MY BE ACCOMPLISHED USING ANY TRANSDUCER CAPABLE OF DETECTING MOTION, BUT HOLOGRAPHIC INTERFEROMETRY OFFERS THE BEST SPATIAL RESOLUTION. ELECTRONIC TV HOLOGRAPHY IS A FAST AND CONVENIENT WAY TO RECORD ODSs FROM WHICH NORMAL MODES CAN BE DETERMINED. SYSTEM USED FOR TV HOLOGRAPHY

8. VIBRATIONAL MODES OF THE HEAD HOLOGRAPHIC INTERFEROGRAMS OF SEVERAL VIBRATIONAL MODES OF THE HEAD OF A HUBER LEXINGTON BANJO.

9. VIBRATIONAL MODES OF THE HEAD

10. HEAD MODES SPECTRUM FROM TAPPING HEAD SHOWING LOW-FREQUENCY HEAD MODES

11. RESONATOR THE RESONATOR VIBRATES VERY LITTLE. ITS MAIN ROLE IS TO DEFINE AN AIR CAVITY WHICH HAS QUITE A LARGE EFFECT ON THE HEAD VIBRATION AT LOW FREQUENCY. INCREASING THE SIZE OF THE RESONATOR-RIM GAP BY MEANS OF A RAEJUSTER INCREASES THE RESONANCE FREQUENCY OF THE ENCLOSED AIR CAVITY

12. EFFECT OF RESONATOR ON SOUND FRACTION OF TOTAL SOUND vs FREQUENCY WITH AND WITHOUT THE RESONATOR

13. BRIDGES BRIDGES ARE MADE OF DENSE HARDWOOD WITH A CAP OF EVEN DENSER WOOD. MOST BRIDGES HAVE 3 LEGS, ONE AT EACH END AND ONE AT THE CENTER. A USEFUL TRICK IS TO DRILL VERTICAL HOLES THROUGH THE OUTER LEGS WITH ALUMINUM RODS TO STIFFEN THE BRIDGE. FRACTION OF SOUND vs FREQUENCY FOR TWO BRIDGES. BRIDGE 1 IS MADE OF A STIFFER WOOD THAN BRIDGE 2.

14. TRANSFER OF VIBRATION ENERGY WITHIN THE BANJO ACCELERATION AMPLITUDES OF VARIOUS PARTS OF THE BANJO WHEN THE BRIDGE IS VIBRATED. BY FAR THE MOST ENERGY IS TRANSFERRED TO THE HEAD, ESPECIALLY AT LOW FREQUENCY (Rae, 2009)

15. SOUND DECAY SOUND SPECTRA FROM 1 st STRING EXCITED 1 INCH FROM THE BRIDGE RECORDED 0-2 s AFTER PLUCKING