FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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1. THE ACOUSTIC HAVE GENERATED IN AIR BY THE IMPACT OF GRINDER BALLS
When two grinder balls are knocked together in ambient air, an impact
sound is generated which has several distinct features. Fig. 1 shows two
typical waveforms picked up by a Bruel & Kjaer 1/4" microphone (# 4135) flat
to 70 kHz and captured on a digital waveform analyzer. The waveform on the
left was produced by the impact of two good balls while the one on the
right, by the impact of a good and a cracked ball. The balls, 3" in
diameter, are hand held with the target ball near the microphone and the
"anvil", always a good ball, on the opposite side. A close examination of
these waveforms reveals several distinct features. First of all, an initial
pulse is always present at the beginning of each waveform, whether the balls
are cracked or not. Also common to both waveforms is the low frequency
rumble that follows. This rumble is due to reflections on surrounding
structures and low frequency room resonances. Tests conducted in an
echo-free room did not show such low frequencies. Following the initial
pulse, high frequency resonances are present in both waveforms. In the case
of the "good" impact waveform, the amplitude of the resonance is small, its
frequency is around 40 kHz and its damping is low. In the case of the
"cracked" impact, the resonance's amplitude is much greater, while its
frequency is lower (around 5-15 kHz) and it is more damped. These
features were individually studied and the results are presented in the
following discussion.
The initial pulse
An initial pulse of width around 200 ys such as the one of Fig. 1
appears at the beginning of every waveform recorded, whether good or cracked
balls are used for the impact. This relatively low frequency pulse
( 3 kHz) can be explained by considering the overall motion of the balls as
a source of acoustic waves in air.
Let us first recall the relation between particle displacement and
acoustic pressure p for plane waves in air (6):
p = - poc 2
where: po is the density of air
c is the velocity of sound in air
x is the equilibrium position.
We also have for plane waves propagating in one direction in air:
Replacing in (1), we obtain:
Se
ôx
e = f(ct - x)
6e 1 6e
i.e. — =
6x c 5t