a and 4 b here a positive sound pressure lobe 42 and a negative sound pressure lobe 44 still exist the desired null direction was u03b8 65 u00b0 u2245 1 134 radians to point the null in this direction the amplitudes should again be equal and opposite in sign but the phase difference between the sources should now be maintained at u03b4 u2212 d c u03c9cos 1 134 note that the phase difference is a function of the frequency in the particular example of fig4 the frequency is taken as u03c9 2 ue89e ue89e u03c0 1000 ue89e ue89e hz the separation of the acoustic sources is d 12 mm the speed of sound is c 344 m s yielding a phase difference of it is apparent from fig4 a and 4 b that the maximum still occurs at 0 degrees but the zero or null now occurs at 65 degrees in fact the angle of no transmission can be altered to any angle between 0 and 180 degrees for example fig5 a and 5 b depict a sound directivity pattern for which there will be no transmission behind one end of a loudspeaker by moving the null direction 50 to 0 degrees for any particular frequency then if the signal to one source is time delayed with respect to the other source the null plane becomes a null surface with an asymptote in a particular direction if the desired angle of the null is known the invention can be used to point or steer the null in that direction alternatively by using acoustic sensors such as microphones the null surface may be optimized adaptively for a particular direction that is the null surface can be steered to adaptively follow a microphone with.