Title 9-wave-motion-.pdf ✅

Wave Motion 1. In a sonometer wire the fundamental frequency of the wire is 260Hz. In a sonometer the tension is maintained by suspending a 50.7 kg mass. When the suspended mass is completely submerged in water fundamental frequency becomes 240 Hz. The suspended mass has a volume (A) 0.002m3 (B) 0.0075 m3 (C) 0.004 m3 (D) 0.006 m3 2. A closed organ pipe resonates in its fundamental mode at a frequency of 200 Hz in O2 at a certain temperature. If the pipe contains 2 moles of O2 and, 3 moles of Ozone is now added to it, then what will be the fundamental frequency of same pipe at same temperature? (A) 268.23 (B) 172.7 (C) 149.45 (D) None of these 3. What will be the ratio of amplitudes of the reflected wave to the incident wave in case a sinusoidal wave produced in a stretched string gets reflected and loses 36% of its energy in getting reflected from the fixed end of the string? (A) 6: 10 (B) 8: 10 (C) 1: 1 (D) None of these. 4. A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of - ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sin ωt. Possible equation of the wave is : (A) y(x,t) = Asin [ωt − kx + (π/2)] (B) y(x,t) = Asin [ωt + kx + (π/2)] (C) y(x,t) = Asin [ωt − kx − (π/2)] (D) y(x,t) = Asin [ωt + kx − (π/2)] 5. A railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer standing beside a railway track. The frequency (n) of the sound heard by the observer is plotted against time (t). Which of the following best represents the resulting curve? (A) (B) (C) (d)
6. A stationary observer receives sound waves from two tuning forks, one of which approaches and the other recedes with the same velocity. As this takes place, the observer hears beats with frequency 2Hz. What is velocity of each tuning fork if their oscillation frequency is v0 = 680 Hz and the velocity of sound in air is vs = 340 m/s (A) 5 m/s (B) 0.5 m/s (C) 15 m/s (D) 50 m/s 7. A man holding a sound source at the top of a tower emitting frequency of sound as v = 1000Hz. Suddenly it slips from his hand and falls down with ' g ' acceleration. The sources of frequency of sound heard by the man at t = 4sec. (Velocity of sound = 320 m/s, g = 10 m/s 2 ) (A) 889Hz (B) 890Hz (C) 894Hz (D) 892 Hz 8. A plane wave of light is incident normally onto the left face of a composite slab as shown in the figure. The oscillation at x = 0 are represented by ε(0,t) = Asin ωt. Then the oscillation of the wave for x = l1 + l2 is given by : (Speed of light in vaccum is c and μ1, μ2 are R.I.) (A) ε(l1 + l2,t) = Asin ω (t − μ1l1 − μ2l2 c ) (b) ε(l1 + l2,t) = Asin ω (t − l1 + l2 c ) (C) ε(l1 + l2,t) = Asin ω (t − μ1l1 + μ2l2 c ) (d) None of these. 9. A train moves towards a stationary observer with 34 m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the train's speed is reduced to 17 m/s. The frequency registered is f2. If speed of sound in air is 340 m/s, then the ratio f1 f2 is: (A) 18/19 (B) 1/2 (C) 2 (D) 19/18 10. The displacement time graph for two sound waves A and B are shown in the figure. Then the ratio of their intensities IA/IB is equal to: (A) 1: 4 (B) 1: 16 (C) 1: 2 (D) 1: 1 11. The diagram shows a wave train of amplitude A at time t = 0sec. The phase difference between the oscillation of the particle at x = 0 and x = x1 is φ. The particle at x = x1 is moving upward with velocity v1. Which of the following equations represent the wave equation correctly? (A) Asin (−φx + tv1 A ) (b) Asin (φ x x1 + t v1 Asin φ )
(C) Asin (φ x x1 + t v1 Acos φ ) (D) Asin (φ x x1 + t tv1 A ) 12. In the given arrangement a source is placed at the fixed end of the spring with spring constant 100 N/m and the receiver is attached to the moving end of the spring, which in turn is connected to a box of mass 4 kg, which is oscillating horizontally with an amplitude of oscillation 2 m. If the source emits a frequency of 990 Hz then : (Speed of sound = 330 m/s ) (A) Maximum frequency received by the receiver is 990 Hz (B) Minimum frequency received by the receiver is 990 Hz (C) Frequency band width received by the receiver is 960 Hz − 1020 Hz. (D) Maximum and minimum frequencies are received at the extreme positions 13. A pure frequency note is played by two speakers in phase, distant 2 m apart, Along a line 3 m in front of the speakers, the intensity is heard as a minimum immediately in front of each speaker and there is only one maximum between these points. The frequency of the note is : [Take velocity of sound = 350 m/s ] (A) 286 Hz (B) 128 Hz (C) 512 Hz (D) 275 Hz 14. A train of sound waves is propagated along a wide pipe and it is reflected from an open end. If the amplitude of the waves is 0.002 cm, the frequency 1000 Hz and the wavelength 40 cm, the amplitude of vibration at a point distant 10 cm from open and inside the pipe will be (A) 0.004 cm (B) 0.001 cm (C) 0 (D) 0.002 cm 15. L1 and L2 are two small loud speakers which emit sound waves of the same amplitude but with a phase difference of π. A small receiver M moves along the perpendicular bisector of L1L2 in the direction as shown in the figure. The intensity of the sound recorded in the receiver is : (a) continuously decreasing tending to zero at a very large distance (b) alternates between a constant maximum and zero minimum (c) alternates between a diminishing maximum and increasing minimum (d) remains constant equal to zero MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. Displacement of particles in a string in x-direction and is represented by y. Account the following expression for y, those describing wave motion are (A) cos kxsin ωt k 2x 2 − ω 2 t 2 (C) cos2 (kx + ωt) (D) cos (kx 2 − ω 2 t 2 ) 17. y(x,t) = 0.8 (4x+5t) 2+5 represents a moving pulse where x and y are in meter and t in seconds. Then (A) Pulse is moving in +x direction (B) In two seconds it will travel a distance of 2.5 m (C) It's maximum displacement is 0.16 m (D) It's a symmetric pulse 18. Two sound waves of equal intensity I, generates beats. The intensity of sound Is produced in beats will be (A) I (B) 4I (C) 2I (D) 0 < Is < 4I 19. The equation of transverse displacement of a string clamped at both ends is y = 0.06sin ( 2πx 3 ) cos (120πt), where x, y are in meters and t is in second. The length of the string is 1.5 m and its mass is 3 × 10−2 kg. Then (A) wavelength, frequency and speed of progressive
waves are 3 m, 60 Hz and 180 m/s, respectively. (B) tension in the string is 648 N (C) amplitude at a distance x = 0.375 m is 4.2 cm at any time t. (D) wavelength, frequency and speed of progressive wave are 3 m, 80 Hz and 240 m/s 20. A wave pulse moving in the positive x-direction along the x-axis is represented by the wave function y(x,t) = 2.0 (x−3.0t) 2+1 , where x and y are in centimeters and t is in seconds. Then : (A) The speed of particle at time t = 1sec. and x = 3 cm is zero (B) The speed of particle at time t = 1sec. and x = 3 cm is 2 cm/s (C) The speed of the pulse is 3.0 cm/s (D) The speed of the pulse is 0.33 cm/s 21. Two whistles A & B each have a frequency of 500 Hz. A is stationary and B is moving towards the right (away from A) at a speed of 50 m/s. An observer is between the two whistles moving towards the right with a speed of 25 m/s. The velocity of sound in air is 350 m/s. Assume that there is no wind. Which of the following is/are true ? (A) the apparent frequency of whistle B as heard by A is 437 Hz approximately (B) the apparent frequency of whistle B as heard by observer is 469 Hz approximately (C) the difference in the apparent frequencies of A and B as heard by the observer is 4.5 Hz (D) the apparent frequencies of the whistles as observed by each other are the same 22. The equation of motion of a longitudinal wave is y = 0.15sin [4πt − πx] Where x&y are measured in meters an t in second. (A) The distance between two successive points having phase difference π is 1 m (B) The wave travels along negative x-axis (C) The frequency of the wave is 2 Hz (D) At 20 cm. Displacement of the particle, kinetic energy of the latter is zero. At t = 4sec. 23. Along the straight line joining two consecutive displacement-nodes in a pure stationary sound wave, at different points. (A) the S.H.M.'s will be in different phases (B) the velocities are in phase (C) the accelerations are in phase (D) the frequencies are equal 24. Mark out the correct statement(s) w.r.t. wave speed and particle velocity for a transverse travelling mechanical wave on a string. (A) The wave speed is same for the entire wave, while particle velocity is different for different points at a particular instant. (B) Wave speed depends upon property of the medium but not on the wave properties. (C) Wave speed depends upon both the properties of the medium and on the medium and on the properties of wave. (D) Particle velocity depends upon properties of the wave and not on medium properties. 25. Let a disturbance y be propagated as a plane wave along the x-axis. The wave profiles at the instants t = t1 and t = t2 are represented respectively as : y1 = f(x1 − vt1 ) and y2 = f(x2 − vt2 ). The wave is propagating without change of shape. (A) The velocity of the wave is v (B) The velocity of the wave is v = (x2 + x1 )/ (t2 + t1 ) (C) The particle velocity is vp = vf ′ (x − vt) (D) The phase velocity of the wave is v 26. A wire of 9.8 × 10−3 kg/m passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of 30∘ with the horizontal. Masses m and M are tied at the two ends of wire such that m rests on the plane and M hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of 100 m/s. (A) m = 20 kg (B) M = 5 kg (C) m M = 1 2 (D) m M = 2 27. Three simple harmonic waves, identical in frequency n and amplitude A moving in the same direction are superimposed in air in such a way, that the first, second and the third wave have the phase angle φ,φ + (π/2) and (φ + π), respectively at a given point P in the superposition. Then as the waves progress, the superposition will result in . (A) A periodic, non-simple harmonic wave of amplitude 3 A (B) A stationary simple harmonic wave of amplitude 3 A (C) A simple harmonic progressive wave of amplitude A (D) The velocity of the superposed resultant wave will be the same as the velocity of each wave 28. A sonometer string AB of length 1 m is stretched by a load and the tension T is adjusted so that the