1.
Five waveforms moving with equal speeds on the xx-axis,
y1=8sin(ωt+kx),y2=6sin(ωt+kx+π2),y3=4sin(ωt+kx+π),y_1 = 8\sin(\omega t + kx),\quad y_2 = 6\sin\left(\omega t + kx + \dfrac{\pi}{2}\right),\quad y_3 = 4\sin(\omega t + kx + \pi),

y4=2sin(ωt+kx+3π2),y5=42sin(ωtkx+π4)y_4 = 2\sin\left(\omega t + kx + \dfrac{3\pi}{2}\right),\quad y_5 = 4\sqrt{2}\sin\left(\omega t - kx + \dfrac{\pi}{4}\right)

are superimposed on each other. The resulting wave is