Wave Motion & Waves on String PYQs Set 2 (PDF)

Set 2 of 5 · Questions 31-60 of 141

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Motion & Waves on String · Set 2 (Q31-60)
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31. $The equation of the progressive wave is y = asin 2 π (nt - \frac{x}{5}) . The ratio of maximum particle velocity to wave velocity is$ (1) $\frac{πa}{5}$ (2) $\frac{2 πa}{5}$ (3) $\frac{3 πa}{5}$ (4) $\frac{4 πa}{5}$ 32. $In the wave equation y = 0.5 sin \frac{2 π}{λ} (400 t - x) m the velocity of the wave will be:$ (1) $200 m/s$ (2) $2002 m / s$ (3) $400 m/s$ (4) $4002 m/s$ 33. $The equation of a wave travelling on a string is y = sin [20 πx + 10 πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is:$ (1) $10 cm$ (2) $2.5 cm$ (3) $20 cm$ (4) $5.0 cm$ 34. $A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x -direction in 0.3 sec . The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?$ (1) $y = 2 cos (0.83 x - 3.35 t) cm$ (2) $y = 2 sin (0.83 x - 3.5 t) cm$ (3) $y = 2 cos (0.13 x - 0.5 t) cm$ (4) $y = 2 cos (3.35 x - 0.83 t) cm$ 35. $Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin (450 t - 9x) where distance and time are measured in SI units. The tension in the string is:$ (1) $12.5 N$ (2) $7.5 N$ (3) $10 N$ (4) $5 N$ 36. $The speed of a longitudinal wave in a metallic bar is 400 m / s . If the density and Young's modulus of the bar material are increased by 0.5 % and 1 %, respectively then the speed of the wave is changed approximately to____m / s .$ (1) $398$ (2) $401$ (3) $399$ (4) $402$ 37. $Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is v_{1}, and that in the other string having radius of cross section R /2 is v_{2} . Then \frac{v _{2}}{v _{1}} =$ (1) $8$ (2) $4$ (3) $2$ (4) $2$ 38. $A man sitting in a moving train hears the whistle of the engine. The frequency of the whistle is 600 Hz$ (1) $The apparent frequency as heard by him is smaller than 600 Hz$ (2) $The apparent frequency is larger than 600 Hz$ (3) $The frequency as heard by him is 600 Hz$ (4) $None of the above$ 39. $A wire of length L and mass per unit length 6.0 \times 10^{- 3} kgm^{- 1} is put under tension of 540 N . Two consecutive frequencies that it resonates at are 420 Hz and 490 Hz . Then L in meters is:$ (1) $8.1 m$ (2) $2.1 m$ (3) $1.1 m$ (4) $5.1 m$ 40. $When a string is divided into three segments of length λ_{1}, λ_{2} and λ_{3} the fundamental frequencies of these three segments are v_{1}, v_{2} and v_{3} respectively. The original fundamental frequency (v) of the string is$ (1) $ν = ν_{1} + ν_{2} + ν_{3}$ (2) $v = v1 + v2 + v3$ (3) $\frac{1}{ν} = \frac{1}{ν _{1}} + \frac{1}{ν _{2}} + \frac{1}{ν _{3}}$ (4) $\frac{1}{ν} = \frac{1}{ν _{1}} + \frac{1}{ν _{2}} + \frac{1}{ν _{3}}$ 41. $A travelling harmonic wave is represented by the equation y (x, y) = 10^{- 3} sin (50 t + 2 x), where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?$ (1) $The wave is propagating along the positive x -axis with speed 25 ms^{- 1}$ (2) $The wave is propagating along the negative x-axis with speed 25 ms^{- 1}$ (3) $The wave is propagating along the negative x-axis with speed 100 ms^{- 1}$ (4) $The wave is propagating along the positive x-axis with speed 100 ms^{- 1}$ 42. $In sonometer experiment, the bridges are separated by a fixed distance. The wire which is slightly elastic, emits a tone of frequency ' n' when held by tension ' T'. If the tension is increased to ' 4 T', the tone emitted by the wire will be of frequency$ (1) $n$ (2) $2 n$ (3) $Slightly greater than 2 n$ (4) $Slightly less than 2 n$ 43. $A progressive wave is given by y = 12 sin (5 t - 4 x) . On this wave, how far away are the two points having a phase difference of 90^{\circ} ?$ (1) $\frac{π}{4}$ (2) $\frac{π}{8}$ (3) $\frac{π}{16}$ (4) $\frac{π}{32}$ 44. $To propagate both longitudinal and transverse waves, a material must have$ (1) $bulk and shear moduli$ (2) $only bulk modulus$ (3) $only shear modulus$ (4) $Young's and bulk modulus.$ 45. $A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe.$ (1) $a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.$ (2) $a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.$ (3) $a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.$ (4) $a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.$ 46. $A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this strings is$ (1) $155 Hz$ (2) $205 Hz$ (3) $10.5 Hz$ (4) $105 Hz$ 47. $A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m << M) . When the car is at rest, the speeed of transverse waves in the string is 60 ms^{- 1} . when the car has acceleration a, the wave-speed increases to 60.5 ms^{- 1} . The value of a in terms of gravitational acceleration g, is closest to:$ (1) $\frac{g}{30}$ (2) $\frac{g}{5}$ (3) $\frac{g}{10}$ (4) $\frac{g}{20}$ 48. $The equation of a simple harmonic wave is given by y = 5 sin \frac{π}{2} (100 t - x) where x and y are in metre and time is in second. The period of the wave in second will be$ (1) $0.04$ (2) $0.01$ (3) $1$ (4) $5$ 49. $A wave travelling along uniform string represented by Y = Asin (ωt - kx) is superimposed on another wave travelling along the same string represented by Y = Asin (ωt + kx) . The resultant is$ (1) $a wave travelling along + x direction.$ (2) $a standing wave having nodes at x = (n - \frac{1}{2}) \frac{λ}{2}, where n = 1, 2, 3,$ (3) $a wave travelling along - x direction.$ (4) $a standing wave having nodes at x = \frac{nλ}{2}, where n = 0, 1, 2, \dots \dots \dots \dots .$ 50. $A longitudinal wave is represented by x = 10 sin 2 π (nt - \frac{x}{λ}) . The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:$ (1) $2 π$ (2) $5 π$ (3) $π$ (4) $5 π 2$ 51. $If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become$ (1) $\frac{n}{4}$ (2) $2 n$ (3) $n$ (4) $\frac{n}{2} .$ 52. $If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is [NEET 2022]$ (1) $2 : 1$ (2) $1 : 2$ (3) $1 : 2$ (4) $1 : 1$ 53. $A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope?$ (1) $6$ (2) $3$ (3) $12$ (4) $9$ 54. $The equation of a transverse wave travelling along a string is y (x, t) = 4.0 sin (20 \times 10^{- 3} x + 600 t) mm, where x is in mm and t is in second. The velocity of the wave is:$ (1) $- 60 m / s$ (2) $- 30 m / s$ (3) $+ 30 m / s$ (4) $+ 60 m / s$ 55. $A transverse wave propagating along x ‐axis is represented by y (x, t) = 8.0 sin (0.5 πx - 4 πt - π /4) where x is in metres and t is in seconds. The speed of the wave is$ (1) $8 m / s$ (2) $4 πm / s$ (3) $0.5 πm / s$ (4) $π /4 m / s .$ 56. $A wave in a string has an amplitude of 2 cm. The wave travels in the + ve direction of x axis with a speed of 128 m / s and it is noted that 5 complete waves fit in 4 m length ofthe string. The equation describing the wave is$ (1) $y = (O . 02) m sin (15.7 x - 2010 t)$ (2) $y = (O . 02) m sin (15.7 x + 2010 t)$ (3) $y = (O . 02) m sin (7.85 x - 1005 t)$ (4) $y = (O . 02) m sin (7.85 x + 1005 t)$ 57. $A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:$ (1) $180 m / s, 80 Hz$ (2) $320 m / s, 80 Hz$ (3) $320 m / s, 120 Hz$ (4) $180 m / s, 120 Hz$ 58. $The time of reverberation of a room A is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A ?$ (1) $1$ (2) $2$ (3) $4$ (4) $1/2.$ 59. $When a string of length l is divided into three segments of length l_{1}, l_{2} and l_{3} . The fundamental frequencies of three segments are n_{1}, n_{2} and n_{3} respectively. The original fundamental frequency ‘n’ of the string is$ (1) $n = n_{1} + n_{2} + n_{3}$ (2) $n = n_{1} + n_{2} + n_{3}$ (3) $\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$ (4) $\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$ 60. $Two travelling waves produces a standing wave represented by equation, y = 1.0 mm cos (1.57 c m^{- 1}) \times sin (78.5 s^{- 1}) t The node closest to the origin in the region x>0 will be at x=\dots\dots. cm.$