12.14 Calculate the wave and group velocities of water waves at (a) 1 = 2 cm, (b) 1 = 8.0 cm, and (c) 1 = 20.0 cm. The wave velocity of short waves such as these are given by g + 12 d where 1 is the wavelength in meters, 7 is the surface tension in newtons per meter, which at room temperature is 0.073 N/m, g is the acceleration due to gravity, 9.80 m/s?, and d is the density of the liquid in kilograms per cubic meter.12.16 Two simple hamonic motions at right angles are represented by y = 3 sin 21:: and z m 5 sin (23:: Sari-1). Fmd the equation for the resultant path, and plot this path by the. method indicated in Fig. 121.. Verify at least two points on this path by substitution in the resultant equation. 12.9 Two sources vibrating according to the equations y, = 4 sin 21:: and y; = 3 sin 21:: send out waves in all directions with a velocity of 2.40 mfs. Find the equation of modem of a particle 5 m from the rst scarce and 3 m from the second. Note: a: 1- 2n- radfs. Ans. y = 6.08 sin (2m - 25.3\"} 24.8 (a) Calculate the degree of polarization of the light due to Rayleigh scattering at 70 with the direction of the primary beam. (b) Calculate the intensity of this light relative to that scattered straight backward