SOUND AND VIBRATION,
GENERATED BY IMPACT
ON THIN ICE
Mikhail Mironov
Andreyev Acoustics Institute
Moscow
1
ICSV19, Vilnius.July 11, 16-50.
The main goal of the talk is experimental
illustration of some delicate point in the problem
of sound generation by vibration. This is
coincidence frequency effect. The statement of
the problem is as follows.
impact point
air
thin plate
water
2
z
The field of the pressure in air may be
find formally by means of double
Fourier transform (all indications are
standard):
x
p( x, z, t )  (2 )
i  a
2
 ddkP(, k , z )e
 it  ikx
i (  / ca ) 2  k 2 z
e
 F ( , k )
P( , k , z ) 

2
2   h   ( k 2 ) 1 / 2  2  12 1 Eh 3 k 4
( / ca )  k
i
w
2
bifurcation points
- sound in air
poles - bending
waves in the plate
Singularities in the integrand
3
z
x
Im k
k-plane
Re k
bifurcation
points
poles
What happens, when poles and bifurcation point appeare to be
close each other at some frequency? Or, what happens if
propagation velocities of sound in air and bending wave in ice
plate are coincided? This is just coincidence situation. Strong
interaction between vibration of solid (ice) and sound (air)
is realized at the coincidence frequency
The goal of the presentation is the experimental illustration of
the strong effect. So, we pass from the dry theory to the
natural, vivid and beautiful experiment.
4
This is the forest pond with thin (~3 cm) ice layer.
Trace 2,
155.6 m
Trace 1,
92.6 m
Photo of the pond,
Autumn 2005
Space photo of the pond
(Google maps)
The impacts over ice were made at one bank of the
pond and were detected (in air) at the opposite one.
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1 - 97 м
Trace 1
T  150ms
150 ms
2 - 157 м
Trace 2
T  245ms
245 ms
6
The spectra of the impact sound
Short trace
- black
Long trace
- red
The sound spectra are rather narrow 0.8 – 1.0 kHz.
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The qualitative explanation of the effect is
rather simple. The bending oscillation of the ice is
the source of the sound, that is recorded in air. The
impact on the ice generates the wide spectrum of
bending waves, propagating along the ice plate.
It is important that the bending waves have
dispersion. The higher is the frequency the greater
is the phase velocity. At some frequency fc, that is
called coincidence frequency, the phase velocity of
the wave coincides with the air sound velocity ca. At
this frequency the acoustic wave propagates sliding
along the ice and the energy transfer from the ice
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plate to the sound wave in air is the most effective.
Immediately after the impact the components
of the spectrum at the coincidence frequency start
to radiate sound into the air. As the group velocity
of bending waves is about twice as much as the
phase one, the wave packet, bearing the radiating
harmonics, propagates to the observation point
permanently leaving behind the sound, radiated
earlier in the air.
Impact
mic
Generated sound
Wave packet of
bending waves
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The sound signal appears at the observation point
only when the wave packet come to this point.
After that the sound from the distant points
radiated earlier comes. The sound signal vanishes
only when the sound from the start point comes.
Impact
Generated sound
Wave packet of
bending waves
10
Bending waves dispersion and coincidence frequency
cg
cph
ca
E pl  10 Па - plate Young module of ice
10
1
ca - coincidence frequency –
fc 
c  0.080
2
h inversely proportional to h
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Pulse duration is equal to the difference between arrival time of the
head of the bending waves at coincidence frequency and arrival time
of the sound wave of the impact itself
L L L 
ca 
T     1 
ca c g c a 
cg 
L
T  0.573 
ca
- sound impulse
duration
L - the distance; ca - sound velocity in air
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Pulse duration
Duration
theoretical
Duration
experimental
Short trace
T  167 ms
T  150ms
Long trace
T  270ms
T  245ms
h=0.029 m
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Mamyshev, Odyntsov (Baikal Lake,
2005 – 2007 YY), near settlment Bolshie
Ice thickness, m
Frequency, Hz
Koty
theory
experiment
22 days
14
Thank you for attention
15
“When the autumn came and the film had just begun
to cover the ponds, we were impatiently watching
them freeze … I can still hear that glassy
chatoyant clinking made by the pebbles bouncing
against the thin ice as we threw them from the
bank...” «С осени, когда пруды начинали покрываться
пленкой, мы с нетерпением следили за их замерзанием… До
сих пор еще в моих ушах стоит переливчатый стеклянный
звон от камней, бросаемых с берега по тонкому льду…».
Vladimir Korolenko. Collected works in 10
volumes. v.5. The story of my contemporary.
Moscow, Hudozhestvennaya literatura – 1954
Quoting of
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