I'm not sure this will help, but...
Grab a clean sheet of paper and arrange it horizontally on your desk before you.
With a bold writing tool, draw a horizontal line midway up the sheet On the left most end of the line , label the line ZERO.
. On the RIGHT end of the horizontal zero line put a horizontal arrow pointing right and the word "time".
About 1 1/2 inches in from the left side of the sheet, draw a bold vertical line. Put a big "Volt" label somewhere above the "zero" label
At the top part of the vertical line put a +V label. at the bottom of the Vertical line put a -V label.
There, you have established a graph space.
Now, at the "origin" or the zero crossing of the Volt and the "time" lines on the left side of the page, midway up. produce a sine curve that goes from the origin, up towards the top of the page, peaks, and then returns to the ZERO time line but does not cross below. Draw one full sine wave cycle. More if you like. where the sine wave contacts the horizontal zero time line the second time, write a small 60hz at the tangent point.
Now grab a different color writing tool.
Again start drawing a sine wave that originates at the intersection of the horizontal and vertical lines. The line proceeds UP and to the right to the same maximum extent as the first sine wave, but in 1/2 the distance to the right (time) and then descends THROUGH the zero line an equal AMPLITUDE below the zero line as it had been ABOVE the zero line only moments before. Turn this new sine wave back up to meet the zero time line at the same point as the first sine wave contacts the zero line.
Clear as mud ;-) But the exercise is worth doing.
Details to note.
120V single phase does NOT CROSS the zero voltage ground. (and it does not matter if you had made the first sine wave below the horizontal zero line)
The Frequency of the applied Voltage is 60 times per second (50 if in the UK etc) That is, the A/C voltage rises from zero to a maximum and back to zero in one cycle.
The actual AMPLITUDE ( maximum voltage) does not effect wave form or cycle time. If viewed on an o-scope, Both 240 and 120 wave forms could be made to appear identical with a tweak of a pair of adjustment knobs. In fact, under heavy service load, both 120 and 240 Volt supplies will SAG, that is the voltage will "droop" to a less than peak value.
240 V single phase CROSSES the zero voltage line with TWICE the total AMPLITUDE of the sine wave in exactly the same time. 1/60 th of a second. Half that time the voltage will be one sign (+) relative to ground, and the other half the time the voltage will be the opposite sign. (-) The PEak Voltage for 240V systems is measured "leg to leg". No ground required!
One Cycle for both 120 and 240 single phase is the time (horizontal distance on the graph you made) And that is constant for both. Entirely based on engine speed for an IC engine powered generator. (Inverter units are MAGIC)