CPP:1 Oscillations and Waves: 1. Find the angular frequency and the amplitude of harmonic oscillations of a particle if at a distance X1 & X2 from the equilibrium position its velocity equals V1 & V2 respectively. 2. A point moves along the X axis according to the law X=asin2(ῳt-π/4). Find: a) The amplitude and period of oscillations. Also draw the plot x(t). b) The velocity projection vx as a function of the coordinate x. Draw the plot vx(x). 3. At the moment t=0 a point starts oscillating along the x axis according to the law x = a sin ῳt. Find the mean value of its velocity vector projection. 4. A point participates simultaneously in two harmonic oscillations of the same direction: x1=acosῳt and x2=acos2ῳt. Find the maximum velocity of the point. 5. A point oscillates along the x axis according to the law x = a cos (ῳt – π/4). Draw approximate plots a) of displacement x, velocity projection vx , and acceleration projection ῳx as function of time. b) velocity projection vx and acceleration projection ῳx as function of coordinate x. 6. A 2 m long rope, having a mass of 80 g is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N . a) Find the frequencies of the fundamental and the first two overtones. b) Find the wavelength in the fundamental and first two overtones. 7. Two wires are kept tight between same pair of supports. The tensions in the wires are in the ratio 2:1, the radii are in the ratio 3:1 and the densities are in the ratio 1:2 . find the ratio of their fundamental frequencies. 8. Two trains are travelling towards each other both at a speed of 90 km/h. If one of the trains sounds a whistle at 500Hz , what will be the apparent frequency heard in the other train? Take speed of sound in air = 350m/s. 9. A source emitting sound at frequency 4000Hz, is moving along the Y axis with a speed of 22m/s. A listener is situated on ground at the position (660m,0). Find the frequency of the sound received by the listener at the instant the source crosses the origin. Speed of the sound in air is 330 m/s. 10. Two sources of sound S1 and S2 , emitting waves of equal wavelength 20 cm , are placed with a sepration of 20 cm between them. A detector can be moved on a line parallel to S1S2 and at a distance of 20 cm from it. Initially the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through which detector should be shifted to detect a minimum of sound. 11. Find the fundamental first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is 340 m/s. 12. A particle is subjected to two simple harmonic motions , one along the X-axis and the other on a line making an angle of 450 with the X-axis. The two motions are given by X = X0 sin ῳt and S = S0 sin ῳt Find the amplitude of the resultant motion. Note: Visit the centre and be the part of test analysis session to get the solutions.
Posted on: Fri, 14 Mar 2014 10:30:07 +0000
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