PERIOD OF SINE WAVE

The period of a sine wave is the length of the interval along the x axis that completes one cycle of the sine wave. If b = 1, the period is 2 Pi. As b > 1 increases the period get shorter. To compute the period for b = 4, divide 2 pi by 4. So if you look at the graph y = sin bx from where 0 < x < 6.28 you will see 4 complete cycle of the sine wave.

If 0 < b < 1, then the length of the interval for completing one cycle of the sine wave increases. For example if b = 1/2, then the length of the interval along the x axis would need to be 12.56.