A failure to study the basic information first is often the cause of a project's failure. You get so eager and passionate about the task at hand that some pesky details that could have guaranteed success instead come back to bite you. When you put together your dream audio system, there is an impetus to just connect it and turn it up, but some careful planning should accompany your enthusiasm or you're likely to end up with blown speakers, a fried amplifier or both.
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Choose speakers that match the amplifier's impedance level. The impedance is measured in ohms, and both the amplifier and speakers will be clearly marked with their capabilities. If you select speakers with 4 ohm impedance and an amplifier delivering 8 ohm, the speakers impede the signal coming from the amplifier to a lesser degree (lower numbers equal lower impedance) and the amplifier will struggle to fill the gap. This could burn out your amplifier prematurely.
Compare oranges to oranges. Look for the RMS wattage of both the speakers and the amplifier, if it is given. You can think of RMS as the average power. Other power notations you may see are "peak power," "program power" and "continuous power." Peak power for a speaker is the amount of power required to move the speaker cone to its most forward position, while continuous power is the amount of power available in the amplifier at any given instant. Program power is a slippery concept conceived by speaker manufacturers. It is a measure of the speaker power rating while playing music rather than a steady tone, which is used to determine peak and RMS power. Comparing unlike numbers (such as the continuous power rating of the amplifier with the program power of the speakers) gives an incomplete picture of the setup and could result in speaker driver failure.
Be aware that amplifiers will overdrive their capabilities. An amp rated at 100 watts RMS is capable of pulsing much higher than that, with the accompanying distortion that often reveals itself in bass tones. If you're lucky enough to see clearly identifiable RMS ratings for both the speakers and the amplifier, and the impedance matches, then a simple 100 watt amplifier matched to 100 watt speakers might be sufficient. But it is always safer to double the power rating of the speaker to account for the amplifier's ability to hit higher peak power.
If the rating for the speakers is given as program power or music power, consider that RMS power is roughly half of program power. If your amplifier produces 100 watts of clean sound (that will spike to 200 with distortion), then your speakers' RMS power needs to be 100 to 200 watts. That means you are looking for program power of 200 to 400 watts.