Measuring stiffness with sound

It is very useful to know the engineering properties of the timber in logs before they are sent to the sawmill. Time and energy spent sawing up a log and kiln drying the battens is wasted if that timber later fails to meet the grade for construction. It would be much better to put that log to another use.

The science of sound allows us to do just that. The speed of sound through any material is related to the material's stiffness. In fact, stiffness equals density times the speed of sound squared.

That means if we can measure the speed of sound and the density we can calculate stiffness.

To do this we measure how long it takes the sound to travel from one end of the piece of timber to the other. Then it’s simply a case of speed equals distance divided by time. To explore the science further why not look at our whack-a-stick simulation or read about our exhibit at the Royal Society Summer Science Fair 2007?



This was one of the first videos we made. Annie and Heraa had just started their Nuffield Science Bursaries and we were practicing using the video camera. It just so happened that on the day, Peter Carter from Fibregen was visiting the laboratory to talk about his acoustic testing tool with John and Andy from the SIRT project.

We decided it was a good opportunity to make a short video, so Annie and Heraa asked Peter how it worked and we videoed Annie doing a demonstration.

This tool, the HM200, is called the Director, but people also call it the "Hitman". It is designed to work in busy, noisy timber yards but in the quiet of your own home or classroom you can make your own "non-destructive acoustic testing device". All you need is a microphone and a computer with some software that will analyse the frequency of sound. We have found that the free software called Audacity can do this well enough for a demonstration.

When you hit the end of the wooden batten with a hammer, the main sound you can hear is the sound of the first mode of resonance. The frequency of the first mode of resonance is the time it takes the sound to travel along the batten, bounce off the end and travel back down the length of the batten. This means the wavelength of the first mode of resonance is twice the length of the batten.

It sounds complicated at first, but it’s actually quite simple. All you need to do is hit the piece of timber and analyse the sound to find out what frequency it was mainly made off. So long as everything is working as it should, that is your first mode frequency.

To calculate the speed of sound in the timber:

(Speed of sound) = (wavelength) x (frequency) = 2 x (batten length) x (frequency)

And to calculate stiffness:

(Stiffness) = (density) x (speed of sound) x (speed of sound)

Here is some proof that we did not fake anything for the video. We took the audio recorded from the video and opened it in Audacity (we've extracted the sound of the hammer strikes so you can do this yourself). We then selected the sound of the hammer strike and selected "plot spectrum" from the "analyze" menu.

What we want to look at is the frequency spectrum – that's the graph with frequency on the horizontal axis and the level on the vertical axis. The higher the level the more of that frequency there is in the sound.

The sound contains lots of different frequencies, but we are mainly interested in the highest peak. This is a frequency of 554 Hz.

And if we look at what the figure on the laptop in the video it says 558 Hz. Pretty close huh?



Did you notice the time on the laptop clock? We don't work that late! That was New Zealand time. The laptop was Peter's and that's where he lives.