CBSE Questions for Class 11 Engineering Physics Waves Quiz 12 - MCQExams.com

Three simple harmonic motions in the same direction having the same amplitude $$a$$ and period are superposed. IF each differs in phase from the next by $${45}^{o}$$ then
  • the resultant amplitude $$(1+\sqrt{2})a$$
  • the phase of the resultant motion relative to the first is $${90}^{o}$$
  • the energy associated with the resulting motion is $$(3+2\sqrt{2})$$ times the energy associated any single motion
  • the resulting motion is not simple harmonic
Equations of motion in the same direction are 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:
  • $$2a\cos \frac{\theta }{2}$$
  • $$\sqrt{2}a \ cos \ \theta$$
  • $$4a \ cos \ \theta/2$$
  • $$\sqrt{2}a \ cos \ \theta/2$$
Equations of motion in the same direction are given by:
$$y_1 = 2a \ sin \ (\omega t - kx)$$
$$y_2 = 2a \ sin \ (\omega t - kx - \theta)$$
The amplitude of the medium particle will be:
  • $$2a\cos \frac{\theta }{2}$$
  • $$\sqrt{2}a \ cos \theta$$
  • $$4a \ cos \theta/2$$
  • $$\sqrt{2}a \ cos \theta/2$$
A small mass executes linear SHM about $$O$$ with amplitude $$a$$ and period $$T$$. Its displacement from $$O$$ at time $$T/S$$ after passing through $$O$$ is
  • $$a/S$$
  • $$\cfrac{a}{2\sqrt{2}}$$
  • $$a/2$$
  • $$\cfrac{a}{\sqrt{2}}$$
If the fundamental frequency of string is $$220 \mathrm { cps }$$, the frequency of fifth harmonic will be
  • $$44\mathrm { cps }$$
  • $$55 \mathrm { cps }$$
  • $$1100 \mathrm { cps }$$
  • $$440 \mathrm { cps }$$
A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance $$\frac{2A}{3}$$ from equilibrium position. The new amplitude of the motion is  
  • $$\dfrac{A}{3}\sqrt {41}$$
  • 3A
  • $$A\sqrt3$$
  • $$\dfrac{7A}{3}$$
A particle executes a SHM of time T, find the time taken by the particle to go directly from its mean position to half the amplitude
  • $$\dfrac{T}{2}$$
  • $$\dfrac{T}{8}$$
  • $$\dfrac{T}{12}$$
  • $$\dfrac{T}{4}$$
The phase (at a time t) of a particle in simple harmonic motion tells
  • Only the position of the particle at time t
  • Only the direction of motion of the particle at time t
  • Both the position and direction of motion of the particle at time t
  • Neither the position of the particle nor its direction of motion at time t
The graph plotted between the velocity and displacement from mean position of a particle executing S,H.M. is
  • circle
  • ellipse
  • parabola
  • straight line.
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
  • $$
    \frac{a+b}{a b}
    $$
  • $$
    \frac{\sqrt{a}+\sqrt{b}}{a b}
    $$
  • $$
    \frac{\sqrt{a} \pm \sqrt{b}}{a b}
    $$
  • $$
    \sqrt{\frac{a+b}{a b}}
    $$
A particle performs SHM of amplitude $$A$$ along a straight line. When it is at a distance $$\cfrac{\sqrt{3}}{2}A$$ from mean position, its kinetic energy gets increased by an amount $$\cfrac{1}{2}m \omega {A}^{2}$$ due to an impulsive force. Then its new amplitude becomes.
  • $$\cfrac{\sqrt{5}}{2}A$$
  • $$\cfrac{\sqrt{3}}{2}A$$
  • $$\sqrt{2}A$$
  • $$\sqrt{5}A$$
The amplitude of vibration of a particle is given by $${ a }_{ m }=\dfrac { { a }_{ 0 } }{ { a }w^{ 2 }-bw+c } $$ Where $${ a }_{ 0 },a,b$$ and $$ c$$ are positive. The condition for a single resultant frequency is
  • $${ b }^{ 2 }=4ac$$
  • $${ b }^{ 2 }>4ac$$
  • $$\\ { b }^{ 2 }=5ac\\ $$
  • $$\\ { b }^{ 2 }=7ac$$
A particle performs S.H.M. of amplitude A along a straight line. When it is at a distance $$\frac{\sqrt 3}{2}$$ A form measure position, its kinetic energy gets increased by an amount $$\frac{1}{2}$$ m $$\omega^2A^2$$ due to an impulsive force. Then new amplitude becomes:
  • $$\frac{\sqrt 5}{2}A$$
  • $$\frac{\sqrt 3}{2}A$$
  • $$\sqrt2 A$$
  • $$\sqrt5 A$$
Two equations of two SHM are
$$x=a \ sin(\omega t - \alpha) \ and \ y=b \ cos(\omega t - \alpha)$$
The phase difference between the two is 
  • $$0^o$$
  • $$\alpha^o$$
  • $$90^o$$
  • $$180^o$$
Two particles are executing SHM of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their magnitude. What is the phase difference between them?
  • $$\pi / 6$$
  • $$4 \pi / 6$$
  • $$\pi / 3$$
  • $$2 \pi / 6$$
A particle moving along a straight line with a constant acceleration of - 4 m per second square passes through a point on the line with a velocity of + 8 metre per second at the moment when the distance travelled by the particle in 6 second in 5 seconds
  • $$5 m/s^2$$
  • $$6 m/s^2$$
  • $$8 m/s^2$$
  • $$2 m/s^2$$
Four waves are expressed as
(i) $$y _ { 1 } = a _ { 1 } \sin \omega t$$                                            (ii) $$y _ { 2 } = a _ { 2 } \sin 2 \omega t$$
(iii) $$y _ { 3 } = a _ { 3 } \cos \omega t$$                                         (iv) $$y _ { 4 } = a _ { 4 } \sin ( \omega t + \phi )$$
The interference is possible between
  • (i) and (iii)
  • (i) and (ii)
  • (ii) and (iv)
  • Not possible at all
A wave equation which given the displacement along the Y direction is given by $$y = 10^{-4} \sin (60t+2x)$$ where x and y are in meters and t is time in seconds. This represents a wave 
  • Traveling with a velocity of 30 m/s in the negative x direction
  • Of wavelength $$\pi $$ metre
  • Of frequency 30/$$\pi $$hertz
  • Of amplitude $$10^{ -4 }$$ metre
Displacement of a particle performing S.H.M. is given by  $$x = 0.01$$   $$\sin \pi ( t + 0.05 ) ,$$  where  $$x$$  is in meter and t is in seconds. The time period in second is : 
  • $$2$$
  • $$0.01$$
  • $$0.02$$
  • $$0.1$$
The displacement equation of a simple harmonic oscillator is given by 
$$x = 6 \sin \left[\dfrac{\pi}{8} + \dfrac{\pi}{16}t\right] m $$ when t = 2 seconds is 
  • 1.3m
  • 1.5m
  • $$3\sqrt{3} m$$
  • $$3 \sqrt{2}$$ m
On the superposition of the two waves given as $${y}_{1}={A}_{0}\sin{(\omega t-kx)}$$ and $${y}_{2}={A}_{0}\cos {(\omega t-kx+\cfrac{\pi}{6}})$$ the resultant amplitude of oscillation will be
  • $$\sqrt{3}{A}_{0}$$
  • $$\cfrac{{A}_{0}}{2}$$
  • $${A}_{0}$$
  • $$\cfrac{3}{2}{A}_{0}$$

 The displacement of a particle ( in meters ) from its mean position is given by the equation $$y = 0.2\left( {{{\cos }^2}\dfrac{{\pi t}}{2} - {{\sin }^2}\dfrac{{\pi t}}{2}} \right)$$. The motion of the above particle is. 
  • not simple harmonic
  • Simple harmonic with amplitude of 0.2 m
  • Simple harmonic with a period equal double that of a second's pendulum
  • Simple harmonic with an amplitude of 0.4 m
Figure given showsa sinusoidal wave on a string.If the frequency of the wave is 150 Hz and the mass per unit length of the string is 0.2 g/s.the power transmitted by the wave is
1572938_634eae79b34242f7be1c52828ec7c7aa.png
  • 2.34 W
  • 3.84 W
  • 4.80 W
  • 5.78 W
Equation $${ y }_{ 1 }=0.1sin\left( 100\pi t+\dfrac { \pi  }{ 3 }  \right) $$ and $${ y }_{ 2 }=0.1$$ cos $$\pi t$$ The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is 
  • $$\dfrac { -\pi }{ 6 } $$
  • $$\dfrac { \pi }{ 3 }$$
  • $$\dfrac { -\pi }{ 3 } $$
  • $$\dfrac { \pi }{ 6 } $$
Number of waves of a light of wavelength  $$5000 \mathrm { A } ^ { \circ } ,$$  in a thickness of  $$0.2 \mathrm { mm } ,$$  of air is
  • $$100$$
  • $$200$$
  • $$250$$
  • $$400$$
The equation of a progressive wave is $$Y= a sin(200 t-x)$$, where x is in meter and t is in second. The velocity of wave is
  • $$200 $$ m/sec
  • $$100 $$ m/sec
  • $$50 $$ m/sec
  • None
The equation of a wave is given by 
$$ Y\quad =\quad A\quad sin\quad \omega \left( \frac { x }{ v } -k \right)  $$
Where $$ \omega $$ is the angular velocity and v is the linear velocity.The dimensions of K is
  • LT
  • T
  • $$ T^{-1} $$
  • $$ T^2 $$
Two points are located at a distance of $$10\ m$$ and $$15\ m$$ from the source of oscillation. The period of oscillation is $$0.05\sec$$ and the velocity of the wave is $$300\ m/\sec$$. What is the phase difference between the oscillations of two points?
  • $$\dfrac {\pi}{6}$$
  • $$\dfrac {\pi}{3}$$
  • $$\dfrac {2\pi}{3}$$
  • $$\pi$$
Which of the following figure about reflection of transverse or longitudinal waves is CORRECT?  $$ (V_w = velocity \ of \ wave,  v_p = particle\ velocity) $$
The equation $$y =A\cos^2\left(2\pi\, nt -2\pi \dfrac{x}{\lambda}\right)$$ represents a wave with
  • amplitude $$A/2$$, frequency $$2n$$& wavelength $$\lambda/2$$
  • amplitude $$A/2$$, frequency $$2n$$& wavelength $$\lambda$$
  • amplitude $$A$$, frequency $$2n$$& wavelength $$2\lambda$$
  • amplitude $$A$$, frequency $$n$$& wavelength $$\lambda$$
For a wave $$ y= y_0 sin ( \omega t - kx ) $$, for what value of $$ \lambda $$ , is the maximum particle velocity equal to two times the wave velocity :-
  • $$ \pi y_0 $$
  • $$ 2 \pi y_0 $$
  • $$ \pi y_0/2 $$
  • $$4 \pi y_0 $$
Which of the following statement is incorrect superposition of waves?
(i) After superposition frequency,wavelength and velocity of resultant wave remains same
 (ii) After superposition amplitude of resultant wave is equal to amplitude of either wave 
 (iii) Mechanical wave cannot superposed with electromagnetic wave
 (iv) For superposition two waves should have equal wavelength,frequency and amplitude
  • I & III Only
  • I & II Only
  • I,II, & III Only
  • II & IV Only
The equation $$y = a \sin^2 \left(2 \pi nt - \dfrac{2\pi x}{\lambda}\right)$$ represents a wave with
  • Amplitude $$a$$, frequency $$n$$ and wavelength $$\lambda$$
  • Amplitude $$a$$, frequency $$2n$$ and wavelength $$2\lambda$$
  • Amplitude $$a/2$$, frequency $$2n$$ and wavelength $$\lambda$$
  • Amplitude $$a/2$$, frequency $$2n$$ and wavelength $$\lambda/2$$
The displacement equation of a progressive wave is y = 3 sin (200 t-5 x), Where the distance x and y are in meter and time t in second. The speed of the wave is:
  • $$ 20 m s^{-1} $$
  • $$ 40 m s^{-1} $$
  • $$ 60 m s^{-1} $$
  • $$ 80 m s^{-1} $$
If the amplitude of a wave at a distance $$r$$ from a point source is $$A$$, the amplitude at a distance $$2r$$ will be
  • $$2A$$
  • $$A$$
  • $$A/2$$
  • $$A/4$$
The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is $$2\pi/3$$. If the phase of one particle is $$\pi/6$$, find the displacement at this instant, if amplitude is $$A$$.
  • $$A/3$$
  • $$2A/3$$
  • $$3A/4$$
  • $$A/2$$
At any instant a wave travelling along the string is shown in fig. Here, point $$'A'$$ is moving upward. Which of the following statements is true?
1702576_1195eda7f6244860b2bf16d75cc43b66.png
  • The wave is travelling to the right
  • The displacement amplitude of wave is equal to displacement of $$B$$ at this instant
  • At this instant $$'C'$$ also directed upward
  • None of these
A wave has a wavelength of 3m. The distance between a crest and adjacent trough is
  • 0.75 m
  • 1.5 m
  • 3 m
  • 1 m
A wave pulse in a string is described by the equation $$y_1=\dfrac{5}{(3x-4t)^2+2}$$ and another wave pulse in the same string is described by $$y_2=\dfrac{-5}{(3x+4t-6)^2+2}$$. The values of $$y_1,y_2$$ and $$x$$ are in metres and $$t$$ in seconds. Which of the following statement is correct?
  • $$y_1$$ travels along -x- direction and $$y_2$$ along +x-direction
  • Both $$y_1$$ and $$y_2$$ travel along -x-direction
  • Both $$y_1$$ and $$y_2$$ travel along +x-direction
  • At $$x=1m,y_1$$ and $$y_2$$ always cancel
  • At time $$t=1s,y_1$$ and $$y_2$$ exactly cancel everywhere
A wave pulse moves along a stretched rope in the direction shown.
Which diagram shows the variation with time t of the displacement s of the particle P in the rope? 

1648527_ae7fce4164a44c30a1971b5a8d831c1a.png
The wavelength of the first line of Lyman series is $$\lambda$$. The wavelength of the first line in Paschen series is ________.
  • $$108/7$$
  • $$27/5$$
  • $$7/108$$
  • $$5/27$$
A sinusoidal wave travelling in the same direction have amplitude of $$3\ cm$$ and $$4\ cm$$ and difference in phase by $$\pi/2$$. The resultant amplitude of the superimposed wave is :
  • $$7\ cm$$
  • $$5\ cm$$
  • $$2\ cm$$
  • $$0.5\ cm$$
The equation of standing wave is $$y=a\cos kx \sin \omega t$$ which one of following graphs is for the wave at $$t=\dfrac{T}{4}$$?
  • none of the above
The number of waves each of wavelength $$10\ cm$$ produced in string of $$100\ cm$$ length, is:
  • $$1$$
  • $$10$$
  • $$20$$
  • $$30$$
Equation of a plane wave is given by $$4\sin \dfrac{\pi}{4}\left[2t+\dfrac{x}{8}\right]$$. The phase difference at any given instant of two particles $$16\ cm$$ apart is :
  • $$60^o$$
  • $$90^o$$
  • $$30^o$$
  • $$120^o$$
Wave of frequency $$500\ Hz$$ has a phase velocity $$360\ m/s$$. The phase difference between two displacement at a certain point at time $$10^{-3}\ s$$ apart will be :
  • $$\pi$$ radian
  • $$\dfrac{\pi}{2}$$ radian
  • $$\dfrac{\pi}{4}$$ radian
  • $$2\ pi$$ radian
Velocity of sound waves in air is $$330\ m/s$$. For a particular sound in air, a path difference of $$40\ cm$$ is equivalent to a phase difference of $$1.6\ \pi$$. The frequency of this wave is:
  • $$165\ Hz$$
  • $$150\ Hz$$
  • $$660\ Hz$$
  • $$330\ Hz$$
The phase change between incident and reflected sound wave from a fixed wall is:
  • $$0$$
  • $$\pi$$
  • $$3\pi$$
  • $$\dfrac{\pi}{2}$$
Two waves represented by $$y = a \sin (\omega t - kx)$$ and $$y = a \cos (\omega t - kx)$$ are superposed. The resultant waves will have an amplitude.
  • $$a$$
  • $$\sqrt{2a}$$
  • $$2a$$
  • $$0$$
Two point lie on a ray are emerging from a source of simple harmonic wave having period $$0.045$$. The wave speed is $$300\ m/s$$ and points are at $$10\ m$$ and $$16\ m$$ from the source. They differ in phase by :
  • $$\pi$$
  • $$\pi/2$$
  • $$0$$ or $$2\pi$$
  • $$none\ of\ these$$
0:0:1


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