Stereo system cuts on and off makes popping noise in speakers sometimes whats wrong with it ?

Wrong polarity. Maybe your conversation plug is not matching your car. Power is going to ground

the speakers maybe blown out, there mite be a short in the system, the antenna maybe loose or have short in the connector, there a short in an electronic component in the radio, it also could be a grounding issue, when you hit a bump it looses it connection or the unit has short in the receiver and it cuts out the signal in the radio station, losing power some where, if i was you go to stereo shop or buy new radio, all the money you would spend looking or trying to repair would cost you a lot of money, troubleshooting, radio, speakers, wiring, shop supples, no warranty after wards,
good luck

use a test light and a battery. the black is ground, orange is constant and yellow is your turn on and off (ignition). then take a 9volt battery to check your speaker wires. front should be green and light green and gray and light gray. double check it has ben a while, rear is blue and light blue, a yellow and brown. you do not need any other wires in the harness unless you are using a power antenna or amp which you can use the yellow wire for ignition. double check with test light and 9volt battery. the 9volt battery will make the speaker pop noise, you then know you have a speaker when it makes that noise.

factory stock radio:? , not custom aftermarket radio added and wired in to car wrong?
well unplug the radio connectors. does it pop now.
yes, then its not the speakers. popping.. how can they , not connected?
no, then , check for 12vdc at the radio power connector wire
with key pulled. (off)
got power on the radio now,. that is wrong.

use a rubber hose to your ear to find true object popping.

It could be a ground wire. I'm curious did the previous owner install the radio? Sometimes people just install a radio to the nearest power,ground and remote wire without any precautions on what they tap in to. Part of what you are hearing is alternator and/or ignition noise. Between the two noises my concern is that the installer might have tapped into a blower motor wire for either power or ground. The noise itself can be fixed with a 20 amp noise filter such as this one http://www.amazon.com/Heavy-Automotive-Noise-Filter-270-055/dp/B000T306DY but I suspect a bigger issue. Either you or someone knowledgeable with car audio installation should pull that radio out and check all the connections and where they are tapped in to and install it properly. The engine noise itself can be fixed with the noise filter. This popping sound I feel is a short from mis installation. I have seen cars get dash fires from this. I never like to worry people but I am also honest. I would tend to this soon. Good luck.

Sounds like you have major electrical problems. I would say a short for sure, it sounds like water is getting inside your door panel for one. Check the fuse box, make sure the box itself is secured, then check the fuses. making sure they are in tight. Pay close attention to the Accessory fuse, it controls alot of what you are describing.

Okay it is very simple but if you don't know what your doing you should google this info "1999 ford mustang stereo wiring diagram" and something should pop up and you can usually print it out or download usually I print them out.

Good Luck!

he may have left a bare wire that is powered that is shortning out when touching metal, speaker wires are connected to back of stereo and still run a current even when disconnected from speaker end if touching metal may corse a short it sounds like its just touchig metal every bow and then when driving and bumpy

Get a AA battery, solder a wire ti each end. This is called a "popper"
Hold one wire of the AA on one speaker wire. Tap the other AA wire to the other speaker wire. The speaker will make a "popping" noise. Mark the wire as to the location, and so on. To determine polarity (- or +) you must be able to see the speaker. If it jumps UP when you "pop" it, look at the polarity of the AA battery.
That is the proper polarity of the wires. If it sucks IN, when you "pop" it........you're backwards. If this is over you're head......$30 @ a stereo store and it's over!.....Have fun.

You need to attach the blue wire on the stereo harness to the blue and white wire on the car adapter harness. they installed a small amplifier to power the rear door speakers and unless you connect those two wires then the speakers will not work.