Download TEP 1.5.14 -00 Absorption of ultrasound in air TEP 1.5.14

TEP
1.5.14
-00
Absorption of ultrasound 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, 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. This can be detected by measuring the signal of a receiver.
Material
1 Ultrasonic unit
1 Power supply f. ultrasonic unit, 5 VDC, 12 W
1 Ultrasonic transmitter on stem
1 Ultrasonic receiver on stem
2 Slide mount f. opt. profile-bench, ℎ = 80 mm
13900-00
13900-99
13901-00
13902-00
08286-02
2
1
1
1
1
Base f. opt. profile-bench, adjustable
Optical profile-bench, 𝑙 = 150 cm
Digital multimeter
Connecting cord, red, 𝑙 = 500 mm
Connecting cord, blue, 𝑙 = 500 mm
08284-00
08281-00
07128-00
07361-01
07361-04
Fig. 1: Experimental set-up
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TEP
1.5.14
-00
Absorption of ultrasound in air
Tasks
1. Confirm the law of absorption and determine the absorption coefficient for the far-field.
2. Verify that the emitted wave is a spherical wave near to the transmitter.
Set-up
Perform the experimental set-up according to Fig. 1. Adjust the transmitter and the receiver to be at the
same height on the optical bench, their longitudinal axes coincident.
Connect the transmitter, positioned at the head end of the optical bench, to the TR1 diode socket on the
right of the ultrasonic unit and operate it in continuous mode “cont”. Connect the receiver to the left BNC
socket (prior to the in-build amplifier). Connect the signal received at the analog output subsequent to
amplification and rectification to the digital multimeter to measure the signal’s amplitude (i.e. voltage).
To avoid the distortion of measurements due to sound reflections install the experiment as far away from
cupboards and walls as possible. Especially do not set up the optical bench exactly perpendicular to any
surfaces. Reflections from the working surface on which the set-up stands can be reduced by using any
sound-absorbing material (e.g. sheets of foam, cloth, woolen blanket) between transmitter and receiver.
Furthermore no person should stand in the direct vicinity of the experiment when the measured values
are read from the display of the multimeter.
Procedure
To avoid a change of settings during measurements it is beneficial to carry out one series of measurements for each task independently.
1. Task: Start the measurement at a distance of 40 cm between transmitter and receiver, then increase the distance in steps of 5 cm up to a maximum of approximately 130 cm.
2. Task: Start the measurements with a distance of 10 cm and increase it in steps of 2 cm up to a
maximum of 40 cm.
At the start of each measurement series adjust the received signal in such manner that the multimeter
reads a maximum of 3.3 to 3.4 V at a measuring range of 20 V. Do not change amplification or signal
amplitude for the rest of the measurements. To ensure proportionality between input signal and the analog output signal, avoid operating the amplifier in the saturation range. Should such a case occur and the
“OVL” diode lights up, adjust the transmitter amplitude and the input amplification. You have to repeat
the measurements prior to these adjustments.
Theory
Longitudinal sound waves require a medium for their propagation, in contrast to transverse electromagnetic waves which can also propagate in vacuum. Should a loudspeaker diaphragm, for example, vibrate
with the frequency 𝜈, 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. All particles will vibrate around their fixed positions
while the momentum moves on as the so-called sound wave. Further transmittance 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 local temperature equalization between
areas of compression (higher temperature) and rarefaction (lower temperature).
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TEP
1.5.14
-00
Absorption of ultrasound in air
From a point source emitting into the whole solid angle the propagation of the longitudinal wave behaves
like a growing sphere. In that case, the amplitude of the wave is directly proportional to the energydensity on the surface of the sphere where the total energy of the growing surface is constant. So we obtain for one chosen wave of energy 𝐸 and surface area 𝐴 = 𝜋𝑟 2 the energy density
𝜚 = 𝐸⁄ 2 = 𝐼
𝜋𝑟
which gives the intensity of this propagating wave.
In this experiment the sound pressure 𝑝 is regarded and we obtain
(1)
𝑝 ∝ 1⁄𝑟 with 𝐼 ∝ 𝑝2
(2)
as the pressure squared is proportional to the sound intensity. This reduction of intensity (or pressure)
with distance is also called “geometric dilution” as it results purely from the growth of the geometric surface of the sphere transporting the energy.
At larger distances, spherical waves can be regarded as approximate plane waves. For plane sound
waves, the law of absorption describes the weakening of the alternating sound intensity 𝐼(𝑟) as follows.
𝐼(𝑟) = 𝐼0 𝑒 −2𝛼 𝑟
(3)
There 𝐼0 is the initial intensity of the sound wave, 𝐼(𝑟) is the intensity at distance 𝑟 and 𝛼 is the absorption coefficient which depends on frequency, temperature, the degrees of freedoms of the atoms and
molecules in the gas and the relative humidity.
From the proportionality between sound pressure and intensity follows
𝑝(𝑟) = 𝑝0 𝑒 −𝛼 𝑟 .
(4)
For technical purposes the decibel units have been introduced to measure logarithmic signal gains and
losses. This weakening 𝐿𝑑𝐵 is calculated by
𝐼
𝑝
0
0
𝐿𝑑𝐵 = 10 log (𝐼 ) = 20 log (𝑝 ) .
(5)
Evaluation and results
In the following the evaluation of the obtained values is described with the help of example values. Your
results may vary from those presented here.
Task 1: Confirm the law of absorption and determine
the absorption coefficient for the far-field.
To determine the absorption coefficient from the
measurements it is convenient to plot the measured
voltage over the distances with semi-logarithmic scale
as can be deduced from eq. (4). In Fig. 2 can be
seen, that the absorption law is only valid for distances greater than ∼ 0.6 m. For smaller distances the
measurements deviate significantly from the fitted
curve. From the slope of the semi-logarithmic representation 𝛼 can be directly determined with satisfactory accuracy and under the given experimental conditions (𝜈 = 40 kHz , 𝑇 = 20°C , 50% relative humidity)
for the far-field region as 𝛼 ≃ 2.1 m−1 .
This is in good agreement with literature values in the
range of 1 to 3 m-1 for similar experimental conditions
(e.g. A. Valdišauskas, L. Jakevičius, Ultragarsas
Fig. 2: Semi-logarithmic plot of receiver voltage 𝑼 over
no. 1, issue 50, 2004, p. 46-49).
distance 𝒍 between transmitter and receiver.
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Absorption of ultrasound in air
Task 2: Verify that the emitted wave is a spherical
wave near to the transmitter.
Assuming spherical waves emanating from the source
of sound and disregarding the absorption due to the
medium the signal intensity must be subject to the reduction of 1⁄𝑙 (see eq. 2). In Fig. 3 the receiver voltage 𝑈 shows a linear dependence of the reciprocal
distance 𝑙 with a very strong correlation of
𝑅=0.99997. Thereby the spherical nature of the sound
wave near the emitter is confirmed.
Fig. 3: Receiver voltage 𝑼 as a function of the reciprocal
distance 𝟏⁄𝒍 from the source of sound.
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