Title 12-wave-motion-.pdf ✅

Wave Motion 1. Equations of a stationary and a travelling waves are as follows : y1 = asin kxcos ωt and y2 = asin (ωt − kx) The phase difference between two points x1 = π 3k and x2 = 3π 2k are φ1 and φ2 respectively for the two waves. The ratio is φ1 φ2 : (A) 1 (B) 5/6 (C) 3/4 (D) 6/7 2. Speed of sound wave in air : (A) is independent of temperature. (B) increases with pressure. (C) increases with increase in humidity. (D) decreases with increase in humidity. 3. A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions, (A) density remains constant (B) Boyle's law is obeyed (C) bulk modulus of air oscillates (D) there is no transfer of heat 4. Equation of a plane progressive wave is given by y = 0.6sin 2π (t − x 2 ). On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is : (A) y = 0.6sin 2π (t + x 2 ) (B) y = −0.4sin 2π (t + x 2 ) (C) y = 0.4sin 2π (t + x 2 ) (D) y = −0.4sin 2π (t − x 2 ) 5. A train whistling at constant frequency is moving towards a station at a constant speed V. The train goes past a stationary observer on the station. The frequency n of the sound as heard by the observer is plotted as a function of time t. Identify the expected curve. (A) (B) (C) (D) 6. During propagation of a plane progressive mechanical wave : (A) all the particles are vibrating in the same phase (B) amplitude of all the particles is equal. (C) particles of the medium executes S.H.M.
(D) wave velocity depends upon the nature of the medium. 7. The transverse displacement of a string (clamped at its both ends) is given by : y(x,t) = 0.06sin (2πx/3)cos (120πt). All the points on the string between two consecutive nodes vibrate with : (A) same frequency (B) same phase (C) same energy (D) different amplitude 8. A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/s. Given that the speed of sound in still air is 340 m/s, (A) the frequency of sound as heard by an observer standing on the platform is 400 Hz (B) the speed of sound for the observer standing on the platform is 350 m/s (C) the frequency of sound as heard by the observer standing on the platform will increase (D) the frequency of sound as heard by the observer standing on the platform will decrease 9. A string of length 1 m and linear mass density 0.01 kg/m is stretched to a tension of 100 N. When both ends of the string are fixed, the three lowest frequencies for standing wave are f1, f2 and f3. When only one end of the string is fixed, the three lowest frequencies for standing wave are n1, n2 and n3. Then: (A) n3 = 5n1 = f3 = 125Hz (B) f3 = 5f1 = n2 = 125Hz (C) f3 = 2n2 = 3f1 = 150Hz (D) n2 = f1+f3 2 = 75Hz 10. A closed organ pipe of cross sectional area 100 cm2 resonates with a tuning fork of frequency 1000 Hz in fundamental tone. The minimum volume of water to be drained out so that the pipe again resonates with the same tuning fork is (take velocity of wave = 320 m/s ) (A) 800 cm3 (B) 1200 cm3 (C) 1600 cm3 (D) 2000 cm3 11. An organ pipe of 3.9πm long, open at both ends is driven to third harmonic standing wave. If the amplitude of pressure oscillation is 1% of mean atmospheric pressure [p0 = 105 N/m2 ]. The maximum displacement of particle from mean position will be: [Given velocity of sound = 200 m/s and density of air = 1.3 kg/m3 ] (A) 2.5 cm (B) 5 cm (C) 1 cm (D) 2 cm 12. A massless rod of length L is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to ' x '. Further it is observed that the frequency of 1 st harmonic in AB is equal to 2 nd harmonic frequency in CD. ′ x ' is: (A) L 5 (B) 4L 5 (C) 3L 4 (D) L 4 13. The ratio of the velocity of sound in hydrogen (γ = 7 5 ) to that in helium (γ = 5 3 ) at the same temperature is: (A) √ 5 42 (B) √ 5 21 (C) √42 5 (D) √ 21 5 14. A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one ninth the tension. Then the fundamental frequency will became. (A) 400 Hz (B) 600 Hz (C) 300 Hz (D) 200 Hz 15. A string fixed at both ends oscillates in 5 segments, length 10 m and velocity of wave is 20 ms−1 . What is the frequency? (A) 5H : (B) 15 Hz
(C) 10Hz (D) 2 Hz 16. A string vibrates according to the equation y = 5sin ( 2πx 3 ) cos 20πt Where x and y are in cm and t in second. The distance between two adjacent nodes is: (A) 3 cm (B) 4.5 cm (C) 6 cm (D) 1.5 cm 17. When two progressive waves y1 = 4sin (2x − 6t) and y2 = 3sin (2x − 6t − π 2 ) are superimposed, the amplitude of the resultant wave is : (A) 5 (B) 6 (C) 5/6 (D) 1/2 18. A transverse wave is described by the equation y = y0sin 2π (ft − x λ ). The maximum particle velocity is equal to four times the wave velocity, if : (A) λ = πy0 4 (B) λ = πy0 2 (C) λ = πy0 (D) λ = 2πy0 19. A car sounding its horn at 480 Hz moves towards a high wall at a speed of 20 ms−1 . If the speed of sound is 340 ms−1 , the frequency of the reflected sound heard by the girl sitting in the car will be closest to : (A) 540Hz (B) 524 Hz (C) 568 Hz (D) 480 Hz 20. Statement I : Two longitudinal waves given by equations y1(x,t) = 2a sin (ωt − kx) and y2(x,t) = asin (2ωt − 2kx) will have equal intensity. Statement II : Intensity of waves of given frequency in same medium is proportional to the square of amplitude only. (A) If Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I (B) If Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I (C) If Statement-I is True, Statement-II is False (D) If Statement-I is False, Statement-II is True 21. The transverse displacement y(x,t) of a wave on a string is given by(x,t) = e −(ax 2+bt 2+2√abxt) . This represents a : (A) Wave moving in −x direction with speed √ b a (B) Standing wave of frequency √b (C) Standing wave of frequency √ 1 b (D) Wave moving in +x direction with speed √ a b 22. A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms−1 at an angle of 60∘ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 ms−1 ), is : (A) 106 Hz (B) 97 Hz (C) 100 Hz (D) 103 Hz 23. The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is : (A) 120 cm (B) 140 cm (C) 80 cm (D) 100 cm 24. If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by : (A) 1 n = 1 n1 + 1 n2 + 1 n3 (B) 1 √n = 1 √n1 + 1 √n2 + 1 √n3 (C) √n = √n1 + √n2 + √n3 (D) n = n1 + n2 + n3
25. The number of possible natural oscillation of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are : (Velocity of sound = 340 ms−1 ) : (A) 4 (B) 5 (C) 7 (D) 6 26. of sound is 343 ms−1 , the frequency of the honk as heard by him will be : (A) 1332 Hz (B) 1372 Hz (C) 1412 Hz (D) 1454 Hz 27. If we study the vibration of a pipe open at both ends, then the following statement is not true. (A) All harmonics of the fundamental frequency will be generated. (B) Pressure change will be maximum at both ends. (C) Open end will be antinode. (D) Odd harmonics of the fundamental frequency will be generated. 28. A wave travelling in the +ve-direction having displacement along y-direction as 1 m, wavelength 2πm and frequency of 1 π Hz is represented by : (A) y = sin (10πx − 20πt) (B) y = sin (2πx − 2πt) (C) y = sin (x − 2t) (D) y = sin (2πx − 20πt) 29. A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is : (A) 240 Hz (B) 260 Hz (C) 254 Hz (D) 246 Hz 30. The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1: 3: 5. (A) 1500 23 cm, 500 23 cm (B) 1500 23 cm, 300 23 cm (C) 300 23 cm, 1500 23 cm (D) 1500 23 cm, 2000 23 cm 31. When a string is divided into three segments of length l1,l2 and l3 the fundamental frequencies of these three segments are v1, v2 and v3 respectively. The original fundamental frequency (v) of the string is : (A) √v = √v1 + √v2 + √v3 (B) v = v1 + v2 + v3 (C) 1 v = 1 v1 + 1 v2 + 1 v3 (D) 1 √v = 1 √v1 + 1 √v2 + 1 √v3 32. Two sources of sound placed closed to each other, are emitting progressive wave given by y1 = 4sin 600πt and y2 = 5sin 608πt An observer located near these two sources of sound will hear : (A) 4 beats per second with intensity ratio 25: 16 between waxing and waning (B) 8 beats per second with intensity ratio 25: 16 between waxing and waning (C) 8 beats per second with intensity ratio 81:1 between waxing and waning (D) 4 beats per second with intensity ratio 81: 1 between waxing and waning 33. The equation of a simple harmonic wave is given by y = 3sin π 2 (50t − x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is : (A) 2π (B) 3 2 π (C) 3π (D) 2 3 π 34. Two waves are represented by the equations y1 = asin (ωt + kx + 0.57) and y2 = acos (ωt + kx)m, where x is in meter and t in sec. The phase difference between them is : (A) 1.0 radian (B) 1.25 radian (C) 1.57 radian (D) 0.57 radian 35. Sound waves travel at 350 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air : (A) decrease by a factor 10 (B) increase by a factor 20 (C) increase by a factor 10 (D) decrease by a factor 20 36. Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of