Wave Motion & Waves on String PYQs Set 4 (PDF)

Set 4 of 5 · Questions 91-120 of 141

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Motion & Waves on String · Set 4 (Q91-120)
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91. $The equations of two waves acting in perpendicular directions are given as x = a cos (ωt + δ) and y = a cos (ωt + α), where δ = α + \frac{π}{2}, the resultant wave represents Waves 135$ (1) $a parabola$ (2) $a circle$ (3) $an ellipse$ (4) $a straight line$ 92. $Forastationary wave, Y = 10 sin (\frac{πx}{15}) cos (48 πt) cm, the distance between a node and the successive antinode is$ (1) $60 cm$ (2) $30 cm$ (3) $7.5 cm$ (4) $15 cm$ 93. $Two waves are represented by the equations y_{1} = a sin (ωt + kx + 0.57) m and y_{2} = a cos (ωt + kx) m, where x is in meter and t in sec. The phase difference between them is$ (1) $1.0 radian$ (2) $1.25 radian$ (3) $1.57 radian$ (4) $0.57 radian$ 94. $A plane progressive wave is given by y = 2 cos 2 π (330 t - x) m . The frequency of the wave is :$ (1) $330 Hz$ (2) $660 Hz$ (3) $340 Hz$ (4) $165 Hz$ 95. $The equation of a sound wave is y = 0.0015 sin (62.4 x + 316 t) . The wavelength ofthis wave is$ (1) $0.3 unit$ (2) $0.2 unit$ (3) $0.1 unit$ (4) $cannot be calculated.$ 96. $The equation of a transverse wave is given by y = 0.05 sin π (2 t - 0.02 x), where x, y are in metre and t is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively$ (1) $50 m, 50 m s^{- 1}$ (2) $100 m, 100 m s^{- 1}$ (3) $50 m, 100 m s^{- 1}$ (4) $100 m, 50 m s^{- 1}$ 97. $A string is stretched between two rigid supports separated by 75 cm . There are no resonant frequencies between 420 Hz and 315 Hz . The lowest resonant frequency for the string is$ (1) $210 Hz$ (2) $180 Hz$ (3) $105 Hz$ (4) $1050 Hz$ 98. $When the length of the vibrating segment of a sonometer wire is increased by 1 %, the percentage change in its frequency is$ (1) $\frac{100}{101}$ (2) $\frac{99}{100}$ (3) $1$ (4) $2$ 99. $For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m . The possible wavelengths (in m) of the waves are$ (1) $1, 2, 3 \dots$ (2) $1, 3, 5 \dots$ (3) $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \dots$ (4) $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \dots$ 100. $A travelling wave represented by y = A sin ((ꞷt - kx) is superimposed on another wave represented by y = A sin (ꞷt + kx). The resultant is:$ (1) $A wave travelling along + x direction$ (2) $A wave travelling along - x direction$ (3) $A standing wave having nodes at x = \frac{nλ}{2}, n = 0, 1, 2 ....$ (4) $A standing wave having nodes at x = (n + \frac{1}{2}) \frac{λ}{2}; n = 0, 1, 2 .....$ 101. $A stretched string resonates with tuning fork frequency 512 Hz when length of the string is 0.5 m . The length ofthe string required to vibrate resonantly with a tuning fork of frequency 256 Hz would be$ (1) $0.25 m$ (2) $0.5 m$ (3) $1 m$ (4) $2 m$ 102. $The phase difference between two waves, represented by y_{1} = 1 0^{- 6} sin (100 t + (\frac{x}{50}) + 0.5) m y_{2} = 1 0^{- 6} cos [100 t + (x /50)] m, where x is expressed in metres and t is expressed in seconds, is approximately.$ (1) $1.07 radians$ (2) $2.07 radians$ (3) $0.5 radians$ (4) $1.5 radians$ 103. $The equation of a wave is represented by y = 1 0^{- 4} sin (100 t - \frac{x}{10}) m, then the velocity of wave will be$ (1) $100 m / s$ (2) $4 m / s$ (3) $1000 m / s$ (4) $10 m / s$ 104. $Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire is$ (1) $\frac{1}{3}$ (2) $\frac{1}{4}$ (3) $\frac{1}{5}$ (4) $\frac{1}{6}$ 105. $A string is clamped at both the ends and it is vibrating in its 4^{th} harmonic. The equation of the stationary wave is. Y = 0.3 sin (0.157 x) cos (200 πt) The length of the string is (All quantities are in SI units.)$ (1) $20 m$ (2) $80 m$ (3) $40 m$ (4) $60 m$ 106. $When a wave travels in a medium, displacement of a particle is given by y = asin 2 π (bt - cx) where a, b, c are constants. The maximum particle velocity will be twice the wave velocity if$ (1) $b = ac$ (2) $b = \frac{1}{ac}$ (3) $c = πa$ (4) $c = \frac{1}{πa}$ 107. $A rope supports of standing wave with a total of 4 nodes. It is fixed at the both ends. Calculate the wavelength of the wave if the length of rope is 6 m .$ (1) $0.67 m$ (2) $1.2 m$ (3) $1.5 m$ (4) $4 m$ 108. $The equation of a simple harmonic wave is given by y = 6 sin 2 π (2 t - 0.1 x), where x and y are in mm and t is in seconds. The phase difference between two particles 2 mm apart at any instant is$ (1) $54^{\circ}$ (2) $72^{\circ}$ (3) $18^{\circ}$ (4) $36^{\circ}$ 109. $The equation of the wave is y = 10 sin (\frac{2 πt}{30} + α) . If the displacement is 5 cm at t = 0 then the total phase at t = 7.5 s will be (sin 30^{\circ} = 0.5)$ (1) $\frac{π}{3} rad$ (2) $\frac{π}{2} rad$ (3) $\frac{2 π}{5} rad$ (4) $\frac{2 π}{3} rad$ 110. $Which of the following equations represents a travelling wave?$ (1) $y = A e^{- x^{2}} (vt + θ)$ (2) $y = Asin (15 x - 2 t)$ (3) $y = A e^{x} cos (ωt - θ)$ (4) $y = Asin xcos ωt$ 111. $A radar sends an electromagnetic signal of electric field (E_{0}) = 2.25 V/m and magnetic field (B_{0}) = 1.5 x 1 0^{- 8} T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a pail of signal (echo) reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time t_{0} from radar, then after how much time echo will reach to the radar?$ (1) $2. 0 x 1 0^{- 5} s$ (2) $4. 0 x 1 0^{- 5} s$ (3) $1. 0 x 1 0^{- 5} s$ (4) $8. 0 x l 0^{- 5} s$ 112. $For production of beats the two sources must have$ (1) $different frequencies and same amplitude$ (2) $different frequencies$ (3) $different frequencies, same amplitude and same phase$ (4) $different frequencies and same phase$ 113. $A wire of length 2 L, is made by joining two wires A and B of same length but different radii r and 2 r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q is:$ (1) $3 : 5$ (2) $4 : 9$ (3) $1 : 2$ (4) $1 : 4$ 114. $A stretched string is vibrating in the second overtone, then the number of nodes and antinodes between the ends of the string are respectively$ (1) $3 and 2$ (2) $2 and 3$ (3) $4 and 3$ (4) $3 and 4$ 115. $The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is traveling is______km/s$ 116. $A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental of 180 Hz will be_____cm$ 117. $The equation of wave is given by Y = 1 0^{- 2} sin 2 π (160 t - 0.5 x + \frac{π}{4}), where x and Y are in m and t in s. The speed of the wave is_______km h^{- 1}$ 118. $A wire of density 8 x 1 0^{3} kg m^{- 3} is stretched between two clamps 0. 5 m apart. The extension developed in the wire is 3. 2 x 1 0^{- 4} m. If Y = 8 x 1 0^{10} N m^{- 2}, the fundamental frequency of vibration in the wire will be_____Hz$ 119. $The displacement equations of two interfering waves are given by y_{1} = 10 sin (ωt + \frac{π}{3}) cm, y_{2} = 5 (sin (ωt) + 3 cos ω t) cm respectively. The amplitude of the resultant wave is_______ cm.$ 120. $A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension______ cm$