David Politzer's Analysis of How the Banjo Bolster Works

Question
What is the difference between the Banjo Bolster and an adjustable piece of foam fitted under the dowel stick or along the side of the rim. Both seem to work the same way. So how is this any different?

Answer
“A steady note of a single pitch, i.e., starting before the Big Bang and lasting long after the Sun is a Red Giant, only contains integer multiples of the fundamental frequency. An ideal string has resonances with integer multiple frequencies. If it isn't quite ideal, the new resonant frequencies will generate their own harmonic series. However, the sudden start of a pluck note excites every resonance with which it has any contact. That is not only all the resonances of the strings but also those of the head and even those of every wood and metal part. In respectable instruments like guitars, these die off much quicker than the bulk of the note. In contrast, banjos are so efficient at turning string vibration into sound that the "nice" sound dies off almost as quickly.

Lots of things are vibrating when you pluck a note, but the thing most efficient at turning that into sound is the head. Essentially because of dipole cancellation of neighboring cells of the head normal modes, higher and higher frequencies are radiated most efficiently from nearer and nearer the edge. Hence, damping the head near the edge will selectively reduce the highest frequency components of the sound. I believe that is the main mechanism behind normal stuffing.

Ric Hollander's Banjo Bolster does not directly damp the head. But it does two conceptually different things to the air inside the pot. (Note: a zeroth order account of banjo physics completely ignores the pot, except as a rigid frame holding the head. That physics story is surprisingly successful, but any player knows that the pot does a lot to the sound.)

First, it reduces air vibration under the edge of the head, which in turn, is the source of the highest frequency components of the sound. This part is rather like normal stuffing, but their effects on lower frequency head motion need not be identical.
And second, it reduces some of the air vibration within the pot (whose pressure oscillations drive the head). Pot air resonances will be damped out, so they are not effective at driving the head. Also, rim resonances that communicate to the head via the air in the pot will also be less effective at making sound.

Open String Plucks

Left Image: With the Banjo Bolster
Right Image: Bare

The image above is my way of laying out the physics/acoustics issue. The open string wave envelopes show that the overall volume is only very slightly diminished. The spectrograms show the dramatic reduction of frequency components that are long-lived but not string harmonics (integer multiples of the pitch). (With those spectrogram settings, there's nothing interesting above 3kHz.) The open string pluck sound is what everyone hears.

Bridge Taps

Left Image: With the Banjo Bolster
Right Image: Bare

The damped string bridge taps reveal the sounds that are produced by a sudden disturbance at the bridge. So, roughly speaking, those are the sounds that do or don't accompany the string sound when it is plucked.

My banjo research buddy at Cambridge University was quite surprised by the effect. He's the one who suggested just listening/looking at the damped string case. Damping strings and tapping on the bridge is something he has been doing with violins and guitars for over forty years. World-class violin luthiers consult him on how the measure aspects of their products.

Of course, there are people who prefer not to stuff, even if they're using steel strings on a mylar head. They will hear a definite difference between the bolster and a sock but be happier without either.”

- David Politzer
(Banjo player and Richard Chace Tolman Professor of Theoretical Physics at the California Institute of Technology. David was awarded the 2004 Nobel Prize in Physics with David Gross and Frank Wilczek for their discovery of asymptotic freedom in quantum chromodynamics. He also does fascinating research into the physics of the banjo!)

Read David's complete article titled "Inharmonic Partials and Banjo Ring" to learn more about how the Banjo Bolster works and its superiority to conventional stuffing methods.

David's Customer Testimonial and a Quote from "Inharmonic Partials and Banjo Ring"

“The eagerly anticipated Banjo Bolster arrived today. There was nothing subtle about its effectiveness. It does just what everyone says.

...The second strategy involves partial damping of the head modes. The method was inspired by an insanely clever device invented, manufactured, and sold by Ric and Deb Hollander. They call it the Banjo Bolster™ (http://www.banjobolster.com). ”