
question_answer1) The equation of a wave is\[y=2\sin \pi (0.5x200t)\], where x and y are expressed in cm and t in sec. The wave velocity is [MP PMT 1986]
A) 100 cm/sec done
clear
B) 200 cm/sec done
clear
C) 300 cm/sec done
clear
D) 400 cm/sec done
clear
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question_answer2) Equation of a progressive wave is given by \[y=0.2\cos \pi \left( 0.04t+.02x\frac{\pi }{6} \right)\] The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of \[\pi /2\]
A) 4 cm done
clear
B) 8 cm done
clear
C) 25 cm done
clear
D) 12.5 cm done
clear
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question_answer3) A travelling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and [MP PMT 1990]
A) The wavelength is 5 m done
clear
B) The frequency is 5 Hz done
clear
C) The velocity of propagation is 5 m/s done
clear
D) The wavelength is 0.2 m done
clear
View Solution play_arrow

question_answer4) The equation of a transverse wave is given by \[y=10\sin \pi (0.01x2t)\] where x and y are in cm and t is in second. Its frequency is [MP PET 1990; MNR 1986; RPET 2003]
A) \[10{{\sec }^{1}}\] done
clear
B) \[2\,{{\sec }^{1}}\] done
clear
C) \[1\,{{\sec }^{1}}\] done
clear
D) \[0.01\,{{\sec }^{1}}\] done
clear
View Solution play_arrow

question_answer5) At a moment in a progressive wave, the phase of a particle executing S.H.M. is \[\frac{\pi }{3}\]. Then the phase of the particle 15 cm ahead and at the time \[\frac{T}{2}\] will be, if the wavelength is 60 cm
A) \[\frac{\pi }{2}\] done
clear
B) \[\frac{2\pi }{3}\] done
clear
C) Zero done
clear
D) \[\frac{5\pi }{6}\] done
clear
View Solution play_arrow

question_answer6) The equation of a wave travelling on a string is \[y=4\sin \frac{\pi }{2}\left( 8t\frac{x}{8} \right)\]. If x and y are in cm, then velocity of wave is [MP PET 1990]
A) 64 cm/sec in ? x direction done
clear
B) 32 cm/sec in ? x direction done
clear
C) 32 cm/sec in + x direction done
clear
D) 64 cm/sec in + x direction done
clear
View Solution play_arrow

question_answer7) The equation of a progressive wave is given by \[y=a\sin (628t31.4x)\] If the distances are expressed in cms and time in seconds, then the wave velocity will be [DPMT 1999]
A) 314 cm/sec done
clear
B) 628 cm/sec done
clear
C) 20 cm/sec done
clear
D) 400 cm/sec done
clear
View Solution play_arrow

question_answer8) Two waves are given by \[{{y}_{1}}=a\sin (\omega tkx)\] and \[{{y}_{2}}=a\cos (\omega \,tkx)\] The phase difference between the two waves is [MP PMT 1993; SCRA 1996; CET 1998; EAMCET 1991; Orissa JEE 2002]
A) \[\frac{\pi }{4}\] done
clear
B) p done
clear
C) \[\frac{\pi }{8}\] done
clear
D) \[\frac{\pi }{2}\] done
clear
View Solution play_arrow

question_answer9) If amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be [MP PMT 1985]
A) 2A done
clear
B) A done
clear
C) A/2 done
clear
D) A/4 done
clear
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question_answer10) The relation between time and displacement for two particles is given by \[{{y}_{1}}=0.06\sin 2\pi (0.04t+{{\varphi }_{1}})\], \[{{y}_{2}}=0.03\sin 2\pi (1.04t+{{\varphi }_{2}})\] The ratio of the intensity of the waves produced by the vibrations of the two particles will be [MP PMT 1991]
A) 2 : 1 done
clear
B) 1 : 2 done
clear
C) 4 : 1 done
clear
D) 1 : 4 done
clear
View Solution play_arrow

question_answer11) A wave is reflected from a rigid support. The change in phase on reflection will be [MP PMT 1990; RPMT 2002]
A) \[\pi /4\] done
clear
B) \[\pi /2\] done
clear
C) \[\pi \] done
clear
D) \[2\pi \] done
clear
View Solution play_arrow

question_answer12) A plane wave is represented by \[x=1.2\sin (314\,t+12.56y)\] Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has [MP PET 1991]
A) A wavelength of 0.25 m and travels in + ve x direction done
clear
B) A wavelength of 0.25 m and travels in + ve y direction done
clear
C) A wavelength of 0.5 m and travels in ? ve y direction done
clear
D) A wavelength of 0.5 m and travels in ? ve x direction done
clear
View Solution play_arrow

question_answer13) The displacement y (in cm) produced by a simple harmonic wave is \[y=\frac{10}{\pi }\sin \left( 2000\pi t\frac{\pi x}{17} \right)\]. The periodic time and maximum velocity of the particles in the medium will respectively be [CPMT 1986]
A) \[{{10}^{3}}\]sec and 330 m/sec done
clear
B) \[{{10}^{4}}\]sec and 20 m/sec done
clear
C) \[{{10}^{3}}\]sec and 200 m/sec done
clear
D) \[{{10}^{2}}\]sec and 2000 m/sec done
clear
View Solution play_arrow

question_answer14) The equation of a wave travelling in a string can be written as \[y=3\cos \pi (100\,tx)\]. Its wavelength is [MNR 1985; CPMT 1991; MP PMT 1994, 97; Pb. PET 2004]
A) 100 cm done
clear
B) 2 cm done
clear
C) 5 cm done
clear
D) None of the above done
clear
View Solution play_arrow

question_answer15) A transverse wave is described by the equation \[Y={{Y}_{0}}\sin 2\pi \left( ft\frac{x}{\lambda } \right)\]. The maximum particle velocity is four times the wave velocity if [IIT 1984; MP PMT 1997; EAMCET; 1998; CBSE PMT 2000; AFMC 2000; MP PMT/PET 1998; 01; KCET 1999, 04; Pb. PET 2001; DPMT 2005]
A) \[\lambda =\frac{\pi {{Y}_{0}}}{4}\] done
clear
B) \[\lambda =\frac{\pi {{Y}_{0}}}{2}\] done
clear
C) \[\lambda =\pi {{Y}_{0}}\] done
clear
D) \[\lambda =2\pi {{Y}_{0}}\] done
clear
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question_answer16) A wave equation which gives the displacement along the Y direction is given by the equation \[y={{10}^{4}}\sin (60t+2x)\], where x and y are in metres and t is time in seconds. This represents a wave [MNR 1983; IIT 1982; RPMT 1998; MP PET 2001]
A) Travelling with a velocity of 30 m/sec in the negative X direction done
clear
B) Of wavelength p metre done
clear
C) Of frequency 30/p Hz done
clear
D) Of amplitude \[{{10}^{4}}\]metre travelling along the negative X direction done
clear
View Solution play_arrow

question_answer17) A transverse wave of amplitude 0.5 m and wavelength 1 m and frequency 2 Hz is propagating in a string in the negative xdirection. The expression for this wave is [AIIMS 1980]
A) \[y(x,\,t)=0.5\sin (2\pi x4\pi t)\] done
clear
B) \[y(x,\,t)=0.5\cos (2\pi x+4\pi t)\] done
clear
C) \[y(x,\,t)=0.5\sin (\pi x2\pi t)\] done
clear
D) \[y(x,\,t)=0.5\cos (2\pi x+2\pi t)\] done
clear
View Solution play_arrow

question_answer18) The displacement of a particle is given by \[y=5\times {{10}^{4}}\sin (100t50x)\], where x is in meter and t in sec, find out the velocity of the wave [CPMT 1982]
A) 5000 m/sec done
clear
B) 2 m/sec done
clear
C) 0.5 m/sec done
clear
D) 300 m/sec done
clear
View Solution play_arrow

question_answer19) Which one of the following does not represent a travelling wave [NCERT 1984]
A) \[y=\sin (xv\,t)\] done
clear
B) \[y={{y}_{m}}\sin k(x+v\,t)\] done
clear
C) \[y={{y}_{m}}\log (xv\,t)\] done
clear
D) \[y=f({{x}^{2}}v\,{{t}^{2}})\] done
clear
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question_answer20) A wave represented by the given equation \[Y=A\sin \left( 10\,\pi \,x+15\,\pi \,t+\frac{\pi }{3} \right)\], where x is in meter and t is in second. The expression represents [IIT 1990]
A) A wave travelling in the positive X direction with a velocity of 1.5 m/sec done
clear
B) A wave travelling in the negative X direction with a velocity of 1.5 m/sec done
clear
C) A wave travelling in the negative X direction with a wavelength of 0.2 m done
clear
D) A wave travelling in the positive X direction with a wavelength of 0.2 m done
clear
View Solution play_arrow

question_answer21) A plane wave is described by the equation \[y=3\cos \left( \frac{x}{4}10t\frac{\pi }{2} \right)\]. The maximum velocity of the particles of the medium due to this wave is [MP PMT 1994]
A) 30 done
clear
B) \[\frac{3\pi }{2}\] done
clear
C) 3/4 done
clear
D) 40 done
clear
View Solution play_arrow

question_answer22) The path difference between the two waves \[{{y}_{1}}={{a}_{1}}\sin \,\left( \omega t\frac{2\pi x}{\lambda } \right)\] and \[{{y}_{2}}={{a}_{2}}\cos \,\left( \omega t\frac{2\pi x}{\lambda }+\varphi \right)\] is [MP PMT 1994]
A) \[\frac{\lambda }{2\pi }\varphi \] done
clear
B) \[\frac{\lambda }{2\pi }\left( \varphi +\frac{\pi }{2} \right)\] done
clear
C) \[\frac{2\pi }{\lambda }\left( \varphi \frac{\pi }{2} \right)\] done
clear
D) \[\frac{2\pi }{\lambda }\varphi \] done
clear
View Solution play_arrow

question_answer23) Wave equations of two particles are given by \[{{y}_{1}}=a\sin (\omega \,tkx)\], \[{{y}_{2}}=a\sin (kx+\omega \,t)\], then [BHU 1995]
A) They are moving in opposite direction done
clear
B) Phase between them is 90? done
clear
C) Phase between them is 180? done
clear
D) Phase between them is 0? done
clear
View Solution play_arrow

question_answer24) A wave is represented by the equation \[y=0.5\sin (10tx)m\]. It is a travelling wave propagating along the + x direction with velocity [Roorkee 1995]
A) 10 m/s done
clear
B) 20 m/s done
clear
C) 5 m/s done
clear
D) None of these done
clear
View Solution play_arrow

question_answer25) A wave is represented by the equation \[y=7\sin \left( 7\pi t0.04\,x\pi +\frac{\pi }{3} \right)\] x is in metres and t is in seconds. The speed of the wave is [MP PET 1996; AMU (Engg.) 1999]
A) 175 m/sec done
clear
B) 49 pm/sec done
clear
C) 49 pm/sec done
clear
D) 0.28 pm/sec done
clear
View Solution play_arrow

question_answer26) The equation of a transverse wave travelling on a rope is given by \[y=10\sin \pi (0.01x2.00t)\] where y and x are in cm and t in seconds. The maximum transverse speed of a particle in the rope is about [MP PET 1999; AIIMS 2000]
A) 63 cm/s done
clear
B) 75 cm/s done
clear
C) 100 cm/s done
clear
D) 121 cm/s done
clear
View Solution play_arrow

question_answer27) As a wave propagates [IITJEE 1999]
A) The wave intensity remains constant for a plane wave done
clear
B) The wave intensity decreases as the inverse of the distance from the source for a spherical wave done
clear
C) The wave intensity decreases as the inverse square of the distance from the source for a spherical wave done
clear
D) Total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times done
clear
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question_answer28) A transverse wave is represented by the equation \[y={{y}_{0}}\sin \frac{2\pi }{\lambda }(vtx)\] For what value of l, the maximum particle velocity equal to two times the wave velocity [CBSE PMT 1998; JIPMER 2001, 02; AFMC 2002]
A) \[\lambda =2\pi {{y}_{0}}\] done
clear
B) \[\lambda =\pi {{y}_{0}}/3\] done
clear
C) \[\lambda =\pi {{y}_{0}}/2\] done
clear
D) \[\lambda =\pi {{y}_{0}}\] done
clear
View Solution play_arrow

question_answer29) A travelling wave in a stretched string is described by the equation\[y=A\sin (kx\omega t)\]. The maximum particle velocity is [IIT 1997 ReExam; UPSEAT 2004]
A) Aw done
clear
B) w/k done
clear
C) dw/dk done
clear
D) x/t done
clear
View Solution play_arrow

question_answer30) A wave travels in a medium according to the equation of displacement given by \[y(x,\,t)=0.03\sin \pi (2t0.01x)\] where y and x are in metres and t in seconds. The wavelength of the wave is [EAMCET 1994; CPMT 2004]
A) 200 m done
clear
B) 100 m done
clear
C) 20 m done
clear
D) 10 m done
clear
View Solution play_arrow

question_answer31) The particles of a medium vibrate about their mean positions whenever a wave travels through that medium. The phase difference between the vibrations of two such particles [SCRA 1994]
A) Varies with time done
clear
B) Varies with distance separating them done
clear
C) Varies with time as well as distance done
clear
D) Is always zero done
clear
View Solution play_arrow

question_answer32) A wave is given by \[y=3\sin 2\pi \left( \frac{t}{0.04}\frac{x}{0.01} \right)\], where y is in cm. Frequency of wave and maximum acceleration of particle will be [RPET 1997]
A) \[100\,Hz,\ 4.7\times {{10}^{3}}\,cm/{{s}^{2}}\] done
clear
B) \[50\,Hz,\ 7.5\times {{10}^{3}}\,cm/{{s}^{2}}\] done
clear
C) \[25\,Hz,\ 4.7\times {{10}^{4}}\,cm/{{s}^{2}}\] done
clear
D) \[25\,Hz,\ 7.4\times {{10}^{4}}\,cm/{{s}^{2}}\] done
clear
View Solution play_arrow

question_answer33) Equation of a progressive wave is given by \[y=4\sin \left\{ \pi \left( \frac{t}{5}\frac{x}{9} \right)+\frac{\pi }{6} \right\}\] Then which of the following is correct [CBSE PMT 1993]
A) \[v=5\,m/\sec \] done
clear
B) \[\lambda =18\,m\] done
clear
C) \[a=0.04\,m\] done
clear
D) \[n=50\,Hz\] done
clear
View Solution play_arrow

question_answer34) With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the propagation direction are [CBSE PMT 1992; Roorkee 2000]
A) Energy, momentum and mass done
clear
B) Energy done
clear
C) Energy and mass done
clear
D) Energy and linear momentum done
clear
View Solution play_arrow

question_answer35) The frequency of the sinusoidal wave \[y=0.40\cos [2000\,t+0.80\,x]\] would be [CBSE PMT 1992]
A) 1000 p Hz done
clear
B) 2000 Hz done
clear
C) 20 Hz done
clear
D) \[\frac{1000}{\pi }Hz\] done
clear
View Solution play_arrow

question_answer36) Which of the following equations represents a wave [CBSE PMT 1994; JIPMER 2000]
A) \[Y=A(\omega \,tkx)\] done
clear
B) \[Y=A\sin \omega \,t\] done
clear
C) \[Y=A\cos kx\] done
clear
D) \[Y=A\sin (atbx+c)\] done
clear
View Solution play_arrow

question_answer37) The equation of a transverse wave is given by \[y=100\,\sin \pi (0.04z2t)\] where y and z are in cm ant t is in seconds. The frequency of the wave in Hz is [SCRA 1998]
A) 1 done
clear
B) 2 done
clear
C) 25 done
clear
D) 100 done
clear
View Solution play_arrow

question_answer38) The equation of a plane progressive wave is given by \[y=0.025\sin (100t+0.25x)\]. The frequency of this wave would be [CPMT 1993; JIPMER 2001, 02]
A) \[\frac{50}{\pi }Hz\] done
clear
B) \[\frac{100}{\pi }Hz\] done
clear
C) 100 Hz done
clear
D) 50 Hz done
clear
View Solution play_arrow

question_answer39) The equation of a sound wave is \[y=0.0015\sin (62.4x+316\,t)\] The wavelength of this wave is [CBSE PMT 1996; AFMC 2002; AIIMS 2002]
A) 0.2 unit done
clear
B) 0.1 unit done
clear
C) 0.3 unit done
clear
D) Cannot be calculated done
clear
View Solution play_arrow

question_answer40) In the given progressive wave equation, what is the maximum velocity of particle\[Y=0.5\sin (10\pi t5x)\]cm [BHU 1997]
A) 5 cm/s done
clear
B) 5p cm/s done
clear
C) 10 cm/s done
clear
D) 10.5 cm/s done
clear
View Solution play_arrow

question_answer41) A pulse or a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with [CBSE PMT 1997]
A) The same phase as the incident pulse but with velocity reversed done
clear
B) A phase change of 180? with no reversal of velocity done
clear
C) The same phase as the incident pulse with no reversal of velocity done
clear
D) A phase change of 180? with velocity reversed done
clear
View Solution play_arrow

question_answer42) The equation of a travelling wave is \[y=60\cos (1800t6x)\] where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is [CBSE PMT 1997; JIPMER 2001, 02]
A) \[3.6\times {{10}^{11}}\] done
clear
B) \[3.6\times {{10}^{6}}\] done
clear
C) \[3.6\times {{10}^{4}}\] done
clear
D) 3.6 done
clear
View Solution play_arrow

question_answer43) The wave equation is \[y=0.30\sin (314t1.57x)\] where t, x and y are in second, meter and centimeter respectively. The speed of the wave is [CPMT 1997; AFMC 1999; CPMT 2001]
A) 100 m/s done
clear
B) 200 m/s done
clear
C) 300 m/s done
clear
D) 400 m/s done
clear
View Solution play_arrow

question_answer44) Equation of the progressive wave is given by : \[y=a\sin \pi (40tx)\] where \[a\] and \[x\] are in metre and \[t\] in second. The velocity of the wave is [KCET 1999]
A) 80 m/s done
clear
B) 10 m/s done
clear
C) 40 m/s done
clear
D) 20 m/s done
clear
View Solution play_arrow

question_answer45) Progressive wave of sound is represented by \[y=a\sin [400\pi \,t\pi x/6.85]\] where \[x\] is in \[m\] and \[t\] is in sec. Frequency of the wave will be [RPMT 1999]
A) 200 Hz done
clear
B) 400 Hz done
clear
C) 500 Hz done
clear
D) 600 Hz done
clear
View Solution play_arrow

question_answer46) Two waves of frequencies 20 Hz and 30 Hz. Travels out from a common point. The phase difference between them after 0.6 sec is [JIPMER 1999]
A) Zero done
clear
B) \[\frac{\pi }{2}\] done
clear
C) \[\pi \] done
clear
D) \[\frac{3\pi }{4}\] done
clear
View Solution play_arrow

question_answer47) The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is \[{{90}^{o}}\]. Then the velocity of wave will be [MH CET 1999]
A) 192 m/s done
clear
B) 360 m/s done
clear
C) 710 m/s done
clear
D) 384 m/s done
clear
View Solution play_arrow

question_answer48) The equation of progressive wave is \[y=0.2\sin 2\pi \left[ \frac{t}{0.01}\frac{x}{0.3} \right]\], where \[x\] and \[y\] are in metre and \[t\] is in second. The velocity of propagation of the wave is [KCET 2000]
A) 30 m/s done
clear
B) 40 m/s done
clear
C) 300 m/s done
clear
D) 400 m/s done
clear
View Solution play_arrow

question_answer49) If the equation of transverse wave is \[y=5\sin 2\pi \left[ \frac{t}{0.04}\frac{x}{40} \right]\], where distance is in cm and time in second, then the wavelength of the wave is [MH CET 2000; DPMT 2003]
A) 60 cm done
clear
B) 40 cm done
clear
C) 35 cm done
clear
D) 25 cm done
clear
View Solution play_arrow

question_answer50) A wave is represented by the equation : \[y=a\sin (0.01x2t)\] where a and x are in cm. velocity of propagation of wave is [EAMCET 1994; AIIMS 2000; Pb. PMT 2003]
A) 10 cm/s done
clear
B) 50 cm/s done
clear
C) 100 cm/s done
clear
D) 200 cm/s done
clear
View Solution play_arrow

question_answer51) A simple harmonic progressive wave is represented by the equation : \[y=8\sin 2\pi (0.1x2t)\] where \[x\] and \[y\] are in cm and \[t\] is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the xdirection is [MP PMT 2000]
A) 18o done
clear
B) 36o done
clear
C) 54o done
clear
D) 72o done
clear
View Solution play_arrow

question_answer52) The intensity of a progressing plane wave in lossfree medium is [Roorkee 2000]
A) Directly proportional to the square of amplitude of the wave done
clear
B) Directly proportional to the velocity of the wave done
clear
C) Directly proportional to the square of frequency of the wave done
clear
D) Inversely proportional to the density of the medium done
clear
View Solution play_arrow

question_answer53) The equation of progressive wave is \[y=a\sin (200\,tx)\]. where \[x\] is in meter and \[t\] is in second. The velocity of wave is [RPMT 2000]
A) 200 m/sec done
clear
B) 100 m/sec done
clear
C) 50 m/sec done
clear
D) None of these done
clear
View Solution play_arrow

question_answer54) A wave is represented by the equation \[y=7\sin \{\pi (2t2x)\}\] where \[x\] is in metres and \[t\] in seconds. The velocity of the wave is [CPMT 2000; CBSE PMT 2000; Pb. PET 2000]
A) 1 m/s done
clear
B) 2 m/s done
clear
C) 5 m/s done
clear
D) 10 m/s done
clear
View Solution play_arrow

question_answer55) The equation of a longitudinal wave is represented as \[y=20\cos \pi (50tx)\]. Its wavelength is [UPSEAT 2001; Orissa PMT 2004]
A) 5 cm done
clear
B) 2 cm done
clear
C) 50 cm done
clear
D) 20 cm done
clear
View Solution play_arrow

question_answer56) A wave equation which gives the displacement along ydirection is given by \[y=0.001\sin (100t+x)\] where x and y are in meterand t is time in second. This represented a wave [UPSEAT 2001]
A) Of frequency \[\frac{100}{\pi }\] Hz done
clear
B) Of wavelength one metre done
clear
C) Travelling with a velocity of \[\frac{50}{\pi }\]ms?1 in the positive Xdirection done
clear
D) Travelling with a velocity of 100 ms?1 in the negative Xdirection done
clear
View Solution play_arrow

question_answer57) A transverse wave is given by \[y=A\sin 2\pi \left( \frac{t}{T}\frac{x}{\lambda } \right)\]. The maximum particle velocity is equal to 4 times the wave velocity when [MP PMT 2001]
A) \[\lambda =2\pi A\] done
clear
B) \[\lambda =\frac{1}{2}\pi A\] done
clear
C) \[\lambda =\pi A\] done
clear
D) \[\lambda =\frac{1}{4}\pi A\] done
clear
View Solution play_arrow

question_answer58) The equation of a wave is represented by \[y={{10}^{4}}\sin \,\left[ 100\,t\frac{x}{10} \right].\] The velocity of the wave will be [CBSE PMT 2001]
A) 100 m/s done
clear
B) 250 m/s done
clear
C) 750 m/s done
clear
D) 1000 m/s done
clear
View Solution play_arrow

question_answer59) A wave travelling in positive Xdirection with \[A=0.2m\] has a velocity of 360 m/sec. if \[\lambda =60m,\] then correct expression for the wave is [CBSE PMT 2002; KCET 2003]
A) \[y=0.2\sin \,\left[ 2\pi \left( 6t+\frac{x}{60} \right) \right]\] done
clear
B) \[y=0.2\sin \,\left[ \pi \left( 6t+\frac{x}{60} \right) \right]\] done
clear
C) \[y=0.2\sin \,\left[ 2\pi \left( 6t\frac{x}{60} \right) \right]\] done
clear
D) \[y=0.2\sin \,\left[ \pi \left( 6t\frac{x}{60} \right) \right]\] done
clear
View Solution play_arrow

question_answer60) The equation of a wave motion (with \[t\] in seconds and \[x\] in metres) is given by \[y=7\sin \,\left[ 7\pi t0.4\pi x+\frac{\pi }{3} \right]\]. The velocity of the wave will be [BHU 2002]
A) 17.5 m/s done
clear
B) \[49\pi \] m/s done
clear
C) \[\frac{49}{2\pi }m/s\] done
clear
D) \[\frac{2\pi }{49}m/s\] done
clear
View Solution play_arrow

question_answer61) Two waves represented by the following equations are travelling in the same medium \[{{y}_{1}}=5\sin 2\pi (75t0.25x)\], \[{{y}_{2}}=10\sin 2\pi (150t0.50x)\] The intensity ratio \[{{I}_{1}}/{{I}_{2}}\] of the two waves is [UPSEAT 2002]
A) 1 : 2 done
clear
B) 1 : 4 done
clear
C) 1 : 8 done
clear
D) 1 : 16 done
clear
View Solution play_arrow

question_answer62) The equation of a progressive wave is \[y=8\sin \left[ \pi \left( \frac{t}{10}\frac{x}{4} \right)+\frac{\pi }{3} \right]\]. The wavelength of the wave is [MH CET 2002]
A) 8 m done
clear
B) 4 m done
clear
C) 2 m done
clear
D) 10 m done
clear
View Solution play_arrow

question_answer63) Which of the following is not true for this progressive wave \[y=4\sin 2\pi \left( \frac{t}{0.02}\frac{x}{100} \right)\] where \[y\] and \[x\] are in cm & \[t\] in sec [CPMT 2003]
A) Its amplitude is 4 cm done
clear
B) Its wavelength is 100 cm done
clear
C) Its frequency is 50 cycles/sec done
clear
D) Its propagation velocity is \[50\times {{10}^{3}}\] cm/sec done
clear
View Solution play_arrow

question_answer64) The equation of a wave is given as \[y=0.07\sin (12\pi x3000\pi t)\]. Where \[x\] is in metre and \[t\] in sec, then the correct statement is [UPSEAT 2003]
A) \[\lambda =1/6m,\ v=250m/s\] done
clear
B) \[a=0.07m,\ v=300m/s\] done
clear
C) \[n=1500,\ v=200m/s\] done
clear
D) None done
clear
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question_answer65) The equation of the propagating wave is \[y=25\sin (20t+5x),\] where \[y\] is displacement. Which of the following statement is not true [MP PET 2003]
A) The amplitude of the wave is 25 units done
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B) The wave is propagating in positive \[x\]direction done
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C) The velocity of the wave is 4 units done
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D) The maximum velocity of the particles is 500 units done
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question_answer66) In a plane progressive wave given by \[y=25\cos (2\pi t\pi x)\], the amplitude and frequency are respectively [BCECE 2003]
A) 25,100 done
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B) 25, 1 done
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C) 25, 2 done
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D) \[50\pi ,\,\] 2 done
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question_answer67) The displacement \[y\] of a wave travelling in the xdirection is given by \[y={{10}^{4}}\sin \,\,\left( 600t2x+\frac{\pi }{3} \right)\] metres, where \[x\] is expressed in metres and \[t\] in seconds. The speed of the wavemotion, in ms?1, is [AIEEE 2003]
A) 200 done
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B) 300 done
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C) 600 done
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D) 1200 done
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question_answer68) The displacement y of a particle in a medium can be expressed as: \[y={{10}^{6}}\sin (100t+20x+\pi /4)m,\] where t is in second and x in meter. The speed of wave is [AIEEE 2004]
A) 2000 m/s done
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B) 5 m/s done
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C) 20 m/s done
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D) \[5\pi \text{ }m/s\] done
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question_answer69) If the wave equation \[y=0.08\sin \frac{2\pi }{\lambda }(200tx)\] then the velocity of the wave will be [BCECE 2004]
A) \[400\sqrt{2}\] done
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B) \[200\sqrt{2}\] done
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C) 400 done
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D) 200 done
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question_answer70) The phase difference between two points separated by 0.8 m in a wave of frequency is 120 Hz is \[\frac{\pi }{2}.\] The velocity of wave is [Pb. PET 2000]
A) 720 m/s done
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B) 384 m/s done
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C) 250 m/s done
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D) 1 m/s done
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question_answer71) A plane progressive wave is represented by the equation \[y=0.1\sin \left( 200\pi t\frac{20\pi x}{17} \right)\] where y is displacement in m, t in second and x is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively are [Pb. PET 2001]
A) 100 Hz, 1.7 m, 170 m/s done
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B) 150 Hz, 2.4 m, 200 m/s done
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C) 80 Hz, 1.1 m, 90 m/s done
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D) 120 Hz, 1.25 m, 207 m/s done
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question_answer72) The equation of a travelling wave is given by \[y=0.5\sin (20x400t)\] where x and y are in meter and t is in second. The velocity of the wave is [UPSEAT 2004]
A) 10 m/s done
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B) 20 m/s done
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C) 200 m/s done
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D) 400 m/s done
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question_answer73) A transverse progressive wave on a stretched string has a velocity of \[10\,m{{s}^{1}}\] and a frequency of 100 Hz. The phase difference between two particles of the string which are 2.5 cm apart will be [MP PMT 1994]
A) \[\frac{\pi }{8}\] done
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B) \[\frac{\pi }{4}\] done
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C) \[\frac{3\pi }{8}\] done
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D) \[\frac{\pi }{2}\] done
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question_answer74) A transverse sinusoidal wave of amplitude a, wavelength l and frequency n is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If \[a={{10}^{3}}\,m\] and \[v=10\,m{{s}^{1}}\], then l and n are given by [IIT 1998]
A) \[\lambda =2\pi \times {{10}^{2}}\,m\] done
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B) \[\lambda ={{10}^{3}}\,m\] done
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C) \[n=\frac{{{10}^{3}}}{2\pi }Hz\] done
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D) \[n={{10}^{4}}\,Hz\] done
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question_answer75) When a longitudinal wave propagates through a medium, the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant [SCRA 1998]
A) Kinetic energy done
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B) Potential energy done
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C) Sum of kinetic energy and potential energy done
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D) Difference between kinetic energy and potential energy done
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question_answer76) Equation of a progressive wave is given by \[y=a\,\sin \pi \,\left[ \frac{t}{2}\frac{x}{4} \right]\,,\] where t is in seconds and x is in meters. The distance through which the wave moves in 8 sec is (in meter) [KCET 1998]
A) 8 done
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B) 16 done
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C) 2 done
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D) 4 done
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question_answer77) The phase difference between two waves represented by \[{{y}_{1}}={{10}^{6}}\sin [100\,t+(x/50)+0.5]m\] \[{{y}_{2}}={{10}^{6}}\cos \,[100\,t+(x/50)]m\] where x is expressed in metres and t is expressed in seconds, is approximately [CBSE PMT 2004]
A) 1.5 rad done
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B) 1.07 rad done
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C) 2.07 rad done
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D) 0.5 rad done
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question_answer78) Equation of motion in the same direction are given by \[{{y}_{1}}=2a\sin (\omega tkx)\] and \[{{y}_{2}}=2a\sin (\omega tkx\theta )\] The amplitude of the medium particle will be [CPMT 2004]
A) \[2a\cos \theta \] done
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B) \[\sqrt{2}a\cos \theta \] done
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C) \[4a\cos \theta /2\] done
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D) \[\sqrt{2}a\cos \theta /2\] done
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question_answer79) A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period) [KCET 2005]
A) \[T/2\] done
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B) \[T/4\] done
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C) T done
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D) \[2T\] done
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question_answer80) If the equation of transverse wave is \[Y=2\sin (kx2t),\] then the maximum particle velocity is [Orissa JEE 2005]
A) 4 units done
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B) 2 units done
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C) 0 done
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D) 6 units done
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