(a) The equation y = \(\alpha\) sin (wt - kx) represents a plane wave travelling in a medium along the x-direction, being the displacement at the point x at time t.

(i) Given that x is in metres and t is in seconds, state the units of k and w

(ii) What physical quantity does \(\frac{W}{k}\) represent? Justify your answer

(iii) State whether the wave is travelling in the positive or negative x-direction.

(b)(i) What are beats?

(ii) A sonometer wire has a frequency of 259 Hz. It is sounded alongside a tuning fork of frequency 256 Hz. Calculate the beat frequency

(iii) The sonometer wire in (b)(ii) above is under a tension of 1200 N. If a metre of the wire has a mass of 0.03 kg, calculate the length l of the wire when it is vibrating in the fundamental mode.

(c) List two similarities between the human eye and the photographic camera.

(a) What is a magnetic field?

(b) With the aid of a labelled diagram describe an experiment to show that a magnetic field exists around a straight wire carrying current.

(c) A 40 \(\mu\)F capacitor in series with a 40 Q resistor is connected to a 100 V, 50 Hz a.c. supply.

(i) Draw a circuit diagram of the arrangement

(ii) Calculate the: I. impedance in the circuit; II. current in the circuit III. potential difference across the capacitor.

(a)(i) State Einstein's equation of photoelectric effect

(ii) What conservation principle does the equation represent?

(b) List three applications of photocells

(c) A photo emissive surface has a threshold frequency of 4.02 x 10\(^{14}\)Hz. If the surface is illuminated by light of frequency 5.0 x 10\(^{15}\)Hz, calculate the:

(i) threshold wavelength;

(ii) work function;

(iii) kinetic energy of the emitted photoelectrons. [ c = 3.0 x 10\(^{8}\) ms\(^{-1}\), h = 6.63 x 10\(^{-34}\) Js]

 A particle is projected at an angle of 30° to the horizontal with a speed of 250 ms\(^{-1}\). Calculate the;

(a) total time of flight of the particle;

(b) speed of the particle at its maximum height. [ g = 10 ms\(^{-2}\)]

State;

(a) the difference between plane polarized light and ordinary light;

(b) two uses of polaroids.