Mechanics
Mechanical Vibration, Acoustics
Optical determination of velocity of sound in liquids 1.5.10-00
What you can learn about …
Ultrasonics
Sound velocity
Frequency
Wavelength
Sound pressure
Stationary waves
Debye-Sears effect
Principle:
A stationary ultrasonic wave in a
glass cell full of liquid is traversed by
a divergent beam of light. The sound
wavelength can be determined from
the central projection of the sound
field on the basis of the refractive
index which changes with the sound
pressure.
What you need:
Ultrasonic generator
13920.99
1
Laser, He-Ne 1.0 mW, 230 VAC
08181.93
1
Glass cell, 150 x 55 x 100 mm
03504.00
1
Lens holder
08012.00
1
Lens, mounted, f = +20 mm
08018.01
1
Screen, metal, 300 mm x 300 mm
08062.00
1
Optical profile bench, l = 1000 mm
08282.00
1
Base for optical profile bench, adjustable
08284.00
2
Slide mount for optical profil bench, h = 80 mm
08286.02
1
Slide mount for optical profil bench, h = 30 mm
08286.01
4
Swinging arm
08256.00
1
Table top on rod
08060.00
1
Laboratory thermometers, -10...+ 30°C
05949.00
1
Right angle clamp -PASS-
02040.55
1
Support rod, stainless steel 18/8, l = 250 mm, d = 10 mm
02031.00
1
Universal clamp
37718.00
1
Glycerol, 250 ml
30084.25
3
Water, distilled 5 l
31246.81
1
Complete Equipment Set, Manual on CD-ROM included
Optical determination of velocity
of sound in liquids
P2151000
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
Image of a screen.
Tasks:
To determine the wavelength of
sound in liquids, and from this calucate the sound velocity, from the
structure of the centrally projected
image.
Laboratory Experiments Physics 69
LEP
1.5.10
-00
Optical determination of velocity of sound in liquids
Related topics
Ultrasonics, sound velocity, frequency, wavelength, sound
pressure, stationary waves.
Principle
A stationary ultrasonic wave in a glass cell full of liquid is traversed by a divergent beam of light. The sound wavelength
can be determined from the central projection of the sound
field on the basis of the refractive index which canges with the
sound pressure.
Equipment
Ultrasonic generator
Laser, He-Ne 1.0 mW, 230 V AC
Glass cell, 15055100 mm
Lens holder
Lens, mounted, f = +20 mm
Screen, metal, 300300 mm
Optical profile-bench, l = 1000 mm
Base f. opt. profile-bench, adjust.
Slide mount f. opt. pr.-bench, h = 80 mm
Slide mount f. opt. pr.-bench, h = 30 mm
Swinging arm
Table top on rod, 18.511 cm
Thermometer -10...+30 °C
Right angle clamp -PASSSupport rod, l = 250 mm
Universal clamp
11744.93
08181.93
03504.00
08012.00
08018.01
08062.00
08282.00
08284.00
08286.02
08286.01
08256.00
08060.00
05949.00
02040.55
02031.00
37715.00
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
Glycerol, 250 ml
Water, distilled, 5 l
30084.25
31246.81
3
1
Tasks
To determine the wavelength of sound in liquids, and from this
calucate the sound velocity, from the structure of the centrally projected image.
Set-up and procedure
Fig. 1 shows the experiment set-up. The glass cell is 2/3 full of
liquid, and the sound head is immersed in it to a depth of a
few millimetres, with its face parallel to the bottom of the cell.
The laser beam is enlarged with a lens of focal length +20 mm.
The lens is approx. 0 – 20 cm, the projection screen about
50 cm, away from the cell. The laser and the lens are adjusted so that the beam traverses the liquid between the sound
head and the cell bottom.
The experiment is carried out in a semi-darkened room. With
the generator amplitude on the medium setting, the depth of
immersion of the sound head is so adjusted as to produce a
well-defined system of light and dark bands in the projected
image.
The distance between the bands is determined for various liquids and the liquid temperature measured in each case.
Any gas bubbles forming on the surface of the sound head
and the walls of the cell are removed with a rod.
Fig. 1: Experimental set-up for interference measurements.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2151000
1
LEP
1.5.10
-00
Optical determination of velocity of sound in liquids
Fig. 2: Localised distribution of the change in pressure or
refractive index for four phases of a stationary wave.
Phases t = 41 T and t = 43 T, in which the light passing through
the liquid is not deflected, only cause the projected image to
lighten.
The spacing of the interference fringes (/2), and therefore the
wavelength , can be measured from the height d of the projected image and the number N of fringes it contains, using
the equation
= 2
s1
s1 s2
where
=
d
N1
as shown by Fig. 3.
The sound propagation velocity is obtained from
c=·f
where f is the ultrasonic frequency.
Table 1
Theory and evaluation
Fig. 2 shows the relationship between variations in sound pressure p and the location x for four phases of a stationary wave.
The refractive index of the liquid also changes because of the
pressure variations, and the change in refractive index n can
be regarded as proportional to the pressure variation p.
In phases t = 0 and t = 12 T (where T is the vibration period),
well-defined interference fringes occur, spaced apart by /2.
Liquid
N
d
mm
a
mm
l
mm
c
m >s
¢c
m >s
q
°C
Glycerol
alcohol (ethanol)
Water (dist.)
Common salt
solution
(saturated)
12
20
19
47.5
48.5
57.0
3.65
2.31
2.85
2.37
1.50
1.85
1900
1200
1480
20
12
14
25
25
25
17
55.5
3.47
2.25
1800
20
25
Table 1, summarises typical examples of measurements.
The distances are:
s1’ = 50 cm
s1 = 48 cm
s2 = 148 cm
The light passing through the liquid is deflected into the vibration nodes in the regions where there is a considerable local
variation of the refractive index, whereas in the antinode areas
it is hardly deflected at all. The vibration nodes thus appear as
dark bands and the antinodes as light bands in the central
projection.
f = 800 kHz is used as the ultrasonic frequency.
Fig. 3: Path of the rays in the central projection.
Fig. 4: Image of a screen.
2
P2151000
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.5.10
-00
Optical determination of velocity of sound in liquids
The standard error is caluclated in accordance with the law of
error propagation, the individual error values being estimated
as:
s1
s2
d
f
=
=
=
=
Bibliography
* L. Bergmann, Der Ultraschall
(Ultrasonics), Hirzel Verlag
** Handbook of Chemistry and Physics,
The Chemical Rubber Co.
3 mm
3 mm
0.3 mm
5 kHz (see Operating Instructions for the
Ultrasonic Generator).
Remark
Relationship between temperature and sound velocity:
Liquid
Glycerol+
Ethanol
Water (Dist).
+
q
°C
c
m>s
¢c
¢q
m>s °C
Source
20
25
20
25
25
25
1923
1904
1180
1207
1497
1498
– 1.8
– 2.2
– 3.6
–4
+ 2.5
+ 2.4
*
**
*
**
*
**
As glycerol is hygroscopic, smaller values are often found
for a glycerol which has been allowed to stand.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2151000
3
LEP
1.5.10
-00
4
Optical determination of velocity of sound in liquids
P2151000
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
Mechanics
Mechanical Vibration, Acoustics
Temperature dependence of the Velocity of sound in liquids 1.5.12-00
What you can learn about …
Wavelength
Frequency
Velocity of sound in liquids
Compressibility
Density
Ultrasonics
Piezoelectric effect
Piezoelectric ultrasonic
transducer
Principle:
Sound waves are radiated into a liquid by an ultrasonic transmitter and
detected with a piezoelectric transducer. The wavelength of the sound
is found by comparing the phase of
the detector signal for different
sound paths and, when the frequency is known, the velocity of sound as
a function of the temperature of the
liquid is determined.
What you need:
Ultrasonic pickup
13920.00
1
Ultrasonic generator
13920.99
1
Sliding device, horizontal
08713.00
1
Optical profile bench, l = 600 mm
08283.00
1
Base for optical profile bench, adjustable
08284.00
2
Slide mount for optical profil bench, h = 30 mm
08286.01
1
Swinging arm
08256.00
1
Insulating support
07924.00
1
Immersion thermostat TC10
08492.93
1
Accessory set for TC10
08492.01
1
Bath for thermostat, Makrolon
08487.02
1
Laboratory thermometers, -10...+100°C
38056.00
1
Oscilloscope 30 MHz, 2 channels
11459.95
1
Support rod, stainless steel 18/8, l = 100 mm
02030.00
2
Right angle clamp -PASS-
02040.55
2
Universal clamp with joint
37716.00
1
Screened cable, BNC, l = 750 mm
07542.11
2
Adapter BNC socket/4 mm plug pair
07542.27
1
Glycerol, 250 ml
30084.25
1
Water, distilled 5 l
31246.81
1
Connecting cable, 4 mm plug, 32 A, red, l = 10 cm
07359.01
1
Slide mount
08286.00
1
Velocity of sound in water as a function of the temperature.
Complete Equipment Set, Manual on CD-ROM included
Temperature dependence of the Velocity
of sound in liquids
P2151200
Tasks:
The wavelength is found from the
phase position of the sound pickup
signal relative to the generator signal as a function of the sound path
and the velocity of the sound is
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
determined when the ultrasonic frequency is known. The measurement
is made for water and glycerol as the
temperatures of the liquids are
changed step-by-step.
Laboratory Experiments Physics 71
LEP
1.5.12
-00
Temperature dependence of the velocity of sound in liquids
Related topics
Wavelength, frequency, velocity of sound in liquids, compressibility, density, ultrasonics, piezoelectric effect, piezoelectric
ultrasonic transducer.
Principle
Sound waves are radiated into a liquid by an ultrasonic transmitter and detected with a piezoelectric transducer. The wavelength of the sound is found by comparing the phase of the
detector signal for different sound paths and, when the frequency is known, the velocity of sound as a function of the
temperature of the liquid is determined.
Equipment
Ultrasonic pickup
Ultrasonic generator
Sliding device, horizontal
Optical profile bench l = 60 cm
Base f. opt. profile-bench, adjust.
Slide mount f. opt. pr.-bench, h = 30 mm
Swinging arm
Insulating support
Immersion thermostat TC10
Accessory set for TC10
Bath for thermostat, Makrolon
Lab thermometer, -10...+100°C
Oscilloscope, 30 MHz, 2 channels
Support rod, l = 100 mm
Right angle clamp -PASS-
11744.00
11744.93
08713.00
08283.00
08284.00
08286.01
08256.00
07924.00
08492.93
08492.01
08487.02
38056.00
11459.95
02020.00
02040.55
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
Universal clamp with joint
Screened cable, BNC, l = 750 mm
Adapter, BNC-socket/4 mm plug pair
Glycerol, 250 ml
Water, distilled, 5 l
Connecting cord, l = 100 mm, red
37716.00
07542.11
07542.27
30084.25
31246.81
07359.01
1
2
1
1
1
1
Tasks
The wavelength is found from the phase position of the sound
pickup signal relative to the generator signal as a function of
the sound path and the velocity of the sound is determined
when the ultrasonic frequency is known. The measurement is
made for water and glycerol as the temperatures of the liquids
are changed step-by-step.
Set-up and procedure
Fig. 1 shows the experimental set-up. The sound radiating
face of the sound transmitter is wetted with glycerol or water
for better acoustic coupling and lies flat against the wall of the
bath vessel. In order to avoid standing waves due to sound
reflection, the wall of the vessel opposite to the sound transmitter is covered with a sound-absorbing material such as
foam material or crumpled paper.
The ultrasonic generator is set to sine wave operation. The
oscilloscope is triggered internally via channel 1 by means of
the generator monitoring signal. The sound frequency is found
with the oscilloscope which is connected to the ‘Synchr.’
Fig. 1: Experimental set-up: Temperature dependence of the Velocity of sound in liquids.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2151200
1
LEP
1.5.12
-00
Temperature dependence of the velocity of sound in liquids
generator output. The pickup and monitoring signals are set in
phase on the screen by moving the sound pickup and adjusting the phase control on the generator. The sound pickup is
moved from this starting position and the wavelength is determined from the distance l through which it has been moved
and the number n of inphase transition points traversed in the
process.
Fig. 2: Velocity of sound in water as a function of the temperature.
In order to obtain an interferencefree signal it is recommended
to connect the thermostat heating coil to the oscilloscope
earth socket with the crocodile clip.
The experiment is carried out with water and glycerol.
Theory and evaluation
Provided that the oscillatory process is an adiabatic one, the
relationship
c
1
B r · bad
(1)
where is the density and ad the adiabatic compressibility, is
obtained for the velocity of sound in liquids.
The change of the velocity of sound with temperature is in the
main determined by the temperature dependence of the compressibility.
In all liquids with the exception of water the compressibility
increases and the density decreases as the temperature rises.
The velocity of sound decreases approximately linearly as the
temperature rises. Water occupies a special position amongst
liquids; the compressibility is reduced initially as the temperature rises to a minimum of approx. 60°C and only then increases.
The velocity of sound in water therefore has a positive temperature coeffizient initially and, taking into account the density,
which becomes lower as the temperature rises, reaches a
maximum value of 1557 m/s at 74°C. Above this temperature
the velocity of sound decreases.
When there is a change of spacing l between the sound
transmitter and the pickup relative to the starting position
(relative phase = 0), the phase of the received signal is
shifted relative to the transmitted signal by
¢£ ¢l
·2p .
l
(2)
When the spacing is further changed, the signals come into
coincidence again when
l = n · ; n = 1, 2, . . .
(3)
From Eq. (2) and (3) the wavelength can be found to be
l
¢l
¢l
·2p
.
¢£
n
(4)
In Figs. 2 and 3 the velocities of sound found for water and
glycerol in accordance with Eq. (4) and (5) are represented as
a function of the liquid temperature.
In the measurement example the wavelength of sound for a
temperature of the liquid was determined from three separate
measurements with the detector moved through 5 wavelengths each time. The error of the mean value is c = ±4 m/s
for water and c = ± 7 m/s for glycerol.
The measurement example yields a maximum velocity of
sound in the case of water of cmax = (1554 ± 4) m/s at a liquid
temperature of = 72°C.
Note
The liquid in the region of the acoustic field is heated up by
ultrasonic absorption. The measurements should therefore be
made with as small a sound amplitude as possible. Attention
is also to be paid to thorough mixing of the bath.
The sound wavelength is thus shown to be the slope of the
regression straight lines, if the displacement of the detector l
is plotted as a function of the number n. The phase velocity is
obtained with the sound frequency f:
c = · f.
2
P2151200
(5)
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.5.12
-00
Temperature dependence of the velocity of sound in liquids
Fig. 3: Velocity of sound in glycerol as a function of the temperature.
Velocities of sound with temperature coefficient
Liquid
Water
(dist)
Glycerol*
q
°C
c
m>s
¢c
¢q
m>s °C
Source
25
25
20
25
1497
1498
1923
1904
+ 2.5
+ 2.4
– 1.8
– 2.2
1)
2)
1)
2)
* Since glycerol is hygroscopic, a lower velocity of sound is
often measured for stale glycerol.
Bibliography
1) L. Bergmann, Der Ultraschall
(Hirzel Verlag)
2) Handbook of Chemistry and Physics
(The Chemical Rubber Co.)
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2151200
3
LEP
1.5.12
-00
4
Temperature dependence of the velocity of sound in liquids
P2151200
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH • 37070 Göttingen, Germany