Explain the necessity of smoothing the output voltage before applying it to a transistor amplifier

smoothing avoids "hum" in the output of the amplifier

Explanation:

We presume the question is why half-wave or full-wave rectified AC needs to be smoothed before using it to supply power to a transistor amplifier.

Most transistor amplifiers have output voltage that is a function of both the signal input voltage and the power supply voltage. Half-wave or full-wave rectified power goes from full value to zero once or twice in each cycle of the AC power from which it is derived. That modulation of the power voltage can show up as a modulation of the output signal from the amplifier. Such modulation is usually undesirable.

Some amplifier designs have a significant factor of "power supply rejection", meaning large changes in power supply voltage only produce small changes in amplifier output voltage. However, when the supply voltage goes to zero, the amplifier output necessarily goes to zero also. That is, power supply rejection is never perfect and is rarely sufficient to tolerate full-wave or half-wave rectified power without producing some modulation of the amplifier's output.

It is necessary to smooth the power supply voltage in order to reduce or eliminate amplifier output "hum."

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Caveat

If the power supply frequency and its harmonics are well-separated from the amplifier's signal frequency band, modulation on the power supply may be of little or no consequence. Often power supplies operated at an audible frequency, so power for audio amplifiers needs to be quite "clean." There are other power and signal frequency bands for which the results will vary.