an amplifier is electronic equipment that increases strength of a signal and a booster is voltage regulation in (DC) direct current electrical power circuits.
Basically an amplifier increases strength and a booster regulates voltage.
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normal amplifier is a mathametical operation analog the computer, magnetic amplifier is sound operation of the signal
The amp for audio freq. is a AF amplifier. The RF amp is for radio freqs.
The output waveform will be limited to the difference between the supply and ground (or between the positive and negative supplies). This causes distortion of the output waveform.
The signal will move down the cable at from about 1/3 the speed of light to about 9/10 the speed of light, depending on the type of cable used. If there is a booster amplifier in the cable between the antenna and the TV set this will add more delay. You will need to know the length and types of cable used (and look up their signal propagation speed) as well as the delay of your booster amplifier if your system has one to calculate the answer to your question.
The subwoofer is the actual speaker making the loud bass. The amplifier is what powers the subwoofer and makes it work how it does. It only uses the low frequencies from the audio source and amplifies it.