Abstract
In recent decades, ultrasound has begun to play an increasingly important role not only in scientific research, but also in solving a wide range of technical and practical problems: in underwater signaling and communication, ultrasonic flaw detection of metals and alloys, and in medicine, chemistry, and biology. Therefore, the introduction of demonstration experiments with ultrasound into physics lecture courses appears highly appropriate. Some of the experiments carried out by the author of the present note are described below.
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METHODOLOGICAL NOTES
DEMONSTRATIONS ON ULTRASOUND
Ya. S. Maksimov
In recent decades ultrasound has begun to play an ever greater role not only in scientific research, but also in solving a wide range of technical and practical problems: in underwater signaling and communications, ultrasonic flaw detection of metals and alloys, in medicine, chemistry, and biology. Therefore the introduction of demonstration experiments with ultrasound into lecture courses in physics seems highly advisable. Some of the experiments set up by the author of the present note are described below.
To carry them out, a tube generator of ultrasonic oscillations, a quartz holder, the simplest radiometer, and a focusing lens were made. The generator was assembled according to the circuit (Fig. 1) borrowed from the book by B. B. Kudryavtsev, The Application of Ultrasonic Methods in the Practice of Physicochemical Research.
The data for the generator are given in the table:
| Number of turns | Coil diameter in mm | Wire diameter in mm | Method of making the coil | |
|---|---|---|---|---|
| \(L_1\)—intergrid coil | 50 | 70 | 3 | Of copper wire 1.5 mm thick, without a frame. |
| \(L_2\)—tank coil | 60 | 90 | 2.5 | Same |
| \(L_3\)—coil for coupling the quartz with the generator | 40 | 110 | 3.8 | Same |
Capacitor \(C_1\) has a capacitance of 300 cm. Capacitor \(C_2\) is 150 cm. Choke \(D\) is wound on a plexiglass frame with enameled copper wire 0.25 mm in diameter; the number of turns is 500. The generator is supplied from an ELS-2-type power transformer of 70 W capacity; the frequency can be varied within the limits from 0.8 to 5 MHz.
Fig. 1.
The construction of the holder for quartz 20 mm in diameter (quartz frequency 2.85 MHz) is shown in Fig. 2: 1 — brass body, 2 — plexiglass or bakelite insert, 3 — rubber ring (shock absorber); 4 — thin contact brass ring, 5 — flange (upper cover), 6 — quartz, 7 — conical rubber sealing ring, 8 — screws for fastening the flange, 9 — rubber sealing ring, 10 — gland, 11 — contact sleeve.
The holder can be adapted for other quartz dimensions. For this it is necessary to replace the plexiglass or bakelite insert, the flange, and the rubber rings. The construction of the holder makes it possible to immerse the quartz in water. The voltage from the generator is supplied to the quartz by a shielded wire.
Fig. 2.
Figure 3 shows a radiometer made by the author: 1 — steel axis, 2 — mirrors, 3 — aluminum wire 0.75 mm in diameter, 4 — rubber disk 35 mm in diameter and 1.5–2 mm thick.
For making from plexiglass a lens focusing ultrasonic waves, the die shown in Fig. 4 was used. The body \(A\) of the die consists of a thick metal blank. In the lower ...
of the blank there are rims onto which the bottom of the die B is lowered. A metal ball of radius 10 mm is pressed into rod Б. The die was placed in a muffle furnace and heated. Then rod Б was removed and the inner part of the die was filled with Plexiglas shavings. After insertion of rod Б, the die was placed under a press at a pressure of 100 atm. This pressure was maintained until the manometer reading began to decrease. After cooling, the inner part of the die, together with the pressed-in lens, is forced out by the press. The manufactured lens has rims,
Fig. 3. Fig. 4. Fig. 5.
by means of which it is attached to a glass tube (Fig. 5), onto the end of which a rubber ring is first fitted. The diameter of the lens must be equal to the diameter of the quartz. The focal length of the lens is determined by the formula
\[ F=\frac{R}{\frac{c}{c_1}-1}, \]
where \(R\) is the radius of the lens, \(c\) is the velocity of ultrasound in water, and \(c_1\) is the velocity of ultrasound in Plexiglas.
The instruments described make it possible to carry out the following demonstrations.
1. Reflection of Ultrasound
If water is poured into a bath with a glass bottom and quartz, inclined at an appropriate angle, is immersed in it, then the ultrasonic beam, directed obliquely to the horizontal, will remain all the time inside the liquid (waveguide), successively reflecting from the water–glass and water–air boundaries (Fig. 6). When the bath is illuminated from below by an electric arc or a small lamp, a series of equally spaced bright regions is observed on a screen (on the ceiling). These places correspond to the passage of light through the bulges of the liquid surface,
formed by the reflection of ultrasound from the water–air boundary. By placing a flat mirror (a glass plate) in the path of the beam, one can verify that the beam changes its direction according to the laws
Fig. 6.
of geometrical optics. If part of the quartz remains not immersed in water, capillary waves can be observed at the same time.
2. The pressure of ultrasound on an obstacle
If the emitter is placed in a bath with water and the radiometer shown in Fig. 3 is placed in the path of the ultrasonic beam, then the disk of the radiometer is deflected under the action of this beam. The observation can be made with the aid of a light beam reflected by the mirror of the radiometer onto a scale.
Knowing the weight of the disk in water and the weight of the thin aluminum wire on which the disk is suspended, one can, for small angles of deflection, estimate the pressure of the ultrasonic wave, and from it the intensity emitted by the quartz. The pressure can be estimated by the formula
\[ P=\left(m_1 g+\frac{m_2}{2}g\right)\frac{x}{S2H\cos\alpha}\ \frac{\text{dyne}}{\text{cm}^2}, \]
where \(P\) is the pressure of the ultrasonic wave, \(x\) is the number of divisions read on the scale, \(H\) is the distance from the scale to the mirror of the radiometer, \(m_1g\) is the weight of the disk in water, \(m_2g\) is the weight of the aluminum wire in air; \(S\) is the active area of the quartz. For small angles of deflection of the radiometer disk, \(\cos\alpha\) may be taken equal to unity. The formula given is valid for complete absorption by the disk of the energy of the ultrasonic beam.
If the ultrasonic beam partially passes through the disk of the radiometer, this can be taken into account by determining the transparency of the disk. The transparency is determined in the following way. The radiometer disk is removed from the suspension and another (rubber) disk is hung in its place. Under the action of ultrasound it is deflected, and its deflection \(k_0\) is determined from the radiometer scale. Without changing the intensity of the emitter, the first radiometer disk, whose transparency is to be determined, is placed between the quartz and the new disk. Under the action of the wave passing through this disk, the radiometer will be deflected by \(k\) divisions. Then, obviously, the transparency of the disk is \(D=\dfrac{k}{k_0}\). Taking the transparency into account, the total pressure is determined by the formula
\[ P=\frac{\left(m_1g+\frac{m_2}{2}g\right)x}{(1-D)S2H}\ \frac{\mathrm{dyn}}{\mathrm{cm}^2}. \]
Denoting the constant quantities by
\[ B=\frac{\left(m_1g+\frac{m_2}{2}g\right)}{(1-D)2S}, \]
we obtain:
\[ P=B\frac{x}{H}\ \frac{\mathrm{dyn}}{\mathrm{cm}^2}. \]
The radiation pressure on a wall completely absorbing ultrasound is equal to:
\[ P=\frac{I}{c}, \]
where \(I\) is the intensity of radiation, and \(c\) is the speed of ultrasound in water. Therefore,
\[ I=Pc\ \frac{\mathrm{erg}}{\mathrm{cm}^2\cdot\mathrm{sec}}. \]
3. Absorption of Ultrasound
If, in the preceding experiment, a sheet of filter paper is placed between the quartz and the deflected radiometer disk, the radiometer reading decreases. That ultrasound is absorbed can also be shown in the first experiment demonstrating the laws of incidence and reflection of ultrasound: touching the surface of the water with a rubber stopper at the place where the ultrasonic beam is reflected from the air leads to the disappearance of the subsequent reflections of the beam. The same picture is observed when the stopper is placed on the bottom of the bath at the place where the ultrasonic beam is reflected from the glass.
4. Absorption of ultrasound is accompanied by heating of the absorbing medium
If a thermocouple (constantan—copper) is placed in a thin 2–3 mm rubber disk and connected to a mirror galvanometer, then when an ultrasonic beam falls on the disk, the light pointer of the galvanometer will show a deflection.
5. Ultrasonic waves can be focused
A glass tube with a lens (Fig. 5) is filled with alcohol to such a depth that the alcohol level coincides with the focus of the lens. A rubber ring is slipped onto the quartz holder; it forms raised edges above the flange. Water is poured over the quartz up to these edges. The lens is placed in the water above the quartz so that its bottom is parallel to the quartz. When the quartz is operating, a fountain will shoot up from the surface of the alcohol. The height of the fountain will depend on the voltage applied to the quartz. With the generator described above, a fountain 10–12 cm high was obtained. For better visibility of the fountain, the tube should be taken somewhat higher than the focal distance, and its edges should have a flared rim (as shown in Fig. 5), so that the droplets of the fountain fall back into the tube and maintain a constant level of alcohol above the lens.
I express my deep gratitude to the mechanic of the physics laboratory, V. A. Shumilov, for making a number of the instruments described.