JEE Main & Advanced Physics Wave Mechanics Question Bank

done Stationary Waves Total Questions - 39

• question_answer1)
  The distance between the nearest node and antinode in a stationary wave is [MP PET 1984; CBSE PMT 1993; AFMC 1996; RPET 2002]
  A)
             l     done clear
  B)
             \[\frac{\lambda }{2}\] done clear
  C)
             \[\frac{\lambda }{4}\]       done clear
  D)
             2l done clear
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• question_answer2)
  In stationary wave                                    [MP PET 1987; BHU 1995]
  A)
             Strain is maximum at nodes done clear
  B)
             Strain is maximum at antinodes done clear
  C)
             Strain is minimum at nodes done clear
  D)
             Amplitude is zero at all the points done clear
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• question_answer3)
  The phase difference between the two particles situated on both the sides of a node is                [MP PET 2002]
  A)
             0°    done clear
  B)
             90° done clear
  C)
             180°                                          done clear
  D)
             360° done clear
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• question_answer4)
  Which of the property makes difference between progressive and stationary waves                      [MP PMT 1987]
  A)
             Amplitude                              done clear
  B)
             Frequency done clear
  C)
             Propagation of energy      done clear
  D)
             Phase of the wave done clear
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• question_answer5)
  Stationary waves are formed when [NCERT 1983]
  A)
             Two waves of equal amplitude and equal frequency travel along the same path in opposite directions done clear
  B)
             Two waves of equal wavelength and equal amplitude travel along the same path with equal speeds in opposite directions done clear
  C)
             Two waves of equal wavelength and equal phase travel along the same path with equal speed done clear
  D)
             Two waves of equal amplitude and equal speed travel along the same path in opposite direction done clear
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• question_answer6)
  For the stationary wave \[y=4\sin \,\left( \frac{\pi x}{15} \right)\cos (96\,\pi t)\], the distance between a node and the next antinode is[MP PMT 1987]
  A)
             7.5  done clear
  B)
             15 done clear
  C)
             22.5                                           done clear
  D)
             30 done clear
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• question_answer7)
  The equation of stationary wave along a stretched string is given by \[y=5\sin \frac{\pi x}{3}\cos 40\pi t\], where x and y are in cm and t in second. The separation between two adjacent nodes is         [CPMT 1990; MP PET 1999; AMU 1999; DPMT 2004; BHU 2005]
  A)
             1.5 cm                                      done clear
  B)
             3 cm done clear
  C)
             6 cm                                          done clear
  D)
             4 cm done clear
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• question_answer8)
  The equation \[\overrightarrow{\varphi \,}(x,\,t)=\overrightarrow{j\,}\sin \,\left( \frac{2\pi }{\lambda }v\,t \right)\cos \,\left( \frac{2\pi }{\lambda }x \right)\] represents [MNR 1994]
  A)
             Transverse progressive wave done clear
  B)
             Longitudinal progressive wave done clear
  C)
             Longitudinal stationary wave done clear
  D)
             Transverse stationary wave done clear
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• question_answer9)
  The equation of a stationary wave is \[y=0.8\cos \,\left( \frac{\pi x}{20} \right)\sin 200\,\pi t\], where x is in cm and t is in sec. The separation between consecutive nodes will be [MP PET 1994]
  A)
             20 cm                                       done clear
  B)
             10 cm done clear
  C)
             40 cm                                       done clear
  D)
             30 cm done clear
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• question_answer10)
  In a stationary wave, all particles are  [MP PMT 1994]
  A)
             At rest at the same time twice in every period of oscillation done clear
  B)
             At rest at the same time only once in every period of oscillation done clear
  C)
             Never at rest at the same time done clear
  D)
             Never at rest at all done clear
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• question_answer11)
  A wave represented by the given equation \[y=a\cos (kx-\omega \,t)\] is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is                  [IIT 1988; MP PMT 1994, 97; AIIMS 1998; SCRA 1998; MP PET 2001; KCET 2001; AIEEE 2002; UPSEAT 2004]
  A)
             \[y=a\sin (kx+\omega \,t)\]   done clear
  B)
             \[y=-a\cos (kx+\omega \,t)\] done clear
  C)
             \[y=-a\cos (kx-\omega \,t)\] done clear
  D)
             \[y=-a\sin (kx-\omega \,t)\] done clear
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• question_answer12)
  At a certain instant a stationary transverse wave is found to have maximum kinetic energy. The appearance of string at that instant is                                                             [AIIMS 1995]
  A)
             Sinusoidal shape with amplitude A/3 done clear
  B)
             Sinusoidal shape with amplitude A/2 done clear
  C)
             Sinusoidal shape with amplitude A done clear
  D)
             Straight line done clear
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• question_answer13)
  The equation\[y=0.15\sin 5x\cos 300t\], describes a stationary wave. The wavelength of the stationary wave is [MP PMT 1995]
  A)
             Zero                                          done clear
  B)
             1.256 metres done clear
  C)
             2.512 metres                         done clear
  D)
             0.628 metre done clear
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• question_answer14)
  In stationary waves, antinodes are the points where there is      [MP PMT 1996]
  A)
             Minimum displacement and minimum pressure change done clear
  B)
             Minimum displacement and maximum pressure change done clear
  C)
             Maximum displacement and maximum pressure change done clear
  D)
             Maximum displacement and minimum pressure change done clear
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• question_answer15)
  In stationary waves all particles between two nodes pass through the mean position [MP PMT 1999; KCET 2001]
  A)
             At different times with different velocities done clear
  B)
             At different times with the same velocity done clear
  C)
             At the same time with equal velocity done clear
  D)
             At the same time with different velocities done clear
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• question_answer16)
  Standing waves can be produced                          [IIT-JEE 1999]
  A)
             On a string clamped at both the ends done clear
  B)
             On a string clamped at one end and free at the other done clear
  C)
             When incident wave gets reflected from a wall done clear
  D)
             When two identical waves with a phase difference of p are moving in the same direction done clear
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• question_answer17)
  A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is [CBSE PMT 1998; MH CET 2002; AIIMS 2000; BHU 2001]
  A)
             1.21 Å                                       done clear
  B)
             2.42 Å done clear
  C)
             6.05 Å                                       done clear
  D)
             3.63 Å done clear
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• question_answer18)
  In stationary waves, distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be [CMEET Bihar 1995]
  A)
             Zero                                          done clear
  B)
             p/2 done clear
  C)
             p     done clear
  D)
             3p/2 done clear
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• question_answer19)
  Stationary waves of frequency 300 Hz are formed in a medium in which the velocity of sound is 1200 metre/sec. The distance between a node and the neighbouring antinode is                                        [SCRA 1994]
  A)
             1 m done clear
  B)
             2 m done clear
  C)
             3 m done clear
  D)
             4 m done clear
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• question_answer20)
  Which two of the given transverse waves will give stationary waves when get superimposed [RPET 1997; MP PET 1993]                    \[{{z}_{1}}=a\cos (kx-\omega \,t)\]                                      .....                    \[{{z}_{2}}=a\cos (kx+\omega \,t)\]                                     .....                    \[{{z}_{3}}=a\cos (ky-\omega \,t)\]                                      .....
  A)
             A and B                                    done clear
  B)
             A and C done clear
  C)
             B and C                                    done clear
  D)
             Any two done clear
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• question_answer21)
  A standing wave is represented by \[Y=A\sin (100t)\cos (0.01x)\]            where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of wave is      [CBSE PMT 1994; AFMC 2002]
  A)
             \[{{10}^{4}}\,m/s\]             done clear
  B)
             \[1\,m/s\] done clear
  C)
             \[{{10}^{-4}}\,m/s\] done clear
  D)
             Not derivable from above data done clear
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• question_answer22)
  A wave of frequency 100 Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of 10 cm from the fixed end of the string. The speed of incident (and reflected) wave are [CBSE PMT 1994]
  A)
             40 m/s                                     done clear
  B)
             20 m/s done clear
  C)
             10 m/s                                     done clear
  D)
             5 m/s done clear
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• question_answer23)
  \[y=a\cos (kx+\omega t)\] superimposes on another wave giving a stationary wave having node at x = 0. What is the equation of the other wave                   [BHU 1998; DPMT 2000]
  A)
             \[-a\cos (kx+\omega t)\] done clear
  B)
             \[a\cos (kx-\omega t)\] done clear
  C)
             \[-a\cos (kx-\omega t)\]  done clear
  D)
             \[-a\sin (kx+\omega t)\] done clear
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• question_answer24)
  Two waves are approaching each other with a velocity of 20 m/s and frequency\[n\]. The distance between two consecutive nodes is                                               [Pb. PMT 1999]
  A)
             \[\frac{20}{n}\]                    done clear
  B)
             \[\frac{10}{n}\] done clear
  C)
             \[\frac{5}{n}\]                      done clear
  D)
             \[\frac{n}{10}\] done clear
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• question_answer25)
  Energy is not carried by which of the following waves [RPMT 1998; AIIMS 1998, 99]
  A)
             Stationary                              done clear
  B)
             Progressive done clear
  C)
             Transverse                             done clear
  D)
             Electromagnetic done clear
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• question_answer26)
  The stationary wave produced on a string is represented by the equation\[y=5\cos (\pi x/3)\sin 40\pi t\]. Where x and y are in cm and \[t\] is in seconds. The distance between consecutive nodes is                                   [MP PMT 2000]
  A)
             5 cm                                          done clear
  B)
             \[\pi \] cm done clear
  C)
             3 cm                                          done clear
  D)
             40 cm done clear
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• question_answer27)
  Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed 10 ms?1. If the minimum time interval between two instants when the string is flat is 0.5 s, the wavelength of the waves is                                                     [Roorkee 2000]
  A)
             25 m                                         done clear
  B)
             20 m done clear
  C)
             15 m                                         done clear
  D)
             10 m done clear
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• question_answer28)
  ?Stationary waves? are so called because in them [MP PMT 2001]
  A)
             The particles of the medium are not disturbed at all done clear
  B)
             The particles of the medium do not execute SHM done clear
  C)
             There occurs no flow of energy along the wave done clear
  D)
             The interference effect can?t be observed done clear
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• question_answer29)
  Two waves are approaching each other with a velocity of 16 m/s and frequency n. The distance between two consecutive nodes is                           [CPMT 2001; Pb. PMT 1999]
  A)
             \[\frac{16}{n}\]                    done clear
  B)
             \[\frac{8}{n}\] done clear
  C)
             \[\frac{n}{16}\]                    done clear
  D)
             \[\frac{n}{8}\] done clear
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• question_answer30)
  Stationary waves                                               [Kerala (Med.) 2002]
  A)
             Transport energy done clear
  B)
             Does not transport energy done clear
  C)
             Have nodes and antinodes done clear
  D)
             Both (b) and (c) done clear
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• question_answer31)
  In a stationary wave all the particles                       [KCET 2002]
  A)
             On either side of a node vibrate in same phase done clear
  B)
             In the region between two nodes vibrate in same phase done clear
  C)
             In the region between two antinodes vibrate in same phase           done clear
  D)
             Of the medium vibrate in same phase done clear
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• question_answer32)
  When a stationary wave is formed then its frequency is [Kerala (Engg.) 2002]
  A)
             Same as that of the individual waves done clear
  B)
             Twice that of the individual waves done clear
  C)
             Half that of the individual waves done clear
  D)
             None of the above done clear
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• question_answer33)
  In stationary waves                                [RPMT 1998; JIPMER 2002]
  A)
             Energy is uniformly distributed done clear
  B)
             Energy is minimum at nodes and maximum at antinodes done clear
  C)
             Energy is maximum at nodes and minimum at antinodes done clear
  D)
             Alternating maximum and minimum energy producing at nodes and antinodes done clear
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• question_answer34)
  Equation of a stationary wave is \[y=10\sin \frac{\pi x}{4}\cos 20\pi t.\] Distance between two consecutive nodes is  [MP PMT 2002]
  A)
             4     done clear
  B)
             2 done clear
  C)
             1     done clear
  D)
             8 done clear
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• question_answer35)
  At nodes in stationary waves  [SCRA 1994; UPSEAT 2000; MP PET 2003; RPET 2003]
  A)
             Change in pressure and density are maximum done clear
  B)
             Change in pressure and density are minimum done clear
  C)
             Strain is zero done clear
  D)
             Energy is minimum done clear
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• question_answer36)
  Consider the three waves \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] as            \[{{z}_{1}}=A\sin (kx-\omega \,t)\], \[{{z}_{2}}=A\sin (kx+\omega \,t)\] and \[{{z}_{3}}=A\sin (ky-\omega \,t)\]. Which of the following represents a standing wave                                        [DCE 2004]
  A)
             \[{{z}_{1}}+{{z}_{2}}\]       done clear
  B)
             \[{{z}_{2}}+{{z}_{3}}\] done clear
  C)
             \[{{z}_{3}}+{{z}_{1}}\]       done clear
  D)
             \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\] done clear
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• question_answer37)
  The following equations represent progressive transverse waves \[{{Z}_{1}}=A\cos (\omega \,t-kx)\], \[{{Z}_{2}}=A\cos (\omega \,t+kx)\], \[{{Z}_{3}}=A\cos (\omega \,t+ky)\] and \[{{Z}_{4}}=A\cos (2\omega \,t-2ky)\]. A stationary wave will be formed by superposing [MP PET 1993]
  A)
             \[{{Z}_{1}}\] and \[{{Z}_{2}}\]                                            done clear
  B)
             \[{{Z}_{1}}\] and \[{{Z}_{4}}\] done clear
  C)
             \[{{Z}_{2}}\] and \[{{Z}_{3}}\]                                            done clear
  D)
             \[{{Z}_{3}}\] and \[{{Z}_{4}}\] done clear
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• question_answer38)
  Two travelling waves \[{{y}_{1}}=A\sin [k(x-c\,t)]\] and \[{{y}_{2}}=A\sin [k(x+c\,t)]\] are superimposed on string. The distance between adjacent nodes is                          [IIT 1992]
  A)
             \[c\,t/\pi \]                            done clear
  B)
             \[c\,t/2\pi \] done clear
  C)
             \[\pi /2k\]                              done clear
  D)
             \[\pi /k\] done clear
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• question_answer39)
  A string vibrates according to the equation \[y=5\sin \,\left( \frac{2\pi x}{3} \right)\,\,\cos \,20\,\pi t\], where x and y are in cm and t in sec. The distance between two adjacent nodes is  [UPSEAT 2005]
  A)
             3 cm                                          done clear
  B)
             4.5 cm done clear
  C)
             6 cm                                          done clear
  D)
             1.5 cm done clear
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