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Chaitanya Bharathi Institute of Technology (Autonomous)

Gandipet, Hyderabad Engineering Physics notes for BE I year I Semester

(Common for all braches) B.E. (1/4) SEMISTER-I ENGINEERING PHYSICS NOTES (2014-15)

UNIT-I

Waves and Oscillations:Simple harmonic motion-Differential equation and its solution-Torsional pendulum-Superposition of two mutually perpendicular linear SHMs of same frequency-Lissajous figures-Damped vibrations-Differential equation and its solution-Logarithmic decrement-Relaxation time-Quality factor-Force vibrations- Differential equation and its solution-Amplitude resonance.

Ultrasonics:Production of ultrasonics by piezoelectric and magnetostriction methods-Detection of ultrasonics-Determination of ultrasonic velocity in liquids-Engineering applications.

MID EXAM QUESTION PAPER PATTERN Max.Marks:20 Time :1Hr.

Answer all questions from Part A and any two from Part B

PART A (3x2 = 6 Marks)

1.Problem 2. Problem 3.SAQ OR Problem

PART B (2x7 = 14 Marks)

4.(a)

(b)

5.(a)

(b)

6.(a)

(b)

SEMESTER1

1 Commencement of classess 15-09-2014

2 I class Test 03-11-14 to 06-11-2014

3 II class Test 27-12-14 to 31-12-2014

4 Last Date of Instructions 02-01-2015

5 Preparation and Practical Examinations 05-01-2015 to 17-01-2015

6 Commencement of Theory Examinations 19-01-2015 & semester II starts on 09-02-2015

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Superposition of two mutually perpendicular linear SHMs of same frequency-Lissajous figures

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WAVES & OSCILLATIONS (Problems)

1.A body of mass 1kg is executing SHM which is given by y =6cos(100t+π/4)cm.What is the (i)amplitude (ii)frequency

(iii)intial phase (iv)velocity (v)acceleration & (vi) maximum kinetic energy(6cm , 50/π, π/4, -600sin(100t+π/4) and

18J respectively)

2.A body oscillates with SHM of amplitude 4cm and a frequency of 5Hz.At time t =0,the body is at its equilibrium

posion (x=0).Write down the equation of SHM (Ans.x = 4sin10πt)

3.A body moves with SHM about a point x=0.At time t=0 it has a displacement of 5cm and zero velocity.If the

frequency of the motion is0.5Hz,find the magnitudes of the displacement,velocity and acceleration at t =1.25sec.

(Ans. -3.535cm 11.5cm/sec and 34.9cm/sec2 )

4.A body moving SHM has a velocity of 4cm/sec at a distance of 4cm from the mean position and 3cm/sec at a distance

4cm from the mean position.Calculate amplitude time period & velocity at mean position. (Ans.5cm 6.28sec and

5cm/sec)

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5.A particle of mass 10gm is describing SHM along a straight line with a period of 2sec and an amplitude of

10cm.What is the kinetic energy when it is 2cm & 5cm from its equilibrium posion (Ans.480π2erg & 375 π2erg )

6.The amplitude of an oscillater of frequency 200cps falls to (1/10) of its intial valve after 2000 cycles.Calculate

(i)relaxation time (ii) quality factor (iii)time in which its energy falls to (1/10)of its intial valve & (iv)damping

constant (Ans. (i)2.174 sec, (ii)2730 (iii)5sec (iv)0.23 )

7.The oscillation of tuning fork of frequency 200cps die away to 1/e times their amplitude in 1 sec.Show that the

reduction in frequency due to air damping is exceeding small. (Ans.oscillatory ,1.71sec)

8.An underdamped harmonic oscillator has its amplitude reduced to (1/10)th of its intial valve after 100 oscillations.If

time period is 2sec,find (i)the damping constant & (ii)decay modulus.(Ans..0115& 86.95s)

9.Prove that in case of damped vibrations the in which the amplitude falls to 1/e times of its intial valve is twice the

time in which the energy falls by the same amount called relaxation time.

10.In a seconds pendulum,the amplitude falls to half its intial valve in 150sec.Find quality factor(341.6)

1.The frequency of tuning fork is 250 Hz.and its qulity factor is 4x104.Find the time taken to reduce its energy is 1/8

of its intial valve. (Ans.52.94sec)

12.Find the time period of a body executing SHM if it has an acceleration of 2 m/s2 when its displacement is

10cm.(14sec)

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DETECTION OF ULTRASONICS

The ultrasonic waves can be detected by the following methods.

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Measurement of wavelength of ultrasonic waves

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ULTRASONICS

1.Calculate the fundamental frequency of vibration when a quartz crystal of thickness 0.15cm is vibrating at

resonance.(Given Y=7.9x1010Nm-2 & ρ=2650kgm-3) (ans.1.8199MHz.)

2. Calculate the fundamental frequency and the first overtone emitted by a quartz crystal of thickness 1mm in a

piezoelectric oscillator.(Given Y=7.9x1010Nm-2 & ρ=2650kgm-3) (Ans.2.7299MHz & 5.459MHz)

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3.A piezo electric quartz plate (X-cut) has a thickness of 1mm.If the velocity of (in crystal) propagation of ultrasonic

wave along the X direction is 5760m/sec,find the fundamental frequency of the crystal.(2.88MHz)

4.A bat emits ultrasonic sound of frequency 200KHz in air.If this sound meets water surface,what is the wavelength

of (i)the reflected sound (ii)the transmitted sound.(speed of sound in air=340m/sec and in water=1486m/sec)

(Ans.1.70x10-3m & 7.43x10-3m)

5.An ultrasonic source of 0.07MHz sends down a pulse towards the seabed which returns after 0.65sec.The velocity of

sound in sea water is 1700m/s.Find the depth of sea and the wavelength of pulse. (d=552.5m & λ=2.4cm)

6.Find the natural frequency of 40mm length of a pure iron rod.(Given Y=115x109Nm-2 & ρ=7250kgm-3)can you use it

in magnetostriction oscillator to produce ultrasonic waves. (49.75kHz.)

Prepared by G.Nataraj Faculty Physics Dept.