Mechanics
Mechanical Vibration, Acoustics
Absorption of ultrasonic in air 1.5.14-00
What you can learn about …
Longitudinal waves
Plane waves
Spherical waves
Propagation of sound waves
Sound pressure
Alternating sound pressure
Sound intensity
Absorption coefficient of
ultrasonic waves
Law of absorption
Principle:
Sound needs a material medium with
which it can enter into reciprocal
action for its propagation, whereby a
loss of energy occurs. The amplitude,
and so also the intensity, decreases
along the propagation path.
What you need:
Ultrasound operation unit
13900.00
1
Power supply 5 VDC/2.4 A with DC-socket 2.1 mm
13900.99
1
Ultrasonic transmitter
13901.00
1
Ultrasonic receiver on stem
13902.00
1
Digital multimeter 2010
07128.00
1
Optical profile bench, l = 1500 mm
08281.00
1
Base for optical profile bench, adjustable
08284.00
2
Slide mount for optical profil bench, h = 80 mm
08286.02
2
Connecting cable, 4 mm plug, 32 A, red, l = 50 cm
07361.01
1
Connecting cable, 4 mm plug, 32 A, blue, l = 50 cm
07361.04
1
Complete Equipment Set, Manual on CD-ROM included
Absorption of ultrasonic in air
P2151400
The change in sound pressure intensity as a function of the distance from the
source of sound.
Tasks:
1. Move an ultrasonic receiver along
the direction of propagation of a
sound wave to measure the sound
intensity as a function of the distance from the source of the
sound.
2. Plot linear and logarithmic graphs
of the values of the sound intensity as a function of the distance.
3. Confirm the law of absorption and
determine the absorption coefficient.
4. Verify that the emitted wave is a
spherical wave near to the transmitter.
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
Laboratory Experiments Physics 73
LEP
1.5.14
-00
Absorption of ultrasonic in air
Related topics
Longitudinal waves, plane waves, spherical waves, propagation of sound waves, sound pressure, alternating sound pressure, sound intensity, absorption coefficient of ultrasonic
waves, law of absorption.
Principle
Sound needs a material medium with which it can enter into
reciprocal action for its propagation, whereby a loss of energy
occurs. The amplitude, and so also the intensity, decreases
along the propagation path.
Equipment
Ultrasonic unit
Power supply f. ultrasonic unit, 5 VDC, 12 W
Ultrasonic transmitter on stem
Ultrasonic receiver on stem
Digital multimeter
Optical profile-bench, l = 150 cm
Base f. opt. profile-bench, adjust.
Slide mount f. opt. profile-bench, h = 80 mm
Connecting cord, l = 50 cm, red
Connecting cord, l = 50 cm, blue
13900.00
13900.99
13901.00
13902.00
07134.00
08281.00
08284.00
08286.02
07361.01
07361.04
1
1
1
1
1
1
2
2
1
1
Tasks
1. Move an ultrasonic receiver along the direction of propagation of a sound wave to measure the sound intensity as a
function of the distance from the source of the sound.
2. Plot linear and logarithmic graphs of the values of the
sound intensity as a function of the distance.
3. Confirm the law of absorption and determine the absorption
coefficient.
4. Verify that the emitted wave is a spherical wave near to the
transmitter.
Set-up and procedure
Set up the experiment as shown in Fig. 1. Adjust the transmitter and the receiver to be at the same height on the optical
bench, with their longitudinal axes coincident. Connect the
transmitter, positioned at the head end of the optical bench, to
the TR1 diode socket of the ultrasonic unit and operate it in
continuous mode “Con“. Connect the receiver to the left BNC
socket (prior to the amplifier). Connect the signal received to
the analog output of the digital multimeter to have it displayed
subsequent to amplification and rectification. To ensure proportionality between the input signal and the analog output
signal, avoid operating the amplifier in the saturation range.
Should such a case occur and the “OVL“ diode light up,
reduce either the transmitter amplitude or the input amplification.
Fig.1: Experimental set-up
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P2151400
1
LEP
1.5.14
-00
Absorption of ultrasonic in air
It is purposeful to carry out two series of measurements. In the
first of these, in which the absorption of the ultrasonic wave in
air is to be examined (far field measurement), start measurement with a distance x between the transmitter and receiver
of x 40 cm, then increase this in steps of (5-10) cm. In the
second series, to examine for spherical wave characteristics
of the emitted wave (near field measurement), start measurement with a distance of x 10 cm between transmitter and
receiver, then increase this in 2 cm steps up to 40 cm.
Adjust the signal received to a maximum of 3.3-3.4 V at the
start of each measurement series.
Note:
The experimental results can be influenced by reflected
sound. Such interference can be avoided to a great extent by
installing the experimental set-up as far as possible away from
walls and cupboards. Reflections from the working surface on
which the set-up stands are particularly troublesome. They
can be reduced by laying sound-absorbing material, such as
sheets of foam or a cloth (woollen blanket), over the optical
bench between the emitter and the receiver. Further to this,
the person carrying out the experiment should not stand too
close to the measurement area when taking readings.
Theory and evaluation
Longitudinal sound waves require a medium for their propagation, in contrast to transverse electromagnetic waves which
can also propagate in a vacuum.
Should a loudspeaker diaphragm, for example, vibrate with
the frequency f, then the particles in the air in front of it will be
excited to vibrate with the same frequency. This periodic particle displacement will cause the density of the air, and so the
air pressure, to be periodically changed at this point (alternating sound pressure). The displaced particles will pass part of
their momentum onto their neighbouring particles, and they
will similarly excite their neighbouring particles. All particles
will vibrate about their fixed positions, while the momentum
moves on as a so-called sound wave. Further transmittance of
the momentum does not occur without loss, on the contrary,
the greater the distance from the source, the weaker the alternating sound pressure becomes. This is caused by internal
friction in air and temperature equalization between positions
of compression (higher temperature) and rarefaction (lower
temperature).
With plane sound waves, the law of absorption is valid for the
weakening of the alternating sound pressure p:
p1x2 p102e ax
Where p(0) is the initial amplitude of the alternating sound
pressure, p(x) is the amplitude at a distance x, and a is the
absorption coefficient, which only has a fixed value under
constant conditions and is dependent on the frequency, the
temperature, the degrees of freedom of the atoms/molecules
of the gas and their relative humidity. As I r p2 is true for the
sound intensity, it follows that the weakening of the sound
intensity is given by:
I1x2 I102 e 2ax
Fig. 2: Logarmithic representation of the receiver voltage U as
a function of the distance x from the source of sound.
(1)
(2)
When the wave emitted by the source of sound is a spherical
wave, and not a plane wave, and when the sound energy is
radiated over the whole solid angle, then the energy would be
evenly distributed over a spherical area that is proportional to
x2. The sound intensity I acting on a unit of area therefore
changes by 1/x2.
In this experiment, however, only the alternating sound pressure and not the sound intensity is measured. This is proportional to the square of the alternating sound pressure (I r p2).
A progressive decrease in the sound pressure of 1/x- is therefore to be expected.
At larger distances, spherical waves can be assumed to
approximate plane waves.
Fig. 2 shows a semi-logarithmic representation of the receiver
voltage U as a function of the distance x between the transmitter and receiver. It can be seen that in the region of the far
field (x > 0.7 m), with a satisfactory accuracy and under the
given experimental conditions (f = 40 kHz; T = 20°C and 50%
relative humidity), the measured values lie on a straight line of
slope:
a
ln U1 ln U2
1.3 m 1
x2 x1
(3)
With a = 1.3 m-1 it follows from equations (1) and (2), after a
distance of 1 m, that:
p/p0 = 0.273 or I/I0 = 0.0743.
2
P2151400
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.5.14
-00
Absorption of ultrasonic in air
On conversion to the decibel units that are technically common, then the weakening L is:
L 20 lg
p
I
10 11.3 dB>m
p0
I0
(4)
It can also be seen from Fig. 2 that for distances x < 0.7 m
(near field), the decrease in the intensity cannot be explained
by absorption in air alone.
When it is assumed that spherical waves emanate from the
source of sound, and the air absorption over these short distances is disregarded, then the intensity must be subject to a
reduction of 1/x (see above). As is to be seen in Fig. 3, this is
the case. Near to the source, the spherical sound propagation
is mainly responsible for the decrease in intensity. It is not until
it has travelled a longer distance that the spherical waves can
be approximately represented by a plane wave, and the weakening can be almost exclusively attributed to the absorption
behaviour of the air.
Fig.3: The receiver voltage U as a function of the reciprocal of
the distance from the source of sound 1/x.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
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Absorption of ultrasonic in air
P2151400
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen