Solution to 1986 Problem 4

(A) The amplitude is A not 2A.
(B) The direction of the velocity can be found by required that the argument of the sine function is a constant:
\begin{align*}\frac{t}{T} - \frac{x}{\lambda} = \mbox{ const}\end{align*}
Increasing t a little bit requires you to increase x a little bit as well in order to maintain this equality, so the velocity in the positive x-direction.
(C) The period is T.
(D) x and t are variables here, so this cannot be right.
(E) Consider the equation above. Let \Delta x be the change in x during a small time interval \Delta t. Then, in order to maintain that equality we must have that
\begin{align*}\frac{\Delta t}{T} - \frac{\Delta x}{\lambda} = 0 \Rightarrow \frac{\Delta x}{\Delta t} = \frac{ \lambda}{T}\en...
So, answer (E) is correct.

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