their sensitivity, and their suitability for use with fiber optic cables. Fiber optic sensors which utilize amplitude modulation of the light(microbend transducers)are also being developed. Parametric transd The nonlinear interaction of sound waves can be used to produce highly directional sound sources with no side lobes and small physical apertures. In spite of their inherent inefficiency, substantial source levels can be achieved and such"parametric sonars"have found a number of underwater applications. Parametric receivers have also been investigated but practical applications have yet to be found. Carbon Microphones Carbon microphones utilize a change in electrical resistance with pressure and are used extensively in telephones. 46.3 Sensitivity and Source level A microphone or hydrophone is characterized by its free-field voltage sensitivity, M, which is defined as the ratio of the output voltage, E, to the free-field amplitude of an incident plane acoustic wave. That is, for an incident wave which in the absence of the transducer is given by P=P0cos(k·R-ot) (46.1) Mis defined by M=E/Po (46.2) In general, M will be a function of frequency and the orientation of the transducer with respect to the wave vector k(i.e, the direction of incidence of the wave). Thus, for a given frequency, M is proportional to the directivity of the transducer. It is usually desirable for a microphone or hydrophone to have a flat(i. e, frequency dependent)free-field voltage sensitivity over the broadest possible range of frequencies to assure fidelity of the output electrical signal. A loudspeaker or projector is characterized in a similar manner by its transmitting current response, S, whic is defined as the ratio of the acoustic source level to the driving current, I In the farfield of a transducer the acoustic pressure is a spherical wave which can be expressed as P(R)=P(0, O)(Ro/R)cos(kR-ot (46.3) where e and o are elevation and azimuth angles and Ro an arbitrary reference distance(usually 1 meter ). Pi (e, o)is defined as the source level. Thus S is given by S=P6,@)I (46.4) which is a function of 8 and o and the frequency a For high-fidelity sound reproduction S should be as flat as possible over the broadest possible bandwidth. For some purposes, however, such as ultrasonic cleaning or long-range underwater acoustic propagation, fidelity is unnecessary and high Q resonant transducers are employed to produce high-intensity sound over a narrow bandwidth 46.4 Reciprocity Most conventional transducers are reversible, that is, they can be used as either sources or receivers of sound (a carbon microphone and a fiber optic hydrophone are examples of transducers which are not reversible).A transducer is said to be linear if the input and output variables are linearly proportional (hot-wire microphones c 2000 by CRC Press LLC© 2000 by CRC Press LLC their sensitivity, and their suitability for use with fiber optic cables. Fiber optic sensors which utilize amplitude modulation of the light (microbend transducers) are also being developed. Parametric Transducers The nonlinear interaction of sound waves can be used to produce highly directional sound sources with no side lobes and small physical apertures. In spite of their inherent inefficiency, substantial source levels can be achieved and such “parametric sonars” have found a number of underwater applications. Parametric receivers have also been investigated but practical applications have yet to be found. Carbon Microphones Carbon microphones utilize a change in electrical resistance with pressure and are used extensively in telephones. 46.3 Sensitivity and Source Level A microphone or hydrophone is characterized by its free-field voltage sensitivity, M, which is defined as the ratio of the output voltage, E, to the free-field amplitude of an incident plane acoustic wave. That is, for an incident wave which in the absence of the transducer is given by P = P0 cos(k · R – wt) (46.1) M is defined by M = E /P0 (46.2) In general, M will be a function of frequency and the orientation of the transducer with respect to the wave vector k (i.e., the direction of incidence of the wave). Thus, for a given frequency, M is proportional to the directivity of the transducer. It is usually desirable for a microphone or hydrophone to have a flat (i.e., frequency independent) free-field voltage sensitivity over the broadest possible range of frequencies to assure fidelity of the output electrical signal. A loudspeaker or projector is characterized in a similar manner by its transmitting current response, S, which is defined as the ratio of the acoustic source level to the driving current, I. In the farfield of a transducer the acoustic pressure is a spherical wave which can be expressed as P(R) = Ps (q, f)(R0/R) cos(kR – wt) (46.3) where q and f are elevation and azimuth angles and R0 an arbitrary reference distance (usually 1 meter). Ps (q, f) is defined as the source level. Thus S is given by S = Ps (q, f)/I (46.4) which is a function of q and f and the frequency w. For high-fidelity sound reproduction S should be as flat as possible over the broadest possible bandwidth. For some purposes, however, such as ultrasonic cleaning or long-range underwater acoustic propagation, fidelity is unnecessary and high Q resonant transducers are employed to produce high-intensity sound over a narrow bandwidth. 46.4 Reciprocity Most conventional transducers are reversible, that is, they can be used as either sources or receivers of sound (a carbon microphone and a fiber optic hydrophone are examples of transducers which are not reversible). A transducer is said to be linear if the input and output variables are linearly proportional (hot-wire microphones