PHY 2101 waves and optics

MULTIMEDIA UNIVERSITY OF KENYA

CAT 1

1. Explain clearly the distinction between transverse waves and longitudinal waves. (3 marks)
2. Distinguish between the epoch and phase of a vibration. (2 marks)
3. Define simple harmonic motion. Give two examples of such a motion. (3 marks)
4. Write down three conditions that are necessary for interference of sound waves. (3 marks)
5. Two parallel simple harmonic vibrations having amplitudes 4 cm and 5 cm respectively are acting simultaneously on a particle. The two vibrations have the same epoch angle equal to π/4 . Find the equation describing the vibration of the particle. (3 marks)
6. State the Huygens’ Principle. (2 marks)
7. A sinusoidal wave traveling in the positive x- direction has an amplitude of 15.0 cm, a wavelength of 40.0 cm, and a frequency of 8.00 Hz. The vertical position of an element of the medium at t = 0 and x = 0 is also 15.0 cm. (i) Find the wave number k, period T, angular frequency v, and speed v of the wave. (ii) Determine the phase constant f and write a general expression for the wave function (6 marks)
8. By considering a particle vibrating simple harmonically, show that its periodic time T can be written as: T = 2π√K where K is the displacement per unit acceleration (3 marks)

ASSIGNMENT 1

1. A 200-g block connected to a light spring for which the force constant is 5.00 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5.00 cm from equilibrium and released from rest as in Figure 15.6. (i) Find the period of its motion. (ii) Determine the maximum speed of the block. (iii) What is the maximum acceleration of the block? (7 marks)
2. Two waves traveling in opposite directions produce a standing wave. The individual wave functions are;
   y₁ = 4.0 sin(3.0x - 2.0t).
   y₂ = 4.0 sin(3.0x - 2.0t).
   Where x and y are measured in centimeters and t is in seconds. (i) Find the amplitude of the simple harmonic motion of the element of the medium located at cm 2.3cm cm. (ii) Find the positions of the nodes and antinodes if one end of the string is at x = 0 (5 marks)
3. A submarine (sub A) travels through water at a speed of 8.00 m/s, emitting a sonar wave at a frequency of 1 400 Hz. The speed of sound in the water is 1 533 m/s. A second submarine (sub B) is located such that both submarines are traveling directly toward each other. The second submarine is moving at 9.00 m/s. (6 marks) (i) What frequency is detected by an observer riding on sub B as the subs approach each other? (ii) The subs barely miss each other and pass. What frequency is detected by an observer riding on sub B as the subs recede from each other? (iii) While the subs are approaching each other, some of the sound from sub A reflects from sub B and returns to sub A. If this sound were to be detected by an observer on sub A, what is its frequency?
4. A double-slit source with slit separation 0.2 mm is located 1.2 m from a screen. The distance between successive bright fringes on the screen is measured to be 3.30 mm. What is the wavelength of the light? (4 marks)
5. Coherent laser light of wavelength 633 nm is incident on a single slit of width 0.25 mm. The observation screen is 2.0 m from the slit. (i) What is the width of the central bright fringe? (ii) What is the width of the bright fringe between the 5th and 6th minima? (4 marks)
6. In one instance, unpolarized light in air is to be reflected off a glass surface (n = 1.5). In another instance, internal unpolarized light in a glass prism is to be reflected at the glass-air interface, where n for the prism is also 1.5. Determine the Brewster angle for each instance. (4 marks)
7. Let P be a particle moving on the circumference of a circle of radius a. represent the motion of such a particle on a displacement time graph (label your axes clearly). (5 marks)