A transverse sinusoidal wave on a taut string is described, at the instant t=0, by the equation
y(x,0)=3.0sin(0.402πx)cm,
where x is measured in metres.
a. (i) Define the following terms for a transverse wave: amplitude, wavelength, crest and trough.
b. (ii) Using only the given expression, determine the numerical values of the amplitude and wavelength of the wave.
c. (iii) Draw one complete graph of displacement y versus position x for the range 0≤x≤0.40m. Clearly label the crests, troughs and the amplitude on your sketch.
d. (iv) If, instead of plotting displacement against position, you were to plot displacement against time for a fixed point on the string, explain qualitatively how the shape of the graph would compare with the graph obtained in part (iii).