Your answer to Q45:  Sorry, your answer is not correct.  You should realize that the waves will interfere constructively. Where have they each moved after 5 s?

Help: Fundamentals of Sound reference: Secs. 1-C, 1-K.

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Hint for Q45:  At a speed of 1/2 ft/s the two pulses each will have moved 2.5 ft in the 5 seconds. Think how they will add together when they are both at the position corresponding to this.

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Correct answer to Q45:  Each pulse moves 2.5 feet in 5 seconds when moving at 2.5 feet per second. This puts the center of each pulse at precisely the same place, namely at x = 5.0 The rules of constructive interference then mean that the pulses instantaneously add up to make a single total pulse.  Placing them "on top of each other" gives a square pulse that is the same width as the original but twice as high. The answer is d).

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Your answer to Q50:  Sorry, your answer is not correct. Consult the definitions.

Help: Fundamentals of Sound reference: Sec. 1-G.

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Hint for Q50:  The only tricky parts of this are the difference beween "amplitude" and "displacement." Look up "amplitude."
 
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Correct answer to Q50:  (a)=(4); (b)= (5); (c)=(1);  (d)=(2); (e)=(3); (d)=(6).
Note the distinction between "amplitude" and "displacement." Amplitude is the maximum distance a point moves from equilibrium (the rest position) to a crest, while the displacement of a point on the wave measures just how far that point, not necessarily a crest, is above equilibrium. Displacement is always less than or equal to amplitude.

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  Your answer to Q55:  Sorry, your answer is not correct.  What have these items got in common with a wave?

Help: Fundamentals of Sound reference: Sec. 1-E.

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Hint for Q55:  Sec.1-F of Fundamentals of Sound points out that one can make a plot of position versus time for certain oscillating objects. How would you do this and what relation would that have to a wave?

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Correct answer to Q55:  In both cases one can plot position away from equilibrium as a function of time. The plot looks just like a sinusoidal waveform.  Indeed any one point of, say, a rope on which a sinusoidal traveling wave is passing moves precisely like one of these oscillating objects. See the detailed discussion in Sec. 1-F. The correct answer is c).

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