CBSE Questions for Class 11 Engineering Physics Waves Quiz 8 - MCQExams.com

Two particles move parallel to $$x$$-axis about the origin with same amplitude and frequency. At a certain instant they are found at a distance $$\dfrac{a}{3}$$ from the origin on opposite sides but their velocities are found to be in same direction.Then the phase difference between two particles will be  
  • $$ cos^{-1}( \dfrac{7}{9})$$
  • $$180^{0}$$
  • $$45^{0}$$
  • None of the above
The ratio of amplitudes of two simple harmonic motions represented by the equations $$y_1=5 \sin \begin{pmatrix}2\pi t + \dfrac{\pi}{4}\end{pmatrix}$$ and $$y_2=2\sqrt{2} (\sin 2\pi t + \cos 1\pi t)$$ is
  • 1 : 1
  • 2 : 1
  • 5 : 2
  • 5 : 4
  • 2 : 5
With propagation of longitudinal waves through a medium, the quantity transmitted is : 
  • matter
  • energy
  • energy and matter
  • energy, matter and momentum
Two simple harmonic motions are represented by
$${ y }_{ 1 }=5\left( \sin { 2\pi t } +\sqrt { 3 } \cos { 2\pi t }  \right) $$
$${ y }_{ 2 }=5\left( \sin { 2\pi t } +\cfrac { \pi  }{ 4 }  \right) $$
The ratio of the amplitude of two S.H.M's is
  • $$1:1$$
  • $$1:2$$
  • $$2:1$$
  • $$1:\sqrt { 3 } $$
If the equation $$y_{1} = A\sin \omega t$$ and $$y_{2} = \dfrac {A}{2}\sin \omega t + \dfrac {A}{2}\cos \omega t$$ represent SHM then the ratio of the amplitudes of the two motions is
  • $$0.5$$
  • $$\sqrt {2}$$
  • $$1$$
  • $$2$$
The equation of simple harmonic wave is given by $$ y=6 \,sin \,2\pi ( 2 t-0.1 x),$$ where $$ x $$ and $$ y $$ are in mm and $$ t $$ is in seconds . The phase difference between two particles $$ 2 mm $$ apart at any instant is 
  • $$ 18^{0}$$
  • $$ 36^{0}$$
  • $$ 54^{0}$$
  • $$ 72^{0}$$
In a ripple tank when one pulse is sent every tenth of a second , the distance between consecutive pulses is $$30 mm$$. In the same depth of water pulses are produced at half second intervals. What is the new distance between consecutive pulses ?
  • $$0.67 mm$$
  • $$ 6.0 mm $$
  • $$ 150 mm$$
  • $$ 600 mm $$
Five waveforms moving with equal speeds on the x-axis
$${ y }_{ 1 }=8\sin { \left( \omega t+kx \right)  } ;{ y }_{ 2 }=6\sin { \left( \omega t+\cfrac { \pi  }{ 2 } +kx \right)  } ;{ y }_{ 3 }=4\sin { \left( \omega t+\pi +kx \right)  } ;$$
$${ y }_{ 4 }=2\sin { \left( \omega t+\cfrac { 3\pi  }{ 2 } +kx \right)  } ;$$
$${ y }_{ 5 }=4\sqrt { 2 } \sin { \left( \omega t-kx+\cfrac { \pi  }{ 4 }  \right)  } $$ are superimposed on each other. The resulting wave is:
  • $$8\sqrt { 2 } \cos { kx } \sin { \left( \omega t+\cfrac { \pi }{ 4 } \right) } $$
  • $$8\sqrt { 2 } \sin { \left( \omega t-kx+\cfrac { \pi }{ 4 } \right) \quad \quad } $$
  • $$8\sqrt { 2 } \sin { kx } \cos { \left( \omega t+\cfrac { \pi }{ 4 } \right) } $$
  • $$8\sin { \left( \omega t+kx \right) } $$
Equations of a stationary wave and a travelling wave are $$y_1=1\,sin(kx)\,cos (\omega t)$$ and $$y_2=a\,sin\,(\omega t-kx)$$.The phase difference between two points $$x_1=\dfrac{\pi}{3k}$$ and $$x_2=\dfrac{3 \pi}{2k}$$ is $$\phi_1$$ for the first wave and $$\phi_2$$ for the second wave.The ratio $$\dfrac{\phi_1}{\phi_2}$$ is
  • 1
  • 5/6
  • 3/4
  • 6/7
A particle moves according to the law $$x = r\cos \dfrac {\pi t}{2}$$. The distance covered by it in the time interval between $$t = 0$$ and $$t = 3s$$ is
  • $$r$$
  • $$2r$$
  • $$3r$$
  • $$4r$$
Two particle executing SHM of same frequency meet at $$x=+A/2$$, while moving in opposite direction. Phase difference between the particles is ($$A \rightarrow$$ Amplitude of both)
  • $$\cfrac{\pi}{6}$$
  • $$\cfrac{\pi}{3}$$
  • $$\cfrac{5\pi}{6}$$
  • $$\dfrac{-2\pi}{3}$$
Two wires made of the same material, one thick and the other thin, are connected to form a composite wire. The composite wire is subjected to some tension. A wave travelling along the wire crosses the junction point. The characteristic that doesn't undergoes a change at the junction point is
  • Frequency only
  • Speed of propagation only
  • Wavelength only
  • The speed of propagation as well as the wavelength
The function $$ sin \omega t - cos \omega t$$ represents
  • a simple harmonic motion with a period $$\frac{\pi}{\omega}$$.
  • a simple harmonic motion with a period $$\frac{2\pi}{\omega}$$.
  • a periodic, but not simple harmonic motion with a period $$\frac{\pi}{\omega}$$.
  • a periodic, but not simple harmonic motion with a period $$\frac 2{\pi}{\omega}$$.
A vibratory motion is represented by
$$ x = 2A cos \omega t + A cos [\omega t + \frac{\pi}{2}] + A cos (\omega t + \pi) + \frac{A}{2} cos [\omega t + \frac{3 \pi}{2}]$$.
The resultant amplitude of the motion is
  • $$\dfrac{9A}{2}$$
  • $$\dfrac{\sqrt5A}{2}$$
  • $$\dfrac{5}{2}A$$
  • $$2A$$
How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its amplitude if the period is $$24\ s$$ and particle starts from rest
  • $$12\ s$$
  • $$2\ s$$
  • $$4\ s$$
  • $$6\ s$$
A string of length 'l' is fixed at both ends. It is vibrating in its 3rd overtone with maximum amplitude 'a'.The amplitude at a distance l/3 from one end is?
  •  $$14a$$
  • $$15$$ a
  • $$10$$ a
  • None of these
In a certain oscillatory system, the amplitude of motion is $$5$$m and the time period is $$4$$s. The time taken by the particle for passing between points which are at distance of $$4$$m and $$2$$m from the centre and on the same side of it will be
  • $$0.30$$s
  • $$0.32$$
  • $$0.33$$
  • $$0.35$$
The equation of a wave is given by
$$y= 10$$ sin$$\left(\dfrac{2\pi}{45} t + \alpha \right)$$.
If the displacement is $$5 cm$$ at $$t=0$$, the the total phase at $$t=7.5 s$$ is
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{\pi}{2}$$
  • $$\dfrac{\pi}{6}$$
  • $$\pi$$
A particle executes SHM with time period $$T$$ and amplitude $$A$$. The maximum possible average velocity in time $${T}/{4}$$ is:
  • $$\cfrac{2A}{T}$$
  • $$\cfrac{4A}{T}$$
  • $$\cfrac{8A}{T}$$
  • $$\cfrac{4\sqrt {2}A}{T}$$
Two wires made of the same material, one thick and other thin, are connected to form a composite wire. The composite wire is subjected to some tension. A wave travelling along the wire crosses the junction point. The characteristic that undergoes a change at the junction point is:
  • Frequency only
  • Speed of propagation only
  • Wavelength only
  • The speed of propagation as well as the wavelength
Equation of plane progressive wave is given by $$y = 0.6 sin 2\pi\left(t - \dfrac{x}{2}\right)$$. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is
  • $$y = 0.6 sin 2\pi\left(t + \dfrac{x}{2}\right)$$
  • $$y =- 0.4 sin 2\pi\left(t + \dfrac{x}{2}\right)$$
  • $$y = 0.4 sin 2\pi\left(t + \dfrac{x}{2}\right)$$
  • $$y =- 0.4 sin 2\pi\left(t - \dfrac{x}{2}\right)$$
Spherical wavefronts, emanating from a point source, Strike a plane reflecting surface. What will happen to these wave fronts, immediately after reflection ?
  • They will remain spherical with the same curvature, both in magnitude and sign.
  • They will become plane wave fronts.
  • They will remain spherical, with the same curvature, but sign of curvature reversed.
  • They will remain spherical, but with different curvature, both in magnitude and sign.
Assertion - On reflection from a rigid boundary there takes place a complete reversal of phase.
Reason - On reflection from a denser medium, both the particle velocity and wave velocity are reversed in sign.
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Both Assertion and Reason are incorrect
Which of the following wave function does represent a travelling wave?
  • $$y=$$tan$$(x - vt)^2$$
  • $$y=$$log$$(x- vt)$$
  • $$y=\dfrac{1}{x+vt}$$
  • None of these
there are $$26$$ tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives $$3$$ beats with the next. The first one is octave of the last. What is the frequency of $$18^{th}$$ tuning fork?
  • $$100 Hz$$
  • $$99 Hz$$
  • $$96 Hz$$
  • $$103 Hz$$
A particle executes SHM of period $$12$$s. After two seconds, it passes through the centre of oscillation, the velocity is found to be $$3.142 cm s^{-1}$$. The amplitude of oscillation is:
  • $$6$$cm
  • $$3$$ cm
  • $$24$$cm
  • $$12$$cm
The amplitude of an electromagnetic wave in vacuum is doubled with no other changes made to the wave. As a result of this doubling of amplitude, which of the following statement is correct?
  • The speed of the wave propagation changes only
  • The frequency of the wave changes only
  • The wavelength of the waves changes only
  • None of these
The displacement of a particle executing simple harmonic motion is given by
$$x = 3 sin [2 \pi t + \frac{\pi}{4}]$$ where x is in metres and t is in seconds. The amplitude and maximum speed of the particle is:
  • $$3m, 2 \pi m s^{-1}$$
  • $$3m, 4 \pi m s^{-1}$$
  • $$3m, 6 \pi m s^{-1}$$
  • $$3m, 8 \pi m s^{-1}$$
Two particles execute simple harmonic motions of same amplitude and frequency along the same straight line. They cross one another when going opposite directions. The phase difference between them when their displacements are one half of their amplitudes is then
  • $$60^0$$
  • $$30^0$$
  • $$120^0$$
  • $$150^0$$
The equation of the stationary wave is
$$y = 2A sin(\dfrac{2 \pi c t}{\lambda}) cos (\dfrac{2 \pi x}{\lambda})$$
Which of the following statements is wrong?
  • The unit of ct is same as that of $$\lambda$$.
  • The unit of x. is same as that of $$\lambda$$
  • The unit of ct is same as that of $$x$$
  • The unit of ct, $$\lambda$$ and $$x$$ are same
In the standing waves that form as a result of reflection of waves from an obstacle, the ratio of the amplitude at antinode to the amplitude at a node is s. The fraction of the energy that passes past the obstacle is:
  • $$\dfrac{4}{s^2}$$
  • $$\dfrac{s + 1}{s - 1}$$
  • $$(\dfrac{s + 1}{s - 1})^2$$
  • non of the above.
The maximum velocity of a body undergoing S.H.M. is $$0.2 m/s$$ and its acceleration at $$0.1 m$$ from the mean position is $$0.4 m/s^{-2}$$ The amplitude of the S.H.M. is:
  • $$0.25 m$$
  • $$0.3 m$$
  • $$0.1 m$$
  • $$1.05 m$$
If the particle was to start at the extreme position i.e x = +A, then what will be the equation of SHM:
  • $$A cos (\omega t)$$
  • $$A sin (\omega t)$$
  • $$A cot (\omega t)$$
  • $$A tan (\omega t)$$

At a particular position the velocity of a particle in SHM with amplitude a is $$\dfrac{{\sqrt 3 }}{2}$$ that at its mean position. In this position, its displacement is:
  • $$\dfrac{a}{2}$$
  • $$\sqrt 3 \dfrac{a}{2}$$
  • $$a\sqrt 2 $$
  • $$\sqrt {2a} $$
A particle executes SHM given by an equation $$x=A sin (\omega t + \pi/6)$$. Where was the particle at t = 0
  • A
  • Mean position
  • A/2
  • A/4
Tapping gently on the surface of water produces concentric ripples. This is due to 
  • circular interference of waves
  • linear interference of waves
  • energy transfer radially
  • vibration of nearby particles
A plane wave of wavelength $$\lambda$$ is incident at an angle $$\theta$$ on a plane mirror. Maximum intensity will be observed at $$P$$, when
1010767_26393a74904841babe205fc4a7cbed08.jpg
  • $$\cos \theta = 3\lambda / 2d$$
  • $$\sec \theta - \cos \theta = 3\lambda / 4d$$
  • $$\cos \theta = \lambda / 4d$$
  • $$\sec \theta - \cos \theta = \lambda / 4d$$
A particle moves according to $$x= a cos \Big(\frac{\pi}{2}t\Big)$$. The distance covered by it in time interval between t=0 to t=2 s is
  • 2a
  • 3a
  • 4a
  • a
Given that $$y = A \sin \left[\left(\dfrac{2 \pi}{\lambda}\right)(ct - x)\right]$$, where $$y$$ and $$x$$ are measured in the unit of length. Which of the following statements is true?
  • The unit of $$\lambda$$ is same that of $$x$$ and $$A$$.
  • The unit of $$\lambda$$ is same that of $$x$$ but may not be same as that of $$A$$.
  • The unit of $$c$$ is same as that of $$2 \pi/ \lambda$$
  • The unit of $$(ct - x)$$is same as that of $$2 \pi/ \lambda$$
Which of these does not represent a wave equation
  • $$y=A sin (\omega t- kx)$$
  • $$y=A sin (\omega t + kx)$$
  • $$y=A cos (\omega t- kx)$$
  • $$y=A (\omega t- kx)$$
A travelling wave is represented by the equation $$y=20 sin 2(x-4t)$$. If y is measured in cms,  what is the amplitude of the wave
  • 20 mms
  • 20 cm
  • 20 m
  • 2 cm
A travelling wave has a velocity of 400 m/s and has a wavelength of 0.5 m. What is the phase difference between two points in the wave that are 1.25 milli secs apart
  • $$2 \pi$$
  • $$2 \pi/3$$
  • $$2 \pi/5$$
  • $$ \pi/6$$
The displacement of a particle varies according to the relation $$x= 4 (cos \pi t + sin \pi t)$$. The amplitude of the particle is 
  • $$-4$$
  • $$4$$
  • $$4\sqrt2$$
  • $$8$$
A progressive wave of wavelength 5 cm moves along +X axis. What is the phase difference between two points on the wave separated by a distance of 3 cm at any instant
  • $$3 \pi/5$$
  • $$6 \pi/5$$
  • $$2 \pi/5$$
  • $$7 \pi/5$$
The equation of a travelling wave is given by $$3sin(\pi/2)(25t-x)$$ where x and y are in meters and t is in seconds. What is the ratio of maximum amplitude to its wavelength
  • 1/4
  • 3/2
  • 3/4
  • 1/2
A mass M, attached to a horizontal spring, executes S.H.M. with amplitude $$A_1$$. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude $$A_2$$. The ratio of $$\left( \frac{A_1}{A_2}\right)$$ is:
  • $$\dfrac{M}{m}$$
  • $$\left(\dfrac{M}{M+m}\right)^{1/2}$$
  •  $$ (M+m)\sqrt{\dfrac{k}{M+m}A_2}$$
  • $$\dfrac{M}{M+m}$$
A magnifier lens focusses a beam of light on a sheet of paper for 5 secs and the paper starts burning. The process described here is
  • Concentrated light produces heat
  • Light energy is converted in to heat energy
  • Photons heating the paper
  • Electrons heating the paper
Phase difference between a compression and its successful rarefaction is $$2 \pi $$radians
  • True
  • False
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: 
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{\pi}{4}$$
  • $$\dfrac{\pi}{6}$$
  • $$\dfrac{\pi}{2}$$
Two waves of same amplitude and frequency with a phase difference of $$\pi/2$$ and travelling in same direction are superimposed each other, the maximum amplitude of the resultant wave is
  • 2A
  • A
  • A$$\sqrt{2}$$
  • A/2
0:0:1


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