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Optical determination of the attenuation of a surface wave generated at the critical-angle
Optical determination of the attenuation of a surface wave generated at the critical-angle Using an optical method a an immersed plane metallic amplitude and attenuation shown that the attenuation
A. FAURE,
G. MAZE
surface wave is detected ‘in situ’, which is the reflection from surface, of an ultrasonic beam propagating in water. The of the beam are measured on a stainless steel sample and it is fits the f4 law, where f is the frequency.
and J. RIPOCHE
Reflection of an ultrasonic beam from a water-metal interface When an infinite ultrasonic plane wave, travelling in water, strikes a plane interface separating liquid from a metal, part of the incident energy is reflected and part is transmitted. In the liquid the pure longitudinal waves give rise to longitudinal and shear waves in the metal. The reflection coefficient, R, the longitudinal wave refraction coefficient, I,, and the shear wave refraction coefficient, T, can be calculated from a function of the angle of incidence 8.’ Y2These coefficients depend on the wave energy and the incident angle as shown in Fig. 1 (stainless steel Z-30 C-l 3).
Reflection
coefficient
measurement
The reflection coefficient, R, as a function of the angle of incidence was measured at the water stainless-steel interface at the frequency 11.8 MHz. Fig. 2 shows the experimental arrangement placed in a waterfilled tank. The emitter is made with a plane circular piece of barium titanate (4 = 10 mm), thickness resonant. The receiver is an omnidirectional transducer made with a small tubular piece of piezoI
The calculations were made using an Olivetti P.652 computer. The first and second critical angles 0~~ and Bc2 appear when L and Tare equal to 0, and R is equal to unity. They are defined as follows sinBc,
=
CI,ICI and
sin Bc2
=
CLK,
(1) 0.6
where CL, C, and Cl are the wave velocity in the liquid, and the longitudinal and the shear wave velocities in the solid respectively (these were investigated for stainless steel) where C, = 5790 ms
Ct = 3100ms
1
Waterstamless-steel
0.4
p = 7877 kg m I
CJ = 0.30 It is noticed that L and T remain equal to 0, and R is equal to 1, whatever the value of the incident angle, greater than the second critical angle 19~~.
Oloh 20
The authors are at Laboratoire d’Electronique et d’Automatique, groupe Ultrasons, Universite de Haute-Normandie, B.P. 4006-76077, Le Havre, Cedex, France. Paper received 5th January 1976.
ULTRASONICS.
SEPTEMBER
1976
(
,
,
40
60
80
Anqleof lncldence WI
Fig. 1. Variations of the reflection and transmission angle incidence for the water stainless-steel interface.
coefficients
vs
205
The results agreed well with the theoretical predictions on both sides of the second critical angle excepting an anomaly which appears for this last value. A very noticeable minimum is measured at the critical incidence (curve A). This is not explained by the elementary theory and corresponds to an apparent lack of energy in the reflected beam, at the measure ment point. We explored this region with a receiver, the diameter of which is smaller than the beam width. We move the receiver with a micrometric screw, on a line perpendicular to the axis of the specular reflected beam (x’ Ox Fig. 2). The results reported in Fig. 4, show the variation of the pressure vs position of the receiver drawn for two incident angles. Curve C is drawn for an incident angle equal to the Rayleigh angle. Fig. 2 Experimental arrangement for measuring the reflection efficient at the interface metal-water
0’12: 25
30
co-
On graph D in Fig. 4, the distribution of pressure in the reflected beam is very different from those obtained at other values; a partition occurs. Hence measurement of the reflection coefficient, without displacemnte of the receiver, is less significant than the exploration of the reflected beam profile Using the first method only enables the anomaly to be detected. This effect has in fact been mentioned by different authors.3 -6 It appears that the slope on the right side, part 2 of the curve is smaller than that of the left side. The partition of the reflected beam is related to the fact that the reflection coefficient is less than unity for the same value of incidence. In this case, the total energy is distributed over a greater surface.
35
Angle of lncrdence WI
Fig. 3 Variation of the reflection coefficient steel interface near the second critical angle.
oL
electric ceramic. The two transducers are supported by the moving arms of a modified optical goniometer with 1’ accuracy. The receiver can be moved in a direction (x’ Ox) perpendicular to the axis of the reflected beam. The pressure distribution (P), in a direction perpendicular to the axis of the ultrasonic beam fits a gaussian function of the form P = PO exp(-_x’),where p = 3.57 x lO”m-‘. The sample was well polished in order to avoid unwanted reflections. Pulsed ultrasonic emission duration 10 ~.ls was used, which is shorter than the time needed for an echo to travel from the transducer to the walls of the basin. An electronic amplifier was connected to the receiver and the output voltage read on an oscilloscope. The results obtained for stainless steel are given in Fig. 3. This figure shows the voltage variation normalized at unity, taking into account the value for incidence greater than 30” which is proportional to the acoustic pressure in water.
206
I
I
I1
I1
I,
1
0
-5
for the water-stainless
I
J IC
,L
5
Tronsducerdlsplacernent
x Cmml
200 2 160-
/“\ D
2
t
+
140-
Fig. 4 Profile of the reflected beams at the incident angle 25”. C, and at the Rayleigh critical angle, D
ULTRASONICS.
SEPTEMBER
1976
The level of water is adjusted so that the path of the light beam is mainly in the air. The figure of diffraction vanishes if the incident waves are extinguished. As the light intensity is weak, the detection is realized with a lock-m amplifier. The ultrasonic beam is modulated by its reference frequency. This method is more sensitive than the direct measurement on an oscilloscope because it increases the signal/noise ratio. The light intensity of the order n,Z,, depends on the amplitude a of the surface wave,r3 such as: Z, Fig. 5 Experimental arrangement fraction by surface wave generated
K - .I,’ (u)
(3)
with u = (4rr a cos i)/h, and where Jn is Bessel’s function of order n.
for the study of the light difof the critical angle.
By taking this phenomenon into account, we obtained the curve B in Fig. 3 where the variations in the maxima of the output receiver voltage are recorded as a function of 8, even if, as in this case, the axis of the receiver does not coincide with the axis of the reflected beam. The minimum remains present. Photographs taken in conjucntion with stroboscopic strioscopy, shows that the wavefronts, corroborates the spreading as for the interface water-aluminium.7 Among the earlier different hypotheses, being forward,*>” we only retain the generation of a surface wave at a critical angle as this brings out energy during the propagation, and so explains the apparent lack of energy. It also explains that the partition, part 2 of curve D in Fig. 4, is attributed to re-emission, which itself corroborates the weaker decrease of the right side of the curve. Its wave number is assigned to be a root of the characteristic equation obtained by Viktorov1’74 when he studied the propagation of an ultrasonic surface wave on a liquid-solid interface. This equation transforms itself in Rayleigh’s equation.
Light diffraction
=
The knowledge of the ratio of the intensities for the first and second orders enables a to be calculated, by comparison with the theoretical graph, of the light intensity ratio:
11
J:
r, =-
(u>
J; (~1
The curves Jf (u) and J: (u) become linear in the log-log coordinates, if small values of the parameter u are considered. We have drawn the variations in the light intensity, measured at the positions corresponding to the first and second orders, as a function of the voltage U applied to the emitter shown in Fig. 6. The amplitude of the corresponding surface wave corrugations, supposed sinusoidal, are shown in the Fig. 7 as a function of the voltage U. The experimental results
by a surface wave
A light beam may be diffracted by a surface wave. Consider for example an air-solid interface, where a surface wave is propagating. s2 is the frequency of the acoustic wave, and A is its wavelength. The wavelength of light is X and the light is incident at an angle i. As yet, we have not made any assumption about the generation of such a surface wave which acts as a grating, where % =
nh/(A cos i)
Q, is the diffraction
(2)
angle for the order n.
An experimental arrangement is used to try to detect the surface wave (Fig. 5). The sample A is supported by a mechanical device allowing three degrees of freedom. The transducer T, placed in water, acts at a variable incidence. In the air, a laser beam (He-Ne, 5 mW) is impinging on the sample. Its axis is contained in the geometrical plane defined by the normal and the axis of the ultrasonic beam. A photodetector tube, adjusted by two micrometric screws, is placed on the axis of the reflected light, which is focused on a pinhole made in the screen in front of the tube. The incident angle of ultrasound is adjusted so that a displacement of the reflected beam is detected by the stroboscopic method.”
ULTRASONICS.
SEPTEMBER
1976
,,-.~*I,. IO0
IO' Voltage WI
Fig. 6 Variations of the light intensity in the first and second diffraction orders, function of the voltage applied to the ultrasonic transducer
207
tion. In this case the beam profile does not present any alterations to those observed by some authors.14 Other experimental data obtained at different frequencies included in the 5 MHz-l 2 MHz range give similar results. Finally the laser beam was moved along the wave surface beam axis. The variation of the amplitude, a was found to be a function of the light beam position h (Fig. 5), related in an exponential form: Q
=
Qo
exp (- oih)
The relationship described by 01 =
01 0
I
IO
I
I
20
30
between
a
and the ultrasonic
frequency fis
b*f4
(5)
where b is a constant value (b = 2.1 x 10ez7).
Voltage CM Fig. 7 Variation of the surface wave amplitude applied to the emitter.
vs the voltage
The average grain diameter D being less than 0.022 mm, the condition A > 10 0, where A is the ultrasonic wavelength, is forfilled. The dependence of the attenuation a on the f 4 tallies with the early experiments.”
Conclusion The reflection, at the second critical angle, of an ultrasonic beam propagated in water, from a plane metallic surface is followed by a surface wave similar to the Rayleigh wave. The determination ‘in situ’ of the attenuation coefficient by an optical method shows that its variation with the frequency is of the order p and agrees with earlier theoretical results based on the grain scattering.
Acknowledgement The authors are grateful to M. Leperd, for valuable discussion and his contribution to the metallographic aspect of the investigation.
References 1 2
Fig. 8
Profile of the surface wave beam
corroborate with the theoretical linear relation between the amplitude, a. and the voltage U. In order to examine the profile of the surface wave beam, measurements of amplitude are made at different points on the surface. Micrometric screws on the phototube X-Y holder enable the coordinates of the considered reflecting point to be evaluated. Fig. 8 gives the experimental data points obtained for stainless steel at 7.28 MHz. We noticed a decrease in the signal which corresponds to the attenua-
208
I 8 9 10
11 12 13 14 15
Brekhovskikh, L. Waves in layered media, Academic Press (1960) Duclos, J., Lagrue, J., Boutiller, J., Roussel, M., CR Acad Sci 275 (B) (1972) 69 Mott, G., JA SA 50 (1972) 819 Viktorov, LA. Rayleigh and lamb waves, Plenum Press (1967) Maze, G., Ripoche, J., CR Acad SC 278 (B) (1974) 6 1 Breazeale, M.A., Adler, L., Smith, H.J. Sov Whys Acousf 21 (1975) Maze, G., Duclos, J., Ripoche, J. Acustica 32 (1975) 181 Schoch, A., Ergeb, Exakt Naturw 23 (1950) 127 Neubauer, W.G., J Applied Phys 2 (1973) 137 Merculova, V.M., Sou Phys Acoust 42 (1971) 191 Viktorov, LA., Grishenko, E.K., Kaekina, T.M., Sov Whys Acoust 9 (1963) 141 Faure, A., Maze, G., Ripoche, J., CR Acad SC 280 (B) (1975) 613 Mayer, W.G., Technical Report AD 655466 Georgetown University, Washington (1967) Hallermeier, R.J., Diachok, O., J Applied fhys 4 1 (1970) 4763 Papadakis, E.P. Physical Acoustics, Acadmic Press Vol IV-B (1970) 290
ULTRASONICS.
SEPTEMBER
1976
A. FAURE,
G. MAZE
surface wave is detected ‘in situ’, which is the reflection from surface, of an ultrasonic beam propagating in water. The of the beam are measured on a stainless steel sample and it is fits the f4 law, where f is the frequency.
and J. RIPOCHE
Reflection of an ultrasonic beam from a water-metal interface When an infinite ultrasonic plane wave, travelling in water, strikes a plane interface separating liquid from a metal, part of the incident energy is reflected and part is transmitted. In the liquid the pure longitudinal waves give rise to longitudinal and shear waves in the metal. The reflection coefficient, R, the longitudinal wave refraction coefficient, I,, and the shear wave refraction coefficient, T, can be calculated from a function of the angle of incidence 8.’ Y2These coefficients depend on the wave energy and the incident angle as shown in Fig. 1 (stainless steel Z-30 C-l 3).
Reflection
coefficient
measurement
The reflection coefficient, R, as a function of the angle of incidence was measured at the water stainless-steel interface at the frequency 11.8 MHz. Fig. 2 shows the experimental arrangement placed in a waterfilled tank. The emitter is made with a plane circular piece of barium titanate (4 = 10 mm), thickness resonant. The receiver is an omnidirectional transducer made with a small tubular piece of piezoI
The calculations were made using an Olivetti P.652 computer. The first and second critical angles 0~~ and Bc2 appear when L and Tare equal to 0, and R is equal to unity. They are defined as follows sinBc,
=
CI,ICI and
sin Bc2
=
CLK,
(1) 0.6
where CL, C, and Cl are the wave velocity in the liquid, and the longitudinal and the shear wave velocities in the solid respectively (these were investigated for stainless steel) where C, = 5790 ms
Ct = 3100ms
1
Waterstamless-steel
0.4
p = 7877 kg m I
CJ = 0.30 It is noticed that L and T remain equal to 0, and R is equal to 1, whatever the value of the incident angle, greater than the second critical angle 19~~.
Oloh 20
The authors are at Laboratoire d’Electronique et d’Automatique, groupe Ultrasons, Universite de Haute-Normandie, B.P. 4006-76077, Le Havre, Cedex, France. Paper received 5th January 1976.
ULTRASONICS.
SEPTEMBER
1976
(
,
,
40
60
80
Anqleof lncldence WI
Fig. 1. Variations of the reflection and transmission angle incidence for the water stainless-steel interface.
coefficients
vs
205
The results agreed well with the theoretical predictions on both sides of the second critical angle excepting an anomaly which appears for this last value. A very noticeable minimum is measured at the critical incidence (curve A). This is not explained by the elementary theory and corresponds to an apparent lack of energy in the reflected beam, at the measure ment point. We explored this region with a receiver, the diameter of which is smaller than the beam width. We move the receiver with a micrometric screw, on a line perpendicular to the axis of the specular reflected beam (x’ Ox Fig. 2). The results reported in Fig. 4, show the variation of the pressure vs position of the receiver drawn for two incident angles. Curve C is drawn for an incident angle equal to the Rayleigh angle. Fig. 2 Experimental arrangement for measuring the reflection efficient at the interface metal-water
0’12: 25
30
co-
On graph D in Fig. 4, the distribution of pressure in the reflected beam is very different from those obtained at other values; a partition occurs. Hence measurement of the reflection coefficient, without displacemnte of the receiver, is less significant than the exploration of the reflected beam profile Using the first method only enables the anomaly to be detected. This effect has in fact been mentioned by different authors.3 -6 It appears that the slope on the right side, part 2 of the curve is smaller than that of the left side. The partition of the reflected beam is related to the fact that the reflection coefficient is less than unity for the same value of incidence. In this case, the total energy is distributed over a greater surface.
35
Angle of lncrdence WI
Fig. 3 Variation of the reflection coefficient steel interface near the second critical angle.
oL
electric ceramic. The two transducers are supported by the moving arms of a modified optical goniometer with 1’ accuracy. The receiver can be moved in a direction (x’ Ox) perpendicular to the axis of the reflected beam. The pressure distribution (P), in a direction perpendicular to the axis of the ultrasonic beam fits a gaussian function of the form P = PO exp(-_x’),where p = 3.57 x lO”m-‘. The sample was well polished in order to avoid unwanted reflections. Pulsed ultrasonic emission duration 10 ~.ls was used, which is shorter than the time needed for an echo to travel from the transducer to the walls of the basin. An electronic amplifier was connected to the receiver and the output voltage read on an oscilloscope. The results obtained for stainless steel are given in Fig. 3. This figure shows the voltage variation normalized at unity, taking into account the value for incidence greater than 30” which is proportional to the acoustic pressure in water.
206
I
I
I1
I1
I,
1
0
-5
for the water-stainless
I
J IC
,L
5
Tronsducerdlsplacernent
x Cmml
200 2 160-
/“\ D
2
t
+
140-
Fig. 4 Profile of the reflected beams at the incident angle 25”. C, and at the Rayleigh critical angle, D
ULTRASONICS.
SEPTEMBER
1976
The level of water is adjusted so that the path of the light beam is mainly in the air. The figure of diffraction vanishes if the incident waves are extinguished. As the light intensity is weak, the detection is realized with a lock-m amplifier. The ultrasonic beam is modulated by its reference frequency. This method is more sensitive than the direct measurement on an oscilloscope because it increases the signal/noise ratio. The light intensity of the order n,Z,, depends on the amplitude a of the surface wave,r3 such as: Z, Fig. 5 Experimental arrangement fraction by surface wave generated
K - .I,’ (u)
(3)
with u = (4rr a cos i)/h, and where Jn is Bessel’s function of order n.
for the study of the light difof the critical angle.
By taking this phenomenon into account, we obtained the curve B in Fig. 3 where the variations in the maxima of the output receiver voltage are recorded as a function of 8, even if, as in this case, the axis of the receiver does not coincide with the axis of the reflected beam. The minimum remains present. Photographs taken in conjucntion with stroboscopic strioscopy, shows that the wavefronts, corroborates the spreading as for the interface water-aluminium.7 Among the earlier different hypotheses, being forward,*>” we only retain the generation of a surface wave at a critical angle as this brings out energy during the propagation, and so explains the apparent lack of energy. It also explains that the partition, part 2 of curve D in Fig. 4, is attributed to re-emission, which itself corroborates the weaker decrease of the right side of the curve. Its wave number is assigned to be a root of the characteristic equation obtained by Viktorov1’74 when he studied the propagation of an ultrasonic surface wave on a liquid-solid interface. This equation transforms itself in Rayleigh’s equation.
Light diffraction
=
The knowledge of the ratio of the intensities for the first and second orders enables a to be calculated, by comparison with the theoretical graph, of the light intensity ratio:
11
J:
r, =-
(u>
J; (~1
The curves Jf (u) and J: (u) become linear in the log-log coordinates, if small values of the parameter u are considered. We have drawn the variations in the light intensity, measured at the positions corresponding to the first and second orders, as a function of the voltage U applied to the emitter shown in Fig. 6. The amplitude of the corresponding surface wave corrugations, supposed sinusoidal, are shown in the Fig. 7 as a function of the voltage U. The experimental results
by a surface wave
A light beam may be diffracted by a surface wave. Consider for example an air-solid interface, where a surface wave is propagating. s2 is the frequency of the acoustic wave, and A is its wavelength. The wavelength of light is X and the light is incident at an angle i. As yet, we have not made any assumption about the generation of such a surface wave which acts as a grating, where % =
nh/(A cos i)
Q, is the diffraction
(2)
angle for the order n.
An experimental arrangement is used to try to detect the surface wave (Fig. 5). The sample A is supported by a mechanical device allowing three degrees of freedom. The transducer T, placed in water, acts at a variable incidence. In the air, a laser beam (He-Ne, 5 mW) is impinging on the sample. Its axis is contained in the geometrical plane defined by the normal and the axis of the ultrasonic beam. A photodetector tube, adjusted by two micrometric screws, is placed on the axis of the reflected light, which is focused on a pinhole made in the screen in front of the tube. The incident angle of ultrasound is adjusted so that a displacement of the reflected beam is detected by the stroboscopic method.”
ULTRASONICS.
SEPTEMBER
1976
,,-.~*I,. IO0
IO' Voltage WI
Fig. 6 Variations of the light intensity in the first and second diffraction orders, function of the voltage applied to the ultrasonic transducer
207
tion. In this case the beam profile does not present any alterations to those observed by some authors.14 Other experimental data obtained at different frequencies included in the 5 MHz-l 2 MHz range give similar results. Finally the laser beam was moved along the wave surface beam axis. The variation of the amplitude, a was found to be a function of the light beam position h (Fig. 5), related in an exponential form: Q
=
Qo
exp (- oih)
The relationship described by 01 =
01 0
I
IO
I
I
20
30
between
a
and the ultrasonic
frequency fis
b*f4
(5)
where b is a constant value (b = 2.1 x 10ez7).
Voltage CM Fig. 7 Variation of the surface wave amplitude applied to the emitter.
vs the voltage
The average grain diameter D being less than 0.022 mm, the condition A > 10 0, where A is the ultrasonic wavelength, is forfilled. The dependence of the attenuation a on the f 4 tallies with the early experiments.”
Conclusion The reflection, at the second critical angle, of an ultrasonic beam propagated in water, from a plane metallic surface is followed by a surface wave similar to the Rayleigh wave. The determination ‘in situ’ of the attenuation coefficient by an optical method shows that its variation with the frequency is of the order p and agrees with earlier theoretical results based on the grain scattering.
Acknowledgement The authors are grateful to M. Leperd, for valuable discussion and his contribution to the metallographic aspect of the investigation.
References 1 2
Fig. 8
Profile of the surface wave beam
corroborate with the theoretical linear relation between the amplitude, a. and the voltage U. In order to examine the profile of the surface wave beam, measurements of amplitude are made at different points on the surface. Micrometric screws on the phototube X-Y holder enable the coordinates of the considered reflecting point to be evaluated. Fig. 8 gives the experimental data points obtained for stainless steel at 7.28 MHz. We noticed a decrease in the signal which corresponds to the attenua-
208
I 8 9 10
11 12 13 14 15
Brekhovskikh, L. Waves in layered media, Academic Press (1960) Duclos, J., Lagrue, J., Boutiller, J., Roussel, M., CR Acad Sci 275 (B) (1972) 69 Mott, G., JA SA 50 (1972) 819 Viktorov, LA. Rayleigh and lamb waves, Plenum Press (1967) Maze, G., Ripoche, J., CR Acad SC 278 (B) (1974) 6 1 Breazeale, M.A., Adler, L., Smith, H.J. Sov Whys Acousf 21 (1975) Maze, G., Duclos, J., Ripoche, J. Acustica 32 (1975) 181 Schoch, A., Ergeb, Exakt Naturw 23 (1950) 127 Neubauer, W.G., J Applied Phys 2 (1973) 137 Merculova, V.M., Sou Phys Acoust 42 (1971) 191 Viktorov, LA., Grishenko, E.K., Kaekina, T.M., Sov Whys Acoust 9 (1963) 141 Faure, A., Maze, G., Ripoche, J., CR Acad SC 280 (B) (1975) 613 Mayer, W.G., Technical Report AD 655466 Georgetown University, Washington (1967) Hallermeier, R.J., Diachok, O., J Applied fhys 4 1 (1970) 4763 Papadakis, E.P. Physical Acoustics, Acadmic Press Vol IV-B (1970) 290
ULTRASONICS.
SEPTEMBER
1976