LEP1514 00Absorption of ultrasonic in air

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:

  The change in sound pressure intensity as a function of the distance from the source of sound.

  1 What you need: Complete Equipment Set, Manual on CD-ROM included Absorption of ultrasonic in air P2151400

  1 Connecting cord, l = 50 cm, blue 07361.04

  2 Connecting cord, l = 50 cm, red 07361.01

  2 Slide mount f. opt. profile-bench, h = 80 mm 08286.02

  1 Base f. opt. profile-bench, adjust. 08284.00

  1 Optical profile-bench, l = 150 cm 08281.00

  Sound needs a material medium with which it can enter into reciprocal ac- tion for its propagation, whereby a loss of energy occurs. The amplitude, and so also the intensity, decreases along the propagation path.

  1 Ultrasonic receiver on stem 13902.00

  1 Ultrasonic transmitter on stem 13901.00

  1 Power supply f. ultrasonic unit, 5 VDC, 12 W 13900.99

  Ultrasonic unit 13900.00

Tasks:

  4. Verify that the emitted wave is a spherical wave near to the trans- mitter.

  3. Confirm the law of absorption and determine the absorption coeffi- cient.

  2. Plot linear and logarithmic graphs of the values of the sound intensi- ty as a function of the distance.

  1. Move an ultrasonic receiver along the direction of propagation of a sound wave to measure the sound intensity as a function of the dis- tance from the source of the sound.

  1 Digital multimeter 07134.00

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  2 Slide mount f. opt. profile-bench, h = 80 mm 08286.02

  Set up the experiment as shown in Fig. 1. Adjust the transmit- ter 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 pro- portionality 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 amplifica- tion.

  Set-up and procedure

  4. Verify that the emitted wave is a spherical wave near to the transmitter.

  3. Confirm the law of absorption and determine the absorption coefficient.

  2. Plot linear and logarithmic graphs of the values of the sound intensity as a function of the distance.

  1. Move an ultrasonic receiver along the direction of propaga- tion of a sound wave to measure the sound intensity as a function of the distance from the source of the sound.

  1 Tasks

  1 Connecting cord, l = 50 cm, blue 07361.04

  2 Connecting cord, l = 50 cm, red 07361.01

  1 Base f. opt. profile-bench, adjust. 08284.00

  Longitudinal waves, plane waves, spherical waves, propaga- tion of sound waves, sound pressure, alternating sound pres- sure, sound intensity, absorption coefficient of ultrasonic waves, law of absorption.

  1 Optical profile-bench, l = 150 cm 08281.00

  1 Digital multimeter 07134.00

  1 Ultrasonic receiver on stem 13902.00

  1 Ultrasonic transmitter on stem 13901.00

  1 Power supply f. ultrasonic unit, 5 VDC, 12 W 13900.99

  Ultrasonic unit 13900.00

  Equipment

  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.

  Principle

  Fig.1: Experimental set-up

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  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 measure- ment 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 measure- ment 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.

Should a loudspeaker diaphragm, for example, vibrate with the frequency f, then the particles in the air in front of it will be

  Note:

  ⫽ 1.3 m

  2

  x

  2

  ⫺ x

  1

  ⫺ 1

  = 0.273 or I/I = 0.0743. a ⫽ ln U

  I 1x2 ⫽ I102e

  ⫺ 2ax

  r p 1x2 ⫽ p102e

  ⫺ ax

  ⬵ ⬵

  Fig.2: Logarmithic representation of the receiver voltage U as a function of the distance x from the source of sound.

  1 ⫺ ln U

• 1

  it follows from equations (1) and (2), after a distance of 1 m, that: p/p

  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.

  (3) With a = 1.3 m

  2 ).

  In this experiment, however, only the alternating sound pres- sure and not the sound intensity is measured. This is propor- tional to the square of the alternating sound pressure (I r p

  2 .

  . The sound intensity I acting on a unit of area therefore changes by 1/x

  2

  (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 x

  is true for the sound intensity, it follows that the weakening of the sound intensity is given by:

  2

  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 p

  With plane sound waves, the law of absorption is valid for the weakening of the alternating sound pressure p: (1)

  excited to vibrate with the same frequency. This periodic par- ticle displacement will cause the density of the air, and so the air pressure, to be periodically changed at this point (alternat- ing 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 alter- nating sound pressure becomes. This is caused by internal friction in air and temperature equalization between positions of compression (higher temperature) and rarefaction (lower temperature).

  Longitudinal sound waves require a medium for their propa- gation, in contrast to transverse electromagnetic waves which can also propagate in a vacuum.

  Theory and evaluation

  A progressive decrease in the sound pressure of 1/x- is there- fore 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 trans- mitter 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:

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  On conversion to the decibel units that are technically com- mon, then the weakening L is: p

  I (4)

  L ⫽ 20 lg ⫽ 10 ⫽ ⫺ 11.3 dB>m p

  I 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 dis- tances 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 weak- ening 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

  1 the distance from the source of sound / . x

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