Waves and Oscillations — DU B.Sc. (Hons) Physics Previous Year Question Papers

B.Sc. (H) Physics NEP 1) Answer any five of the following: (5x3=15) (a) Six simple harmonic oscillations each of same frequency and equal amplitude are superposed. The phase difference $ between any two consecutive oscillations is constant. If the resultant amplitude of the superposition is zero, what is the phase difference $? (b) Two tuning forks with natural frequencies Y1 and Yz, are struck at the same time with equal force. The intensity of the resulting sound beats with a frequency of 1 Hz. If the average frequency is 512 Hz, determine Y1 and yz. (c) The oscillations of a tuning fork of frequency 400 cps wane away to 1/e times its amplitude in 2 second. Calculate its damped frequency. (d) Explain the transient state behavior of a system under forced oscillations. (e) The string of a violin is to be tuned to a frequency of 640 Hz. Its length and mass (from the bridge to the end) are 33 cm and 0.125 g respectively. What tension is required? (f) What are stationary waves? Why are they called so? 2) (a) A particle is subjected to two simple harmonic motions at right angle to each other, of equal amplitudes A, equal frequencies w and a constant initial phase difference n /2. Derive an analytical expression for the resultant oscillation of the particle. Sketch the trajectory for the resultant oscillation. (b) Two tuning forks A and B are used in an optical experiment to produce Lissajous figures. Frequency of fork A is 288 Hz. It is found that the sequence of figures repeats every 20 seconds. When fork B is loaded with a little wax, the time taken for sequence of the figures is found to repeat every 10 seconds. Determine the original frequency of fork B. (c) Show that time period of a compound pendulum is minimum when points of suspension and oscillation are equidistant from its center of gravity. (7,4,4) 3) (a) A particle is subjected to N simple harmonic motions of same frequency. If the amplitude of each oscillation is Ao and $ is the phase difference between successive oscillations, show that the amplitude of the resultant oscillation is given by A = Ao sin (Ng) / sin(ф/2) (b) A uniform spring of force constant k is cut into two pieces whose lengths are in the ratio 1:3. Calculate the force constant of each piece. (c) Show that the values of T, the period of three simple harmonic motions (a), (b) and (c) in the figure are in the ratio 1:VZ: J2. All springs are identical, each of spring constant k and of mass that is negligible compared to mass m. 4) (a) Discuss the effect of damping on oscillatory motion. Write down the equation of motion for damped harmonic oscillator and solve it. Show that for heavily and critically damped cases, there is no oscillatory motion. (b) Find the logarithmic decrement of a damped harmonic oscillator which has an initial amplitude of 20 cm and which reduces to 2 cm after 100 complete oscillations each of period 2.3 seconds. Also find the relaxation time. (10, 5)