Well known there is no amplitude in that case. All the AC equipment doesn't care what kind of amplitude form the most important only is simmetry. In other words the different half-periods have to be the same by the form and time of duration like reflection.
Sorry but neither of those statements are true:
1) There is an amplitude, the modified sine wave has the same peak amplitude as a real sine wave.
2) Plenty of appliances prefer a pure sine wave and a modified sine wave is better than a square wave and there are appliances which require a sinewave If this wasn't true, then why are most cheap inverters on the market modified sine wave? And why is it people bother to buy more expensive pure sine wave inverters?
Why is a modified sine wave inverter better?
It can power a greater range of appliances than a square wave inverter.
Some appliances require the same peak voltage as the sinusoidal mains but aren't bothered about the wave shape, e.g. some non-universal switched mode power supplies. These work by rectifying the mains and converting it to DC, the trouble is, the electronics might not work reliably off 230VDC and might require at least 300VDC. A square wave or even a DC voltage could be used to supply these sorts of appliances but the output voltage would need to be √2 times the normal mains voltage so you'd need a 325V suqarewave, if the appliance was designed for a 230V sine wave. The problem is that a 325V square wave will cause resistive loads to overheat and possibly catch fire so it's a bad idea.
A modified sine wave inverter will be able to run both appliances designed for a peak voltage of 325V and resistive loads which require an RMS voltage of 230V, regardless of the wave shape.
A modified sinewave inverter produces less harmonics than a square wave inverter so it causes less interference and heating of iron cores.
Why is a pure sine wave inverter better than a modified sine wave inverter?
Because it can supply any device designed to work from the mains.
Some appliances require a sinusoidal voltage and can be damaged by a squarewave or modified sine wave. This is because the higher frequency harmonics can cause overheating in some transformers and motors. There are also some circuits such as phase controllers (lamp dimmers) and single phase induction motor starters won't work at all from any other wave shape than a sine wave.