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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, β = 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, π = 150 cm Digital multimeter Connecting cord, red, π = 500 mm Connecting cord, blue, π = 500 mm 08284-00 08281-00 07128-00 07361-01 07361-04 Fig. 1: Experimental set-up www.phywe.com P2151400 PHYWE Systeme GmbH & Co. KG © All rights reserved 1 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 βcontβ. 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 signalβs 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 βOVLβ 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 π, 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). 2 PHYWE Systeme GmbH & Co. KG © All rights reserved P2151400 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 πΈ and surface area π΄ = ππ 2 the energy density π = πΈβ 2 = πΌ ππ which gives the intensity of this propagating wave. In this experiment the sound pressure π is regarded and we obtain (1) π β 1βπ with πΌ β π2 (2) as the pressure squared is proportional to the sound intensity. This reduction of intensity (or pressure) with distance is also called βgeometric dilutionβ 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 πΌ(π) as follows. πΌ(π) = πΌ0 π β2πΌ π (3) There πΌ0 is the initial intensity of the sound wave, πΌ(π) is the intensity at distance π and πΌ 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 π(π) = π0 π βπΌ π . (4) For technical purposes the decibel units have been introduced to measure logarithmic signal gains and losses. This weakening πΏππ΅ is calculated by πΌ π 0 0 πΏππ΅ = 10 log (πΌ ) = 20 log (π ) . (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 βΌ 0.6 m. For smaller distances the measurements deviate significantly from the fitted curve. From the slope of the semi-logarithmic representation πΌ can be directly determined with satisfactory accuracy and under the given experimental conditions (π = 40 kHz , π = 20°C , 50% relative humidity) for the far-field region as πΌ β 2.1 mβ1 . This is in good agreement with literature values in the range of 1 to 3 m-1 for similar experimental conditions (e.g. A. ValdiΕ‘auskas, L. JakeviΔius, Ultragarsas Fig. 2: Semi-logarithmic plot of receiver voltage πΌ over no. 1, issue 50, 2004, p. 46-49). distance π between transmitter and receiver. www.phywe.com P2151400 PHYWE Systeme GmbH & Co. KG © All rights reserved 3 TEP 1.5.14 -00 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 1βπ (see eq. 2). In Fig. 3 the receiver voltage π shows a linear dependence of the reciprocal distance π with a very strong correlation of π =0.99997. Thereby the spherical nature of the sound wave near the emitter is confirmed. Fig. 3: Receiver voltage πΌ as a function of the reciprocal distance πβπ from the source of sound. 4 PHYWE Systeme GmbH & Co. KG © All rights reserved P2151400