JEE Main & Advanced Physics Wave Mechanics Question Bank

done Interference and Superposition of Waves Total Questions - 26

• question_answer1)
  There is a destructive interference between the two waves of wavelength l coming from two different paths at a point. To get maximum sound or constructive interference at that point, the path of one wave is to be increased by                                                                                            [MP PET 1985]
  A)
             \[\frac{\lambda }{4}\]       done clear
  B)
             \[\frac{\lambda }{2}\] done clear
  C)
             \[\frac{3\lambda }{4}\]     done clear
  D)
             \[\lambda \] done clear
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• question_answer2)
  When two sound waves with a phase difference of \[\pi /2\], and each having amplitude A and frequency \[\omega \], are superimposed on each other, then the maximum amplitude and frequency of resultant wave is                 [MP PMT 1989]
  A)
             \[\frac{A}{\sqrt{2}}:\frac{\omega }{2}\]                       done clear
  B)
             \[\frac{A}{\sqrt{2}}:\omega \] done clear
  C)
             \[\sqrt{2}\,A:\frac{\omega }{2}\]                                    done clear
  D)
             \[\sqrt{2}\,A:\omega \] done clear
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• question_answer3)
  If the phase difference between the two wave is 2p during superposition, then the resultant amplitude is                                                                                              [DPMT 2001]
  A)
             Maximum                              done clear
  B)
             Minimum done clear
  C)
             Maximum or minimum     done clear
  D)
             None of the above done clear
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• question_answer4)
  The superposition takes place between two waves of frequency f and amplitude a. The total intensity is directly proportional to                                                          [MP PMT 1986]
  A)
             a     done clear
  B)
             2a done clear
  C)
             \[2{{a}^{2}}\]                        done clear
  D)
             \[4{{a}^{2}}\] done clear
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• question_answer5)
  If two waves of same frequency and same amplitude respectively, on superimposition produced a resultant disturbance of the same amplitude, the waves differ in phase by                             [MP PMT 1990; MP PET 2000]
  A)
             p     done clear
  B)
             \[2\pi /3\] done clear
  C)
             \[\pi /2\]                                 done clear
  D)
             Zero done clear
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• question_answer6)
  Two sources of sound A and B produces the wave of 350 Hz, they vibrate in the same phase. The particle P is vibrating under the influence of these two waves, if the amplitudes at the point P produced by the two waves is 0.3 mm and 0.4 mm, then the resultant amplitude of the point P will be when AP ? BP = 25 cm and the velocity of sound is 350 m/sec 
  A)
             0.7 mm                                    done clear
  B)
             0.1 mm done clear
  C)
             0.2 mm                                    done clear
  D)
             0.5 mm done clear
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• question_answer7)
  Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is ?a? and the phase of A is ahead by \[\frac{\pi }{3}\] than that of B and the distance AP is greater than BP by 50 cm. Then the resultant amplitude at the point P will be, if the wavelength is 1 meter                  [BVP 2003]
  A)
             2a   done clear
  B)
             \[a\sqrt{3}\] done clear
  C)
             \[a\sqrt{2}\]                          done clear
  D)
             a done clear
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• question_answer8)
  Coherent sources are characterized by the same [KCET 1993]
  A)
             Phase and phase velocity        done clear
  B)
             Wavelength, amplitude and phase velocity done clear
  C)
             Wavelength, amplitude and frequency done clear
  D)
             Wavelength and phase done clear
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• question_answer9)
  The minimum intensity of sound is zero at a point due to two sources of nearly equal frequencies, when
  A)
             Two sources are vibrating in opposite phase done clear
  B)
             The amplitude of two sources are equal done clear
  C)
             At the point of observation, the amplitudes of two S.H.M. produced by two sources are equal and both the S.H.M. are along the same straight line done clear
  D)
             Both the sources are in the same phase done clear
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• question_answer10)
  Two sound waves (expressed in CGS units) given by \[{{y}_{1}}=0.3\sin \frac{2\pi }{\lambda }(vt-x)\] and \[{{y}_{2}}=0.4\sin \frac{2\pi }{\lambda }(vt-x+\theta )\]  interfere. The resultant amplitude at a place where phase difference is \[\pi /2\] will be                                [MP PET 1991]
  A)
             0.7 cm                                      done clear
  B)
             0.1 cm done clear
  C)
             0.5 cm                                      done clear
  D)
             \[\frac{1}{10}\sqrt{7}\,cm\] done clear
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• question_answer11)
  If two waves having amplitudes 2A and A and same frequency and velocity, propagate in the same direction in the same phase, the resulting amplitude will be [MP PET 1991; DPMT 1999]
  A)
             3A  done clear
  B)
             \[\sqrt{5}A\] done clear
  C)
             \[\sqrt{2}A\]                         done clear
  D)
             A done clear
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• question_answer12)
  The intensity ratio of two waves is 1 : 16. The ratio of their amplitudes is                                                [EAMCET 1983]
  A)
             1 : 16                                         done clear
  B)
             1 : 4 done clear
  C)
             4 : 1                                           done clear
  D)
             2 : 1 done clear
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• question_answer13)
  Out of the given four waves (1), (2), (3) and (4)                    \[y=a\sin (kx+\omega t)\]                                                                        ......(1)                    \[y=a\sin (\omega t-kx)\]                                                                         ......(2)                    \[y=a\cos (kx+\omega t)\]                                                                       ......(3)                    \[y=a\cos (\omega t-kx)\]                                                                        ......(4) emitted by four different sources \[{{S}_{1}},\,{{S}_{2}},\,{{S}_{3}}\] and \[{{S}_{4}}\] respectively, interference phenomena would be observed in space under appropriate conditions when    [CPMT 1988]
  A)
             Source \[{{S}_{1}}\] emits wave (1) and \[{{S}_{2}}\] emits wave (2) done clear
  B)
             Source \[{{S}_{3}}\] emits wave (3) and \[{{S}_{4}}\] emits wave (4) done clear
  C)
             Source \[{{S}_{2}}\] emits wave (2) and \[{{S}_{4}}\] emits wave (4) done clear
  D)
             \[{{S}_{4}}\] emits waves (4) and \[{{S}_{3}}\] emits waves (3) done clear
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• question_answer14)
  Two waves of same frequency and intensity superimpose with each other in opposite phases, then after superposition the                                                                                      [AFMC 1995]
  A)
             Intensity increases by 4 times done clear
  B)
             Intensity increases by two times done clear
  C)
             Frequency increases by 4 times done clear
  D)
             None of these done clear
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• question_answer15)
  The superposing waves are represented by the following equations :                    \[{{y}_{1}}=5\sin 2\pi (10\,t-0.1x)\], \[{{y}_{2}}=10\sin 2\pi (20\,t-0.2x)\]            Ratio of intensities \[\frac{{{I}_{\max }}}{{{I}_{\min }}}\] will be [AIIMS 1995; KCET 2001]
  A)
             1     done clear
  B)
             9 done clear
  C)
             4     done clear
  D)
             16 done clear
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• question_answer16)
  The displacement of a particle is given by                    \[x=3\sin (5\pi \,t)+4\cos (5\pi \,t)\]            The amplitude of the particle is                                                      [MP PMT 1999]
  A)
             3     done clear
  B)
             4 done clear
  C)
             5     done clear
  D)
             7 done clear
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• question_answer17)
  Two waves                    \[{{y}_{1}}={{A}_{1}}\sin (\omega t-{{\beta }_{1}})\], \[{{y}_{2}}={{A}_{2}}\sin (\omega t-{{\beta }_{2}})\]            Superimpose to form a resultant wave whose amplitude is [CPMT 1999]
  A)
             \[\sqrt{A_{1}^{2}+A_{2}^{2}+2{{A}_{1}}{{A}_{2}}\cos ({{\beta }_{1}}-{{\beta }_{2}})}\] done clear
  B)
             \[\sqrt{A_{1}^{2}+A_{2}^{2}+2{{A}_{1}}{{A}_{2}}\sin ({{\beta }_{1}}-{{\beta }_{2}})}\] done clear
  C)
             \[{{A}_{1}}+{{A}_{2}}\] done clear
  D)
             \[|{{A}_{1}}+{{A}_{2}}|\] done clear
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• question_answer18)
  If the ratio of amplitude of wave is 2 : 1, then the ratio of maximum and minimum intensity is     [MH CET 1999]
  A)
             9 : 1                                           done clear
  B)
             1 : 9 done clear
  C)
             4 : 1                                           done clear
  D)
             1 : 4 done clear
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• question_answer19)
  The two interfering waves have intensities in the ratio 9 : 4. The ratio of intensities of maxima and minima in the interference pattern will be                                      [AMU 2000]
  A)
             1 : 25                                         done clear
  B)
             25 : 1 done clear
  C)
             9 : 4                                           done clear
  D)
             4 : 9 done clear
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• question_answer20)
  If the ratio of amplitude of two waves is 4 : 3. Then the ratio of maximum and minimum intensity will be [MHCET 2000]
  A)
             16 : 18                                      done clear
  B)
             18 : 16 done clear
  C)
             49 : 1                                         done clear
  D)
             1 : 49 done clear
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• question_answer21)
  Equation of motion in the same direction is given by \[{{y}_{1}}=A\sin (\omega t-kx)\], \[{{y}_{2}}=A\sin (\omega t-kx-\theta )\]. The amplitude of the medium particle will be                         [BHU 2003]
  A)
             \[2A\cos \frac{\theta }{2}\]    done clear
  B)
             \[2A\cos \theta \] done clear
  C)
             \[\sqrt{2}A\cos \frac{\theta }{2}\]                                  done clear
  D)
             \[1.2f,\ 1.2\lambda \] done clear
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• question_answer22)
  Two waves having the intensities in the ratio of 9 : 1 produce interference. The ratio of maximum to the minimum intensity, is equal to                             [CPMT 2001; Pb. PET 2004]
  A)
             2 : 1                                           done clear
  B)
             4 : 1                                           done clear
  C)
             9 : 1                                           done clear
  D)
             10 : 8 done clear
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• question_answer23)
  The displacement of the interfering light waves are \[{{y}_{1}}=4\sin \omega \,t\] and \[{{y}_{2}}=3\sin \left( \omega \,t+\frac{\pi }{2} \right)\]. What is the amplitude of the resultant wave  [RPMT 1996; Orissa JEE 2005]
  A)
             5     done clear
  B)
             7     done clear
  C)
             1     done clear
  D)
             0 done clear
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• question_answer24)
  Two waves are represented by \[{{y}_{1}}=a\sin \left( \omega \,t+\frac{\pi }{6} \right)\] and \[{{y}_{2}}=a\cos \omega \,t\]. What will be their resultant amplitude [RPMT 1996]
  A)
             a     done clear
  B)
             \[\sqrt{2}\,a\] done clear
  C)
             \[\sqrt{3}\,a\]                      done clear
  D)
             2a done clear
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• question_answer25)
  The amplitude of a wave represented by displacement equation  \[y=\frac{1}{\sqrt{a}}\sin \omega t\pm \frac{1}{\sqrt{b}}\cos \omega t\]  will be [BVP 2003]
  A)
             \[\frac{a+b}{ab}\]               done clear
  B)
             \[\frac{\sqrt{a}+\sqrt{b}}{ab}\] done clear
  C)
             \[\frac{\sqrt{a}\pm \sqrt{b}}{ab}\]                                 done clear
  D)
             \[\sqrt{\frac{a+b}{ab}}\] done clear
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• question_answer26)
  Two waves having equations                    \[{{x}_{1}}=a\sin (\omega \,t+{{\varphi }_{1}})\], \[{{x}_{2}}=a\sin \,(\omega \,t+{{\varphi }_{2}})\] If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is                              [CBSE PMT 2001]
  A)
             \[\frac{\pi }{6}\]                  done clear
  B)
             \[\frac{2\pi }{3}\] done clear
  C)
             \[\frac{\pi }{4}\]                  done clear
  D)
             \[\frac{\pi }{3}\] done clear
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