3B Scientific Test Vessel - Handbuch (Seite 9)

9
• For precise measurements, also measure the tem-
perature and include this in the comparison.
• When using high voltage at any frequency and when
the transducer is properly aligned, at least 3 orders
of diffraction should be visible.
• The projection experiment is much more sensitive
to the angle of the transducer than the refraction
experiment. Thus for this experiment the conditions
for generating standing waves need to be adhered
to more precisely.
3.2 Debye-Sears effect
The wavelength of the ultra-
sonic waves in the Debye-Sears
experiment (photo left, 4 MHz
in water) can be determined
for various different test fluids
(water, glycerine, cooking oil).
This means measuring the dis-
tance s between the ultra-
sound transducer and the re-
fracted image. Then the num-
ber of orders of refraction N
and distance between the -nth
and +nth bands x can be de-
termined. Since the wavelength of the laser light
λ
L
is
known then:
(1)
λ
λ
s
L =
2N s
x
gives the ultrasonic wavelength
λ
s
. The individual vari-
ables can be calculated as in the following diagram.
The ultrasonic frequency n is measured at the monitor
socket. Then the speed of sound c in the fluid is given
by:
(2) c =
λ
s
ν
Example results:
1. Water
v = 4 MHz, s = 2.90 m, N = 4, x = 4.1 cm,
λ
L
= 650 nm
therefore:
λ
s
= 367.8 µm, c = 1471 m/s
(Table: 1480 m/s at 20°C)
2. Glycerine
v = 4 MHz, s = 2.90 m, N = 2, x = 1.6 cm,
λ
L
= 650 nm
therefore:
λ = 471.2 µm, c = 1885 m/s
(Table: 1900 m/s at 25°C)
3.3 Projection of standing ultrasonic waves
Direct projection of ultrasonic waves can be an inter-
esting extension to
the experiment. The
sound wave is pro-
jected by inserting a
convex lens into the
laser beam so that
the beam is di-
verged. The density
variations in the
standing wave then
appear as light and
dark regions on the
projection screen
(see photograph
right). To determine
the wavelength from
the diffraction im-
age and the geometry involved, as well as the focal length
f of the lens in air (100 mm in this case), corrections due
to the glass walls of the vessel and the test fluid also
need to be considered.
The light refraction method as described in 3.2 is thus
better suited for calculating the wavelength precisely.
The precise equation for
λ
s
in the projection experi-
ment is:
(3)
λ
s
x
N
f
g
n
a
n
s f
g g
n
a a
n
= =
− −
− −
+
−
+ 





2
1
g
1
FL
1 2
g
1 2
FL
The distance a
1
between the glass wall towards the lens
and the distance a
2
can be approximated as half the
internal width of 9.6 cm. The thickness of the glass g
1
and g
2
is about 4 or 5 mm. The refractive indices n
FL
for
the test fluid and n
g
for the glass may be measured or
taken from tables.
x
N = 5
N = 3
N = 4
N = 2
N = 1
N = 0
N = 6
s
g
1
g
2
a
1
a
2
λ
L
λ
s
s
x
N = 3
N = 2
N = 0
N = 1
N = -1
N = -2
N = -3