DIRECTIVITY OF TRANSDUCERS 



these metals) is brought into a magnetic field parallel 

 to its length, its length is changed slightly.' 1 This 

 change of length is independent of the sign of the 

 field and may be either an increase or decrease, de- 

 pending on the nature of the material, its previous 

 treatment, the degree to which it was previously mag- 

 netized, and the temperature. This phenomenon is 

 reversible: in other words, if a previously magnetized 

 rod of nickel is stretched, the magnetization of the rod 

 is decreased; if the same rod is compressed, the mag- 

 netization is increased. 



If a coil of wire is now put around the rod, an emf 

 is induced in it by the changes in the magnetic flux 

 caused by the elastic deformation. In a similar man- 

 ner, changes in the rod's magnetization due to an ex- 

 ternal alternating current induce periodic oscilla- 

 tions in its length. e 



This simple magnetostriction transducer is, in ef- 

 fect, a rod of ferromagnetic material surrounded by a 

 coil. 



It should finally be pointed out that there are, in 

 addition to the reversible transducers which have 

 been considered, irreversible ones. In the carbon 

 microphone, for example, changes in pressure on a 

 diaphragm caused by an impinging sound field pro- 

 duce changes in the electrical resistance of contacts 

 between carbon particles and give rise to an alternat- 

 ing current, provided that a source of constant poten- 

 tial is present. 



2.2 



DIRECTIVITY OF TRANSDUCERS 



The variation with direction of the emitted sound 

 intensity, referred to the transducer acoustic axis,' is 

 called the directivity of the transducer on transmit- 

 ting. In a similar manner, the directivity of the trans- 

 ducer on receiving is defined as the variation of the 

 output voltage for a plane-wave sound of given in- 



d The fractional change in length is approximately ten parts 

 in a million tor fields up lo 1,000 gauss. 



<■ It is to be noted that, since the increase or decrease in length 

 of the magnetostrictive rod is independent of the sign of the 

 magnetic field, an originally unmagnetized rod vibrates al twice 

 the frequency of the impressed field, while a rod which has been 

 sufficiently magnetized by another constant (polarizing) field 

 vibrates at the impressed frequency. Maximum amplitude oc- 

 curs when the impressed and natural frequencies of vibration 

 coincide. 



'The transducer acoustic axis is arbitrarily selected, but is 

 usually chosen to be an axis of symmetry of the instrument, such 

 as the normal lo a plane vibrating diaphragm. 



TO ELECTRICAL 

 TERMINAL 



MAGNETOSTRICTIVE 

 ROD 



ELECTRICAL TERMINAL\_ 

 DIAPHRAGM^ 



Figure 5. Magnetostriction transducer. 



tensity incident in various directions with respect to 

 the axis. 



Directivity on transmitting results from the super- 

 position at a point in space of sound wavelets emitted 

 by different portions of the diaphragm, and conse- 

 quently having different amplitude and phase. On re- 

 ception the directivity is the result of the incidence 

 on different portions of the transducer diaphragm of 

 wavelets of sound which have, at the diaphragm, dif- 

 ferent amplitudes and phases depending on the orien- 

 tation of the diaphragm relative to their direction of 

 propagation. 



In general, the directivity, both on transmitting 

 and on receiving, is determined by the ratio of the 

 sound wave length to the diaphragm dimensions. E 

 For a plane piston diaphragm with dimensions large 

 compared to a wave length, the transmitted sound 

 field is, at large distances from the transducer, cen- 

 tered about the transducer acoustic axis, and the 

 sound is emitted in the form of a "searchlight" beam. 

 Conversely, on reception, the transducer is sensitive 

 only to sound signals incident in directions close to 

 and along the axis. Subsidiary maxima (side lobes) in 

 directions far from the axis usually are present. These, 

 however, are strongly dependent on the exact velocity 

 distribution along the diaphragm, and are customar- 

 ily small compared with the main or searchlight 

 beam. 1 ' If the wave length is large compared to the 

 diaphragm dimensions, the sound is emitted uni- 

 formly in all directions. In this case, the transducer 

 response on reception is independent of the direction 

 of sound incidence. An intermediate case is a "line" 



g Transducers obeying the reciprocity theorem (see Chapters 

 3. 4. and 5) have the same directivity on transmitting and on 

 receiving. 



li By constructing a transducer with a plane diaphragm and 

 with a velocity distribution which is greatest at the center of the 

 diaphragm and which decreases toward the edges (shading), it is 

 possible to obtain a directivity distribution with side lobes much 

 smaller than in the case of a constant velocity distribution; the 

 width of the main beam is, however, larger in this case. 



