Tag Archives: Young’s Modulus

A bamboo guitar Part 3 – bamboo compared to blackwood

In my last entry, I had just finished measuring the fundamental frequencies of my bamboo panels in three different vibrational modes:

  1. along-grain free beam (marimba) mode: 109.0 Hz
  2. across-grain marimba mode: 226.1 Hz
  3. twist (torsional) mode: 80.1 Hz

What I am aiming at is to compare the stiffness of the bamboo material with my usual blackwood, so I can feel smug that what I get from the bamboo guitar will be worthwhile acoustically as well as using a readily renewable resource. With a little help from Gore and Gilet, I can convert these frequencies into measurements of:

  1. stiffness (Young’s modulus) along the grain
  2. stiffness across the grain
  3. shear modulus, or stiffness in the twisting mode

And if I’ve done the same tests on a blackwood panel (and you can bet I have), I can begin to compare the properties of the two materials. So here are the figures for blackwood:

  1. along-grain marimba: 130.1Hz
  2. across-grain marimba: 182.4Hz
  3. twist mode: 80.1Hz

Before I can work out the stiffness moduli for the materials, I need to allow for the fact that the bamboo and blackwood panels were slightly different sizes as well as different in density.

The next step was to calculate the density of each panel (density is mass divided by volume, measured in kg/cubic metres). I weighed the panels and carefully measured their length, breadth and thickness, and came up with these results:

  1. density of bamboo: 490.3 kg/cubic m
  2. density of blackwood: 697.3 kg/cubic m

So blackwood is about one and a half times denser than bamboo.

Using three more equations from Gore and Gilet (Equations 4.5-2, 4.5-3, and 4.5-4, page 4-59) I get:

  1. stiffness along grain: bamboo 10.6 GPa; blackwood 19.8 GPa
  2. stiffness across grain: bamboo 1.4 GPa; blackwood 1.6 GPa
  3. shear (twist) modulus: bamboo 1.3 GPa; blackwood 2.5 GPa

To sum up (pay attention up the back!):

  1. blackwood is 1.9 times stiffer along the grain than blackwood
  2. blackwood is 1.1 times stiffer than bamboo across the grain
  3. blackwood is 1.9 times stiffer in twist than bamboo

I’m now very close to answering my question about what thickness to make my bamboo back panels to match the stiffness of my blackwood ones. Back to another Trevor Gore equation (4.5-7 on page 4-61), which will tell me how many times thicker the bamboo back must be to have the same stiffness as blackwood. After some nail-biting, hair-pulling writing of the expression into a spreadsheet (Jeez, Trevor!), the answer is:


Oh, alright. Settle down. The excitement is too much, I know. Talk about suffering for the sake of art.