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Unformatted text preview: 1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 M ECH ANICAL W AVES PRO BLEM S ASK ED IN JEE & REE Q 1. A wire of density 9x10 3 kg/m 3 is stretched between two clamps 1m apart & is subjected to an extension of 4.9x10- 4 m . What will be the lowest frequency of transverse vibrations in the wire ? [Young’s Modulus of the material 9 x10 10 N/m²] [ REE ’87, 7 ] Q 2. Select correct alternative(s) : [ JEE ’87, 2 ] The displacement of particles in a string stretched in x-direction is represented by y . Among the following expressions for y , those describing wave motion are : (A) cos (kx) sin( ω t) (B) k²x²- ω ²t² (C) cos² (kx + ω t) (D) cos (k²x²- ω ²t²) Q 3. In a sonometer wire the tension is maintained by suspending a 50.7 kg mass from the free end of the wire . The suspended mass has the volume of 0.0075 CuM . The fundamental frequency of the vibration of wire is 260 Hz . If the suspended mass is completely submerged in water , the fundamental frequency becomes ______ Hz . [The density of water is 10 3 kg/m 3 ] [ JEE ’87, 2 ] Q 4. The following equations represent transverse waves z 1 = A . cos (kx- ω t) , z 2 = A . cos (kx + ω t) & z 3 = A . cos (ky- ω t) . Identify the combination(s) of the waves which will produce ; (i) standing waves (ii) a wave travelling in the direction making an angle of 45° with positive x & positive y axes . In each case , find positions at which the resultant intensity is always zero . [ JEE ’87, 7 ] Q 5. A train approaching a hill at a speed of 40 km/h sounds a whistle of frequency 580 Hz when it is at a distance of 1 km from a hill A, wind with a speed of 40 km/h is blowing in the direction of motion of the train . Find : (i) the frequency of the whistle as heard by an observer on the hill & (ii) the distance from the hill at which the echo from the hill is heard by the driver & its frequency . (Velocity of sound in air 1200 km/h) [ JEE ’88, 5 ] Q 6. A wave represented by the equation y = a cos(kx- ω t) is superposed with another wave to form a stationary wave such that the point x = 0 is a node . The equation for other wave is : (A) a sin (kx + ω t) (B) - a cos(kx + ω t) (C) - a cos(kx- ω t) (D) - a sin(kx- ω t) [ JEE ’88, 1 ] Q 7. An organ pipe P 1 is closed at one end vibrating in its first harmonic & another pipe P 2 open at both the ends vibrating in its third harmonic are in resonance with a given tuning fork . The ratio of the length of P 1 to that of P 2 is : (A) 8/3 (B) 3/8 (C) 1/2 (D) 1/3 [ JEE ’88, 2 ] Note : in this question the paper setter has misused the term harmonic for overtone . Read overtone instead of harmonic in the question & then solve ....
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This note was uploaded on 10/05/2011 for the course PHY 203 taught by Professor Grimaldi during the Spring '11 term at St. Mary NE.
- Spring '11