One end of a horizontal hope is attached to a prong of an electrically driven tuning fork that vibrates the rope transversely at 150 Hz. The other end passes over a pulley and supports a 2.50-kg mass. The linear mass density of the rope is 0.05 kg/m. What is the wavelength in millimeters? NOTE Express your final answers accurate to four decimal places; avoid rounding off intermediate values in the solutions to avoid deviation due to rounding-off within the solution

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b) Consider the surface density wave 01 = σι 010e² (wt+40+ar³) " [4 marks] where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 1. Using mathematical arguments show whether the pattern described by σ ₁ is rotating clockwise or anticlockwise. [5 marks] 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral. [5 marks] 3. Consider now a point Po at a distance r = 5kpc from the centre C of the spiral. The point Po is at a peak of the surface density wave. Going outward from Po along the line passing through C and Po, and using a = (3kpc) determine the distance between C and the next peak of the surface density wave. -3 [5 marks]

Problem 3: /25 Points a) If the period of oscillation of a given wave is 3.4 seconds and the wave is travelling at 12 m/s, what is the wavelength of the wave? b) What is the frequency of the 4th harmonic of the wave from part (a)? Problem 4: /25 Points A material has an index of refraction of 1.1 for red light and an index of refraction of 1.2 for blue light. Find the difference in refraction angle between a red light ray and a blue light ray if they both enter the material from air (n = 1) at an of 30 degrees.