Electronic – Continuity test buzzer sounding continuously

Sharp tips are able to poke through insulation, whether it be wire insulation, or the coatings on circuit boards. They are also handy if you need to stick it down into a connector between the wire and the body of the connector. Also, as parts get smaller, you need sharp tips to be able to contact one pin of an I.C. without shorting to the others. Lastly, a sharp point isn't as likely to slip when you look away to read the meter. The flow of current from a point isn't meaningful here because that's only relevant when there's an air gap present.

The response time of the continuity "beep" is important. If you want to test a number of contacts--especially if you're hunting for that one signal in a large set--you want to be able to do it fast. Otherwise, you have to touch the wire, then wait, then move on. It's very unsettling when doing continuity checks to have to rely on the notion that "it didn't beep, therefore there's no continuity". Did I wait long enough? Did I actually contact the wire? This is why you start by touching the meter leads together to be sure the beeper is actually working.

The continuity function is designed to give an audible indication of resistance that is less than some threshold value.

To be useful, it will be designed to respond much more quickly than the display so that a tech can quickly 'buzz out' wiring and such like without waiting for the reading to settle or even taking his or her eyes off the test probes. It's specifically designed so that the voltage does not turn diodes on, it won't respond to resistors above a certain value and so on, so that it (usually) responds to just a fairly solid electrical connection.

The values will vary somewhat by manufacturer, but here is an excerpt from the Fluke 177 DMM manual:

As you can see it has hysteresis and a pulse stretcher that allows brief breaks to be detected. This is done by circuitry that is mostly operating in parallel to the main ADC function. Some crummy cheap meters have a continuity beep that is dependent on waiting for an ADC result, but they are not very useful. Avoid!