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1. Two sinusoidal waves of same frequency and having amplitudes A1 &A2 respectively
superpose coherently. Write the expression for the maximum and minimum values of the
intensity of the resultant wave.
2. Two simple pendulums of mass ‘M’ in and length ‘L’ each are coupled by a spring of force
constant K. Write the expression for angular frequency of normal modes of vibration of the
coupled system.
3. A uniform string of length 2 meter and mass 200 Gms is under a tension of 800N. Calculate the
speed of transverse wave in the string.
4. A Uniform string S1 is connected with another uniform string S2 whose linear mass density is
greater than that of S1 A wave pulse propagating alone one string meets the another at a
junction where a part is transmitted and apart is reflected back as shown in fig
In which string did the wave propagate initially? Explain.
5. A progressive sinusoidal wave is represented by y (x,t)=A sin [(0.2m) x- (0.45) t+ π/6]
where ‘x’ and‘t’ are in meter and second respectively. Determine the speed of propagation of
the wave.
6. A forced oscillator is at resonance with the external periodic force .What is the phase
difference between the driving force and the velocity of the oscillator?
7. Identify the terms in the wave function given by
Ψ(r, t) =A sin (k.r –wt +Φ)
8. Displacement associated with a wave is given by
Y (x, t) = 0.1 cos (0.2x-2t) Where X and Y are given in terms of cm and‘t’ is in second .Calculate the
wavelength, amplitude, frequency and velocity.
9. Calculate the speed of longitudinal wave at NTP. (Given ,density of air at NTP is 1.3x10 -3
gm/cm and Cp/Cv = 1.4)
10. A vertical spring executes S.H.M. with a period of 1 second . When a mass of one gram is
suspended at the lower end of the spring, find the length through which the spring is
stretched.
11. The natural angular frequency of a simple harmonic oscillator of mass 2gram is 0.8 rad/sec. It
undergoes critically damped motion when taken to a viscous medium. Find out the damping
force on the oscillator when its speed is 0.2 cm/sec.
12. Twenty sinusoidal waves of equal amplitudes superpose incoherently to produce a resultant
wave of intensity 0.5 watt /m2 .What would be the resultant intensity if the waves superpose
coherently?
13. Write the wave equation for a one dimensional wave propagating along the (+) ve Y-axis in an
elastic medium of density ƒ and bulk modulus B.
14. Find out the speed of longitudinal wave propagating in a medium of density ρ = 6x103 Kg/m3
and bulk modulus B = 1.2 x 108 N/m2.
15. The displacement of a one- dimensional simple harmonic oscillator of mass 5gms is Y (t) = 2
cos (0.6t + θ) where ‘Y’ and‘t’ are in cm and second respectively. Find the kinetic energy of the
oscillator.
16. In a damped oscillator, the damping force is proportional to the velocity. Mention the
positions at which the damping force vanishes.
17. A plane monochromatic wave traveling in a homogeneous medium meets a denser medium.
What are the charges in (a) amplitude (b) phase (c) speed of propagation (d) phase of the
reflected and transmitted waves in comparison with corresponding properties of incident
wave?
18. Two identical simple pendulums each of mass ‘m’ and length ‘L’ are coupled by a spring of
force constant K. Write the expression for the normal mode frequencies of the coupled
oscillatory system.
19. A monochromatic wave is represented by the wave function ψ (x,t) = (8cm) sin (Пx- Пt/2)
where ‘x’ is in cm and‘t’ is in second. Find the amplitude, frequency and wavelength of the
wave.
20. The maximum amplitude of a forced damped oscillator is 2.5cm .What will be the maximum
amplitude if the damping constant and magnitude of the driving force are doubled.
21. Two waves of same frequency have amplitudes 2units and 3 units respectively. When they
superpose coherently the intensity of the resultant wave is I1. The intensity becomes I2 when
they super pose incoherently. Find the ratio I1/I2.
22. Evaluate the Q-factor of a damped oscillator with resonant frequency 500Hz and damping
coefficient 0.5 per second.