(a) What is a wave motion?
The equation \(y = A \sin \frac{2\pi}{\lambda} (Vt-X)\) represents a wavetrain in which y is the vertical displacement of a particle at distance X from the origin in the medium through which the wave is travelling. Explain, with the aid of a diagram, what A and \(\lambda\) represent.
(b) (i) Describe an experiment to determine the frequency of a note emitted by a source of sound
(ii) A pipe closed at one end is 1 m long. The air in the pipe is set into vibration and a fundamental note is produced. If the velocity of sound in air is 340ms\(^{-1}\), calculate the frequency of the note
(c) State two differences between a sound wave and a radio wave.
(a) State the laws of electromagnetic induction.
(b) (i) Describe a simple experiment to show how an induced e.m.f, can be produced; (ii) State two factors on which the magnitude of the induced e.m.f. depends
(c) Explain what is meant by the r.m.s. value of an alternating current
(d) (i) If the alternating current is represented by \(I = l_{o} \sin \omega t\), state what the symbol \(I, I_{o}, \omega\) and \(\omega t\)represent.
(ii) Calculate the instantaneous value of such a current, if in a circuit it has r.m.s value of 15.0A when its phase angle is 30°.
(a)(i) Explain the terms: photoelectric emission and threshold frequency; (ii) Einstein's photoelectric equation can be written as \(E = hf - hf_{o}\) What does each of the symbols used in the equation above represent?
(b) Calculate the frequency of the proton whose energy is required to eject a surface electron with a kinetic energy of \(1.97 \times 10^{-16} eV\) if the work function of the metal is \(1.33 \times 10^{-16}eV\). \((1 eV = 1.6 \times 10^{-18}J; h = 6.60 \times 10^{-34}JS)\).
(c) In a photoelectric cell, no electrons are emitted until the threshold frequency of light is reached. Explain what happens to the energy of the light before emission of electrons begins. State one factor that may affect the numbers of emitted electrons.
(d) Explain what is meant by the duality of matter, illustrating your answer with observation phenomena.
(a) Using a suitable diagram, explain how the following can be obtained from a velocity-time graph (i) acceleration; (ii) retardation; (iii) total distance covered.
(b) Show that the displacement of a body moving with uniform acceleration a is given by \(s = ut + \frac{1}{2} at^{2}\) where u is the velocity of the body at time t = 0.
(c) A particle moving in a straight line with uniform deceleration has a velocity of 40ms\(^{-1}\) at a point P, 20ms\(^{-1}\) at a point Q and comes to rest at a point R where QR = 50m. Calculate the: (i) distance PQ; (ii) time taken to cover PQ; (iii) time taken to cover PR.
(a) Define the boiling point of a liquid.
(b) Describe an experiment to determine the boiling point of small quantity of a liquid.
(c) A piece of copper of mass 300 g at a temperature of 950°C is quickly transferred to a vessel of negligible thermal capacity containing 250 g of water at 25°C. If the final steady temperature of the mixture is 100°C, calculate the mass of the water that will boil away.
[Specific heat capacity of copper = \(4.0 \times 10^{2} Jkg^{-1} K^{-1}\); Specific heat capacity of water = \(4.2 \times 10^{3} Jkg^{-1} K^{-1}\); Specific latent heat of vaporization of steam = \(2.26 \times 10^{6} Jkg^{-1}\)
(d) State four other effects of heat on a substance other than expansion.
