Many problems call for functions which depend upon more than one variable. For instancea light wave or a sound wave propagated through time and space can be represented in asimplified

form by: y=A \cos \left(2 \pi\left(\frac{x}{\lambda}+\omega t\right)\right) where A is the amplitude, A is the wavelength and w is the frequency of the wave. x and tare position and time respectively. An understanding of this function is essential for manyproblems (e.g. sound, light microscopy, phase microscopy, X-ray diffraction). Draw a graph of y as a function of x assuming t = 0.%3D O Draw a graph of y as a function of t assuming x = 0. - At what values of x and t does the function repeat itself? Draw the function z= A cos 2 (x + a) where a is a constant. (V) At what values of a are the curves y = A cos(2Tx/A) and z = A cos( (x + a)) in phaseand out of phase?

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