Two sinusoidal waves with amplitudes $4.5\mathrm{cm}$ and $3.0\mathrm{cm},$ respectively, move toward each other on a string and experience superposition. As they move past each other, the displacement of the string from equilibrium is complicated. Considering all positions on the string where the waves are overlapping, what are the largest and smallest magnitudes of the displacement of the string?

(I) The two pulses shown in Fig. 15–37 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap.

<IMAGE>

(I) The two pulses shown in Fig. 15–37 are moving toward each other. (c) In Fig. 15–37, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

<IMAGE>

(II) Suppose two linear waves of equal amplitude and frequency have a phase difference ϕ as they travel in the same medium. They can be represented by ₁ ₂ ω θ

D₁ = A sin (kx - ωt)

D₂ = A sin ( kx - ωt + ϕ)

(b) What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not?

In the following figure, two interfering waves are drawn at some instance in time. 

a. Indicate the regions on the graph where constructive interference occurs.
b.Indicate the regions on the graph where destructive interference occurs.