Quantum Physics A Group of Waves3Consider the composition of three waves, yo, Y1, and y2 given byy0 = A sin (ka - wt)(-4) -- (--) ]AsinAk2AY2 =AkAwsin (ka) Express the superposition yo + yı + y2 as a single product of trigonometric functions. Sketchthe resultant wave for t = 0.b) If Ak/k = 10-?, how many zeros does the waveform have within each region of reinforcement(between adjacent zeros of the envelope)?c) If the phase velocity w/k = 10 cm/sec, Ak/k = 10-2, and Aw/w = 10-3, then what is thegroup velocity of the waveform?

Given, y0=Asin(kx-ωt)y1=A2sink-∆k2x-ω-∆ω2ty2=A2sink+∆k2x-ω+∆ω2t

3 A Group of Waves Consider the composition of three waves, yo, Y1, and y2 given by y0 = A sin (kæ – wt) (--4)-- (--4)-] A Ak Aw Y1 = sin A Ak k + Y2 = sin a) Express the superposition yo + y1 + y2 as a single product of trigonometric functions. Sketch the resultant wave for t = 0. b) If Ak/k = 10-², how many zeros does the waveform have within each region of reinforcement (between adjacent zeros of the envelope)? c) If the phase velocity w/k = 10 cm/sec, Ak/k = 10-2, and Aw/w = 10-3, then what is the group velocity of the waveform?

3 A Group of Waves Consider the composition of three waves, yo, Y1, and y2 given by y0 = A sin (kæ – wt) (--4)-- (--4)-] A Ak Aw Y1 = sin A Ak k + Y2 = sin a) Express the superposition yo + y1 + y2 as a single product of trigonometric functions. Sketch the resultant wave for t = 0. b) If Ak/k = 10-², how many zeros does the waveform have within each region of reinforcement (between adjacent zeros of the envelope)? c) If the phase velocity w/k = 10 cm/sec, Ak/k = 10-2, and Aw/w = 10-3, then what is the group velocity of the waveform?