Now we wish to find as and ps, which are not undetermined constants. (the requisite two undetermined con- stants already appear in zn). one strategy of proceeding involves expanding the sine and cosine functions on the left-hand-side of eq. (30) as, cos(ω t + ps.) cos(ω t) cos((ω t) sin(ps.) sin(ω t + p")-sin(ω t) cos(n.) + cos(ω t) sin(a.) using these in eq. (30) and equating coefficients of cos(32t) and sin(32t) leads to, (22- 2) sin(p)-ycos(ps)as (31) (32) ro

Follow these directions and answer the questions. 1. set up the ripple tank as in previous investigations. 2. bend the rubber tube to form a "concave mirror" and place in the ripple tank. the water level must be below the top of the hose. 3. generate a few straight pulses with the dowel and observe the reflected waves. do the waves focus (come together) upon reflection? can you locate the place where the waves meet? 4. touch the water surface where the waves converged. what happens to the reflected wave? 5. move your finger twice that distance from the hose (2f = c of c, center of the curvature) and touch the water again. does the image (the reflected wave) appear in the same location (c of c)? you may have to experiment before you find the exact location. sometimes it is hard to visualize with the ripple tank because the waves move so quickly. likewise, it is impossible to "see" light waves because they have such small wavelengths and move at the speed of light. however, both are examples of transverse waves and behave in the same way when a parallel wave fronts hit a curved surface.