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Phys 212: Waves And Vibrations Question Paper
Phys 212: Waves And Vibrations
Course:Bachelor Of Science
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATIONS FOR THE AWARD OF
BACHELOR OF SCIENCE (GENERAL) AND BACHELOR OF EDUCATION (SCIENCE)
PHYS 212: WAVES AND VIBRATIONS
STREAMS: BSC, BED Y2S1 TIME: 2 HOURS
DAY/DATE: MONDAY 22/4/2013 2.30 PM – 4.30 PM
INSTRUCTIONS:
ANSWER QUESTION ONE AND ANY OTHER TWO QUESTIONS.
QUESTION ONE:
1. (a) Derive the expression for the periodic time of a pendulum, T=2p(l/g)^(1/2)
[7 Marks]
(b) What effect will doubling the amplitude A of a body moving with S.H.M, have on
(i) The period
(ii) The maximum velocity
(iii) The maximum acceleration. [6 Marks]
(c) State and explain using diagrams the three states of damping. [9 Marks]
(d) State and explain the two main factors that determine the speed of a wave in a
medium. [4 Marks]
(e) Draw graphs of a periodic transverse wave and a periodic longitudinal wave.
Indicate on the figures the wavelength and amplitude of each wave.
[4 Marks]
QUESTION TWO
(a) Consider a 2 kg mass connected to a spring whose constant is ?400 Nm?^(-1). What is the natural frequency of vibration? If the system is stretched by 8 cm and then released, at what points are its velocity and acceleration maximized? Will it reach half its maximum velocity at half the amplitude? [10 Marks]
(b) A 500 g mass is connected to a device having a spring constant of ?600 Nm?^(-1). The mass is displaced to the right a distance of x = +5cm from its equilibrium position and then released. What are its velocity and acceleration when the displacement is +3cm and
-3 cm? [10 Marks]
QUESTION THREE
(a) To understand the parameters that affect wave velocity in a vibrating spring, suppose that ?v=(Fl/m)?^(1/2)=100ms
What is the new wave speed V1 for each of the following changes
(i) F1 = 2F
(ii) m1 = 2m
(iii) l1 = 2l [9 Marks]
(b) Transverse waves have a speed of 20ms-1 in a string that has a tension of 8N. What tension is required to give a wave speed of 30ms-1 for the same string? [6 Marks]
(c) A bass guitar string 750 mm long is stretched with sufficient force to produce a fundamental vibration of 220 H2. What is the velocity of the transverse waves in this string? What is the frequency of the third humonic [5 Marks]
QUESTION FOUR
(a) Find the speed of sound in water, which has a bulk modulus of ?2.1 ×10?^9 Pa and a density of ?1.0×10?^3 ?kgm?^(-3) [3 Marks]
(b) A pipe is 2.46 m long. What are the three lowest possible frequencies if the pipe is closed at one end and open at the other? Velocity of sound is ?345ms?^(-1). [7 Marks]
(c) An ambulance travels down a highway at a speed of ?75mih?^(-1), its siren emitting sound at a frequency of 400H3. What frequency is heard by a passenger in a car travelling at ?55mih?^(-1) in the opposite direction as the car.
(i) Approaches
(ii) Moves away from the ambulance?
Velocity of sound in air is ?345ms?^(-1)) 11ml -1.609hm) [8 Marks]
(d) Differentiate between constructive and destructive interference. [2 Marks]
QUESTION FIVE
(a) A student sands several metres infront of a smooth reflecting wall, holding a board on which a wire is fixed at each end. The wire, vibrating in its third harmonic, is 75cm length has a mass of 2.25g and is under a tension of 400N. A second student, moving towards the wall, hears 8.3 hearts per second. What is the speed of the student approaching the wall? (Take the speed of sound in air to be ?340ms?^(-1)). [10 Marks]
(b)
T T
L L
A mass is connected to two rubber heads of length L each under tension, F as shown in the figure above. The mass is displaced vertically by a small distance e y. assuming that the tension odes not change. Show that
(i) The restarting force 2f/y.y
(ii) The system exhibits SHM with a an angular frequency. w=(2F/mL)^(1/2) [10 Marks]
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