In a "typical" side scan sonar system, the beam is narrow in the horizontal plane and broad in the vertical plane. In a typical single beam 100 kHz system this would be 1 degree in the horizontal and 40 degrees in the vertical and for a 500 kHz system .2 degrees in the horizontal and 40 degrees in the vertical.
In the above figure, the pattern is determined be measuring the output of the sonar with a clear hydrophone at a range of angles. It is clear that the beam has a very sharp central axis with weak side lobes. The standard definition of beamwidth is the angular spread between the -3dB, or half power, points.
Note that the transducer is actually radiating sound from both its front and back faces. Transducer designers try to minimize radiation out the back of the transducer, but some "back radiation" will always remain.
The receiving beam pattern of the transducer is the same as the transmitting pattern. This is a reflection of the reciprocity theorem, which states that the transmit and receive responses of a transducer will be the same. For active sonars, then, the effective two-way beamwidth is narrower than that just noted for one-way travel.
The narrow beamwidth is not only necessary for achieving a sharp image of the seafloor, but it helps in rejecting noise from extraneous sources. In the ocean, noise will be reaching the sonar from all directions but the response to all this disturbance will be controlled by the beam pattern.
Thus most of the noise will be rejected, improving the sonar performance.
The vertical beamwidth of a typical 100 kHz sonar is very different than the horizontal. Observe that the fall off after the -3dB points are reached is more gradual than was the case with the horizontal pattern. This explains why signals are received from the waters surface and from the sea floor beneath the sonar. The main axis of the beam is typically angled 10 degrees down from the horizontal, so that most of the energy is directed toward the sea floor where it is needed. The trick to good transducer design is to minimize the nulls in this beam pattern. If there were sharp nulls then the sound reaching the bottom would be very uneven and we would see lite bands on the record where the echoes are very weak.