Stand-alone speakers don't have a connector that will directly interface with an MP3 player, but with a little hackery, you can connect your MP3 player's headphone jack to a speaker. The main issue is that the power produced by an MP3 player is designed to drive the tiny speakers inside headphones, not full-size speakers.
The most basic connection type, and that found on less expensive shelf-style speakers, is that of bare wires in a spring clip. The ends of the speaker wire are stripped of insulation and inserted into spring clips. You can use the same method to connect an MP3 player to a speaker. The 3.5 mm headphone jack has two speaker signals and one split ground wire. The easiest way to figure out the connection is to take an old pair of headphones and cut the wires leading to each ear. Strip the outer layer of insulation so you can see the separate wires inside. The ground wire will be bare -- without insulation -- or the same color as the ground wire from the other side. The left and right wires are typically red and white. Connect the bare left and ground wires to the left speaker's spring clips. Do the same for the right speaker.
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Some higher-end speakers use a five-way connector that can accept clips, pins or banana clips. To connect an MP3 player to a speaker with a five-way connector, you'll need to convert the bare wire into a connection type that will work for the speaker. The connectors can be purchased for just a few dollars. You can make up a quick connector by just attaching the wire from a stripped headphone connector and securing it with electrical tape. If you want something more permanent, you would need to solder the wire to the connector.
The amount of power generally determines how loud a speaker can get. MP3 players are designed to drive tiny speakers in headphones and so don't produce much power. If you are connecting your MP3 player to unpowered speakers -- that is, speakers that don't have on-board amplification -- the volume will be very low. The smaller the speakers, the more volume the MP3 player will be able to produce. Big speakers will only put out a whisper if they don't have any additional power.
Speakers can get an amplified signal either through an internal or external source. Powered speakers have an internal amplifier that takes an un-amplified signal and juices it up. Most powered speakers are designed for use in a professional environment so they use a TRS connection type. You can manually wire a headphone connection to a TRS connector -- the left signal wire connects to the terminal closest to the center of the plug; the right signal wire connects to the middle terminal; and the ground wire connects to the wire farthest from the middle of the connector. If you want to create a permanent connection, you can solder the wires to the connection points.
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