CBSE Questions for Class 11 Engineering Physics Waves Quiz 10 - MCQExams.com

$$x_1 = A\sin(\omega t - 0.1x)$$ and $$x_2 = A\sin(\omega t - 0.1x - \dfrac{\phi}{2})$$. The resultant amplitude of combined wave is:-
  • $$2 A\cos \dfrac{\phi}{4}$$
  • $$A \sqrt{2\cos \dfrac{\phi}{2}}$$
  • $$2 A\cos \dfrac{\phi}{2}$$
  • $$A \sqrt{2(1 + \cos \dfrac{\phi}{4})}$$
Two parallel beams of light of wavelength $$\lambda $$, inclined to each other at angle $$\theta \ ( <  + 1)$$ are inclined on a plane at near normal incidence. The fringe width will be. 
1131323_3d6e291a3dbc46ae8ca3348e92f9cdb6.png
  • $$\dfrac{\lambda }{{2\theta }}$$
  • $$\dfrac{2\lambda }{{\theta }}$$
  • $$\dfrac{\lambda }{{\theta }}$$
  • $$2 \lambda \ \sin \theta $$
Two waves $$E _ { 1 } = E _ { 0 } \sin \omega t$$  and $$E _ { 2 } = E _ { 0 } \sin ( \omega t + 60 )$$ superimpose each other. Find out initial phase of resultant wave?
  • $$30 ^ { \circ }$$
  • $$60 ^ { \circ }$$
  • $$120 ^ { \circ }$$
  • $$0 ^ { \circ }$$
The amplitude of a particle due to superposition of following S.H.Ms. Along the same line is 
$${ X }_{ 1 }=2sin50\pi t\quad ;\quad { X }_{ 2 }=10sin\left( 50\pi t+{ 37 }^{ } \right) $$
$${ X }_{ 3 }=-4sin50\pi t\quad ;\quad { X }_{ 4 }=-12sin50\pi t$$
  • $$4\sqrt { 2 } $$
  • $$4$$
  • $$6\sqrt { 2 } $$
  • None of these
Equation of  two S.H.M. $$ x_1 = 5 sin ( 2 \pi t + \pi /4), $$  $$ x_2 =   5\sqrt { 2 } (sin\quad 2\pi t+cos2\pi t)$$ ratio of amplitude & phase difference will be
  • $$ 2 : 1, 0 $$
  • $$ 1 : 2, 0 $$
  • $$ 1 : 2, \pi /2 $$
  • $$ 2 : 1, \pi / 2 $$
Two simple harmonic motions are represented by the equation $$y_{1} = 10\sin (4\pi t + \pi/4)$$ and $$y_{2} = 5(\sin 3\pi t + \sqrt {3} \cos 3\pi t)$$. Their amplitudes are in the ratio.
  • $$1 : 1$$
  • $$2 : 1$$
  • $$2 : \sqrt {3}$$
  • $$\sqrt {3} : 2$$
A progressive wave  moves with a velocity of $$36 \mathrm { m } / \mathrm { s }$$ in a medium with a frequency of 200Hz. The phase difference betveen two particles seperated by a distance of $$1$$ $$cm$$ is 
  • $$40 ^ { \circ }$$
  • $$20 \mathrm { rad }$$
  • $$\dfrac { \pi } { 9 } \mathrm { rad }$$
  • $$\dfrac { \pi } { 9 } ^{o}$$
A simple harmonic oscillation is represented by the equation y $$= 0.4 sin \left ( \frac{440t}{7}+0.61x \right )$$. Where 'Y' and 'X' are in m and time 't' in seconds respectively. The value of time period in seconds
  • 0.1
  • 0.01
  • 1
  • 10
If a body of mass 36gm moves with S.H.M of amplitude A =13 cm and period T= 12 sec. At a time t= ) the displacement is x = +13 cm.The shortest time of passage from x = +6.5 cm to x = -6.5 is:
  • 4 sec
  • 2 sec
  • 6 sec
  • 3 sec
Three waveforms travelling along a straight line have the forms:
$$2A\sin \left (kx - \omega t + \dfrac {\pi}{3}\right ), \sqrt {3}A \cos \left (kx - \omega t - \dfrac {\pi}{3}\right ), 2\sqrt {3} \cos \left (kx - \omega t + \dfrac {\pi}{3}\right )$$. The amplitude of the resulting waveform is :
  • $$(2 + 3\sqrt {3})A$$
  • $$\sqrt {31}A$$
  • $$\sqrt {19}A$$
  • $$(2 - \sqrt {3})A$$
Two waves having equation $$x _ { 1 } = a \sin \left( \omega t + \phi _ { 1 } \right)$$ and $$x _ { 2 } = a \sin \left( \omega t + \phi _ { 2 } \right)$$ If in the resultant wave the frequency and amplitude remains equals to amplitude of superimposing waves. Then phase difference between them-
  • $$\dfrac { \pi } { 6 }$$
  • $$\dfrac { 2 \pi } { 3 }$$
  • $$\dfrac { \pi } { 4 }$$
  • $$\dfrac { \pi } { 8 }$$
Three simple harmonic motions in the same direction having the same amplitude A and same period are superposed. If each differs in phase from the next by $$45^0$$, then
  • the resulting amplitude is $$\Big ( 1 + \sqrt{3} \Big ) A$$.
  • the resulting motion is not simple harmonic
  • The energy associated with the resulting motion ($$3 + 2 \sqrt{2}$$) times the energy associated with any single motion.
  • The phase of the resultant motion relative to the first is $$90^0$$
Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega$$ along the $$x-axis.$$ Their mean position is separated by distance $$X_0(X_0 > A)$$. If the maximum separation between them is $$(X_0 + A ),$$ the phase difference between their motion is :-
  • $$\dfrac{\pi}{4}$$
  • $$\dfrac{\pi}{6}$$
  • $$\dfrac{\pi}{2}$$
  • $$\dfrac{\pi}{3}$$
Two $$SHMs$$ are given by $$Y_{1}= a\left[ \sin { \left( \dfrac { \pi  }{ 2 }  \right)  } t+\varphi  \right]$$ and $$Y_{2}= b\sin { \left[ \left( \dfrac { 2\pi t }{ 3 }  \right) +\varphi  \right]  }$$ . The phase difference between these two after $$'1'\ sec$$ is:
  • $$\pi$$
  • $$\dfrac {\pi}{2}$$
  • $$\dfrac {\pi}{4}$$
  • $$\dfrac {\pi}{6}$$
Equation of two $$S.H.M,\,\,{x_1} = 5\sin \left( {2\pi t + \pi /4} \right),\,{x_2} = 5$$ $$\sqrt 2 \left( {\sin 2\pi t + \cos 2\pi t} \right)$$. Ratio of amplitude & phase difference will be :
  • $$2:\,1,\,0$$
  • $$1:\,2,\,0$$
  • $$1:2,\,\pi /2$$
  • $$2:1,\,\pi /2$$
The distance between two consecutive crests in a wave train produced in string is 5 m. If two complete waves pass through any point per second, the velocity of wave is:
  • $$2.5 \mathrm { m } / \mathrm { s }$$
  • $$5 \mathrm { m } / \mathrm { s }$$
  • $$10 \mathrm { m } / \mathrm { s }$$
  • $$15 \mathrm { m } / \mathrm { s }$$
A body is on a rough horizontal surface which is moving horizontally in $$SHM$$ of frequency $$2\ Hz$$. The coefficient of static friction between the body and the surface is $$0.5$$. The maximum value of the amplitude for which the body will not slip along the surface is approximately 
  • $$9\ m$$
  • $$6\ m$$
  • $$4.5\ m$$
  • $$3\ m$$
A particle performing $$S.H.M$$ is found at its equilibrium at $$t= 1\ s$$ and it is found to have a speed of $$0.25\ m/s$$ at $$t=2\ s$$.If the period of oscillation is $$6\ s$$.Calculate amplitude of oscillation
  • $$\dfrac { 3 }{ 2\pi } m$$
  • $$\dfrac { 3 }{ 4\pi } m$$
  • $$\dfrac { 6 }{ \pi } m$$
  • $$\dfrac { 3 }{ 8\pi } m$$
A $$4$$ kg particle is moving along the x-axis under the action of the force $$F=-\left(\dfrac{\pi^2}{16}\right)\times N$$. At $$t=2$$sec, the particle passes through the origin and at $$t=10$$ sec its speed is $$4\sqrt{2}$$m/s. The amplitude of the motion is?
  • $$\dfrac{32\sqrt{2}}{\pi}$$m
  • $$\dfrac{16}{\pi}$$m
  • $$\dfrac{4}{\pi}$$m
  • $$\dfrac{16\sqrt{2}}{\pi}$$m
The equation of a progressive wave are
$$Y=sin[200n(t-\cfrac x {330})]$$,where x is in meter and f is in second. The frequency and velocity of wave are
  • $$100 Hz,5m/s$$
  • $$300 Hz,100m/s$$
  • $$100 Hz,330 m/s$$
  • $$30 m/s,5Hz$$
An object of mass m is attached to a spring.The restoring force of the spring is F=$$ - \lambda {x^3},$$ where x is the displacement. the oscillation period  depends on the mass, $$\lambda $$ and oscillation amplitude.suppose the object is initially at rest.If the initial displacement is D then its period is $$\tau $$ .If the initial displacement is 2D, find the period.(Hint: Use dimension analysis.)
  • 8$$\tau $$
  • 2$$\tau $$
  • $$\tau $$
  • $$\tau $$/2
Three waves of amplitude $$10\mu\ m,4\mu\ m$$ and $$7\mu\ m$$ arrive at a point with successive phase difference of $$\pi/2$$. The amplitude of the resultant wave is
  • $$2\mu m$$
  • $$7\mu m$$
  • $$5\mu m$$
  • $$1$$
A transverse progressive wave on a stretched string has a velocity of $$10ms^{-1}$$ and frequency of $$100Hz$$. The phase difference between two particles of the string which nbare $$2.5cm$$ apart will be :
  • $$\cfrac{\pi}{8}$$
  • $$\cfrac{\pi}{4}$$
  • $$\cfrac{3\pi}{8}$$
  • $$\cfrac{\pi}{2}$$
In a string the speed of wave is $$10m/s$$ and its frequency is $$100$$ Hz. The value of the phase difference at a distance $$2.5$$cm will be :
  • $$\pi/2$$
  • $$\pi/8$$
  • $$3\pi/2$$
  • $$4\pi$$
A wave is travelling along a string. At an instant shape of the string is as shown in figure. At this instant, point A is moving upwards. Which of the following statements is/are correct ?
1215906_7aa16dd7e1b44b6eafc24568061e403a.png
  • The wave is travelling to the right
  • Displacement amplitude of the wave is equal to displacement of B at this instant
  • At this instant velocity of C is also directed upwards
  • Phase difference between A and C may be equal to $$\pi/2$$
Two waves having intensity ratio 9 : 1 produce interference. The ratio of maximum to minimum intensity is:
  • 10 : 8
  • 9 : 1
  • 4 : 1
  • 2 : 1
A particle is describing SHM with amplitude  $$'a'.$$  When the potential energy of particle is one fourth of the maximum energy during oscillation, then its displacement from mean position will be:
  • $$\dfrac {a}{4}$$
  • $$\dfrac {a}{3}$$
  • $$\dfrac {a}{2}$$
  • $$\dfrac {2a}{3}$$
The irreducible phase difference in any wave of 5000 A from a source of light is
  • $$\pi$$
  • $$12\pi$$
  • $$12\pi \times{10}^{6}$$
  • $$\pi \times {10}^{6}$$
A stretched sting of length L,fixed at both ends can  sustain stationary waves of wavelength $$\lambda $$ Choose which of the following value of wavelength is not possible?
  • 2 L
  • 4 L
  • L
  • $$\dfrac { L }{ 2 } $$
The amplitude of a $$SHM$$ reduces to $$1/3$$ in first $$20$$ second then in first $$40$$ second its amplitude becomes:
  • $$\dfrac{1}{3}$$
  • $$\dfrac{1}{9}$$
  • $$\dfrac{1}{27}$$
  • $$\dfrac{1}{{\sqrt 3 }}$$
The ratio longest wavelength and the shortest wavelength observed in the five spectral series of emission spectrum of hydrogen is
  • $$\dfrac{4}{3}$$
  • $$\dfrac{525}{376}$$
  • $$25$$
  • $$\dfrac{900}{11}$$
Three waves of amplitude $$10\mu m,4\mu m$$ and $$7\mu m$$ arrival at a point with successive phase difference of $$\pi /2$$. The amplitude of the resultant wave is 
  • $$2\mu m$$
  • $$7\mu m$$
  • $$5\mu m$$
  • $$1$$
Equations $$Y_1=a$$ sin $$\omega t$$ and $$Y_2=a/2$$ sin $$\omega t + a/2$$ cos wt represent S.H.M. The ratio of the amplitude of first to that of second S.H.M. is
  • 1
  • 0.5
  • 2
  • $$\sqrt 2$$
the diagram shows the propagation of a wave. Which points are in same phase ?
1219064_661d92ddf9924fa384483d8352f9d237.png
  • F and G
  • C and E
  • B and G
  • B and F
Two waves are represented as $$y_1 = 2a sin (\omega t + \pi/6)$$ and $$y_2 = -2a cos \Big \lgroup \omega t - \frac{\pi}{6} \Big \rgroup$$. The phase difference between the two waves is
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{4\pi}{3}$$
  • $$\dfrac{3\pi}{3}$$
  • $$\dfrac{5\pi}{6}$$
The time lag between two particles vibrating in a progressive wave separated by a distance $$20$$ m is $$0.02 s$$ . The wave  velocity if the frequency of the wave is $$500 Hz$$ , is  
  • $$1000 ms^{-1}$$
  • $$500 ms^{-1}$$
  • $$2000 ms^{-1}$$
  • $$250 ms^{-1}$$
A particle moves with a simple harmonic motion in a straight line. In the first second starting from rest, it travels a distance $$a$$ and in the next second, it travels a distance $$b$$ in the same direction. The amplitude of the motion is:
  • $$\cfrac {2a^2}{3b-a}$$
  • $$\cfrac {3a^2}{3a-b}$$
  • $$\cfrac {2a^2}{3a-b}$$
  • $$\cfrac {3a^2}{3b-a}$$
A particle executes SHM of amplitude A if $$T_1$$ and $$T_2$$ are the time taken by the particle to traverse from 0 to A/2 and from A/2 to A respectively. Then $$T_1/T_2$$ will be equal to 
  • 1
  • 1/2
  • 1/4
  • 2
For a wave propagating in a medium, identify the property that is independent of the others
  • Velocity
  • Wavelength
  • Frequency
  • All these depend on each other
A wave of frequency $$500Hz$$ travels between X and Y, a distance of $$600 m$$ in 2 sec. How many wavelength are there distance XY:-
  • 1000
  • 300
  • 180
  • 2000
A uniform rope of length $$L$$ and mass $${m_1}$$ hangs vertically from a rigid support . A block of mass $${m_2}$$ is attached to the free end of the rope. A transverse pulse of wavelength $${\lambda _1}$$ is produced at  the lower end of the rope . the wavelength of the pulse when it reaches the top of the rope is $${\lambda _2}$$. The ratio $$\frac{{{\lambda _1}}}{{{\lambda _2}}}$$ is:
  • $$\sqrt {\dfrac{{{m_1}}}{{{m_2}}}} $$
  • $$\sqrt {\dfrac{{{m_1} + {m_2}}}{{{m_2}}}} $$
  • $$\sqrt {\dfrac{{{m_2}}}{{{m_1}}}} $$
  • $$\sqrt {\dfrac{{{m_1} + {m_2}}}{{{m_1}}}} $$
A particle of mass $$m$$ oscillates along $$x-$$axis according to equations $$x=a\sin \omega t$$. The nature of the graph between momentum and displacement of the particle is
  • Straight line passing through origin
  • Circle
  • Hyperbola
  • Ellipse
Two Waves of amplitudes $${ A }_{ 0 }$$ and $$x{ A }_{ 0 } $$ pass through a region. If x >1, the difference in the maximum and minimum resultant amplitude possible is
  • $$(x+1){ A }_{ 0 }$$
  • $$(x-1){ A }_{ 0 }$$
  • $$2x{ A }_{ 0 }$$
  • $$2{ A }_{ 0 }$$
Two particles execute $$SHM$$ of same amplitude of $$20cm$$ with same period along the same line about the same equilibrium position. The maximum distance between the two is $$20cm$$. Their phase difference in radians is :-
  • $$\cfrac{2\pi}{3}$$
  • $$\cfrac{\pi}{2}$$
  • $$\cfrac{\pi}{3}$$
  • $$\cfrac{\pi}{4}$$
 A metal rod 40 cm long is dropped onto a wooden floor and rebounds into air. Compressional waves of many frequencies are thereby set up in the rod. If the speed of compressional waves in the rod is 5500 $$m s ^ { - 1 }$$ what is the - lowest frequency of compressional waves to which the rod resonates as it rebounds?
  • 6875 Hz
  • 16875 Hz
  • 675 Hz
  • 0.11 Hz
Consider the wave represented by $$y=\cos(500t-70x)$$ where $$x$$ is in metres and $$t$$ in seconds. the two nearest points in the same phase have a separation of 
  • $$2\pi/7\ m$$
  • $$2\pi/7\ cm$$
  • $$20\pi/7\ m$$
  • $$20\pi/7\ cm$$
A particle is executing simple harmonic motion between extreme positions given by (-1, -2, -3)cm and (1, 2, 1)cm. Its amplitude of oscillation is
  • 6 cm
  • 4 cm
  • 2 cm
  • 3 cm
Two simple harmonic motions are represented by equations
$$ y _ { 1 } = 10 \sin ( 3 \pi t + \pi / 4 )$$ and
$$y _ { 2 } = 5 ( \sin 3 \pi t + \sqrt { 3 } \cos 3 \pi t ) \times 2 $$
Their amplitudes are in the ratio of 
  • 2
  • 1
  • 3
  • 4
The equation of a stationary wave is $$y=0.8cos\left( \dfrac { \pi x }{ 20 }  \right) \sin 200\pi t$$ where x is in cm and t is in seconds. The separation between consecutive nodes is
  • 10 cm
  • 20 cm
  • 30 cm
  • 40 cm
The displacement of a particle is given by x = 3 sin $$\left( 5\pi t \right) $$+ 4 cos$$\left( 5\pi t \right) $$ The amplitude of particle is 
  • 3
  • 4
  • 5
  • 7
0:0:1


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