A Student Studies the Motion of a Transverse Wave Moving $x$

Multiple Choice

A student studies the motion of a transverse wave moving along a stretched string in the negative $x$ direction. At time $t = 1.0 \mathrm {~s}$ the student takes a photograph of the wave, and she is able to establish that the amplitude of the wave is $10.0 \mathrm {~cm}$ , the wavelength is $3.0 \mathrm {~m}$ , and the piece of string at position $x = 3.0 \mathrm {~m}$ is displaced from its equilibrium position by $- 10.0 \mathrm {~cm}$ . When studying the time behavior of this piece of the string at position $x = 3.0 \mathrm {~m}$ , she finds that it oscillates up and down with a frequency of $0.25 \mathrm {~Hz}$ . Based on these observations, the precise equation describing the wave is

A) $y ( x , t ) = 10 \cos [ 2 \pi ( x / 3 - t / 4 + 1 / 4 ) ]$ cm.
B) $y ( x , t ) = 10 \cos [ 2 \pi ( x / 3 + t / 4 + 1 / 4 ) ]$ cm.
C) $y ( x , t ) = 10 \cos [ 2 \pi ( x / 3 - t / 4 - 1 / 4 ) ]$ cm.
D) $y ( x , t ) = 10 \cos ( 2 \pi x / 3 + t / 4 + 1 / 4 )$ cm.
E) $y ( x , t ) = 10 \cos 2 \pi ( x / 3 ) - t / 4 + 1 / 4$ cm.