Back to simple modulation, for "AM".
One way to get amplitude modulation is to use an analog multiplier, where Vout = X x Y / H, where X and Y are the two input voltages and H is a constant factor.
All three terms and the output are measured in Volts.
The RF (carrier) signal is Y(t) = C x cos(wt), where C is the constant amplitude of the RF carrier.
It comes from the oscillator.
Let the audio signal be A(t), where the waveform A has 0 DC value (since it only goes down to, say, 20 Hz), and the peak-to-peak value is 2 V (so the waveform varies between -1 V and +1 V).
For "regular AM" (which contains the carrier and both sidebands), let Y(t) = C x cos(wt) and X(t) = (1 V) + A(t) , which ranges from 0 to +2 V.
When the audio signal A(t) goes through 0, the output is the carrier C x cos(wt) / H , remembering the scale factor.
For "double-sideband suppressed carrier" (DSB), we drop the extra 1 V and simply let X(t) = A(t), giving the output XY/H = C x cos(wt) x A(t) /H .
When the audio signal A(t) goes through 0, the output is 0.
When the music stops, there is no output for DSB, while the AM output is the carrier power.
The carrier carries no information, and can be considered wasted power.
However, it allows the modulated signal to be de-modulated using a simple diode rectifier and low-pass filter, as found in normal AM radios.