The combination of rays is also sufficient in practice if the cardioid surface is replaced, by a spherical one.
The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a node within the circle; the particular case when b= 2a is known as the trisectrix.
This may be readily accomplished geometrically or analytically, and it will be found that the envelope is a cardioid, i.e.
The two ' bulbs ' shown here are directly attached to the main cardioid.
Examples A classic style of microphone for speech recording in interview situations is a hand-held dynamic cardioid microphone.