CBSE Questions for Class 11 Engineering Physics Waves Quiz 15 - MCQExams.com

Equation Of a Progressive Wave Is Given By 
$$ y=0.2cos\pi \left( 0.04t\quad +\quad 0.02x\quad -\frac { \pi  }{ 6 }  \right)  $$
The Distance Is Expressed In cm And Time In Second. What Will Be The Minimum Distance Between Two Particles Having The Phase Difference Of $$ \pi/2 $$
  • 4 cm
  • 8 cm
  • 25 cm
  • 12.5 cm
The amplitude and time period of a particle of mass 0.1kg executing simple harmonic motion are 1m and 6.28s, respectively, Find its (i) angular frequency ,(ii) acceleration and (iii) velocity at a displacement of 0.5 m
  • $$ 1 rad/sec,-1 ms^{ -2 },\sqrt { 3 } ms^{ -1 } $$
  • $$ 0. rad/sec, -0.5\quad ms^{ -2 },\frac { \sqrt { 3 } }{ 2 } ms^{ -1 } $$
  • $$ 1 rad /sec, -0.5 ms^{-2},\frac {\sqrt{3}}{2} ms^{-1} $$
  • $$ 1rad/sec, -0.5\quad ms^{ -2 },\sqrt { 3 } ms^{ -1 } $$
The equation of the progressive, where  $$t$$  is the time in second,  $$x$$  is the distance in metre is  $$y = A \cos 240 \left( t - \dfrac { x } { 12 } \right).$$  The phase difference (In SI units) between two positions  $$0.5m$$  apart is
  • $$40$$
  • $$20$$
  • $$10$$
  • $$5$$
Two waves having sinusoidal waveforms have different wavelengths and different amplitude. They will be having 
  • Same pitch and different intensity
  • Same quanlity and different intensity
  • Different quanlity and different intensity
  • Same quanlity and different pitch
A particle executes SHM with a time period of 16 second .at time t is equal 2 second the particle crosses the mean position while at t is equal to 4 second its velocity is 4 m per second the amplitude of motion in metre is
  • $$\sqrt 2 /\pi$$
  • $$16 \sqrt 2 /\pi$$
  • $$32 \sqrt 2  /\pi$$
  • $$4 /\pi$$
A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic function:
  • $$y = a\ sin \frac{2\pi t}{T}$$
  • $$y = a\ sin\ vt$$
  • $$y = \frac{a}{T}\ sin \frac{t}{a}$$
  • $$y = \frac {a} {\sqrt 2} [sin \frac{2\pi t}{T} + cos \frac{2\pi t}{T}]$$
A radio station broadcasts at $$760$$ kHz. What is the wavelength of the station?
  • $$395$$ m
  • $$790$$ m
  • $$760$$ m
  • $$197.5$$ m
A particle starts its SHM on a line at initial phase of $$\pi /3$$. It reaches again the point of start after time t. It crosses yet another point P on the same line at successive intervals 2t and 3t respectively. Find the amplitude of the motion. If the particle crosses the point of start at speed 2m/s.
  • $$\cfrac { 8t }{ \pi } $$
  • $$\cfrac { 4t }{ \pi } $$
  • $$\cfrac { 2t }{ \pi } $$
  • $$\cfrac { t }{ \pi } $$

Three waves of equal frequency having amplitudes $$10 \mu m , 4\mu m, 7 \mu m$$ arrive at a given point with successive phase difference of $$\cfrac {\pi}{2}$$ radian. The amplitude of the resultant wave is. 
  • $$5$$ $$\mu m$$
  • $$3$$ $$\mu m$$
  • $$4$$ $$\mu m$$
  • $$2$$ $$\mu m$$
Wave in a medium is represented by the equation $$ y=0.2 sin [ \pi (x-4t) ] $$ meter. the displacement at a point x=50 cm and t=0.25 s is
  • +.01m
  • zero
  • -0.2m
  • +0.2m
Two particles executing SHM of same frequency, meet at x=+A/2, while moving in opposite directions. Phase difference between the particles is 
  • $$\frac{\pi}{6}$$
  • $$\frac{\pi}{3}$$
  • $$\frac{5\pi}{6}$$
  • $$\frac{2\pi}{3}$$
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 $$(\frac{A_1}{A_2}$$ is :-
  • $$(\frac{M}{M+m})^{1/2}$$
  • $$(\frac{M+m}{M})^{3/2}$$
  • $$\frac{M}{M+m}$$
  • $$\frac{M+m}{M}$$
Two waves have equations $${x}_{1}=a\sin{(\omega t+{\phi}_{1})}$$ and $${x}_{2}=a\sin{(\omega t+{\phi}_{2})}$$. If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves. The phase difference between them is:
  • $${\pi}/{6}$$
  • $${2\pi}/{3}$$
  • $${\pi}/{4}$$
  • $${\pi}/{3}$$
If tangent and normal to the curve $$y=2\sin{x}+\sin{2x}$$ are drawn at $$P\left(x=\cfrac{\pi}{3}\right)$$ then area of the quadrilateral formed by tangent, the normal at $$P$$ and the coordinate axes is 
  • $$\cfrac{\pi}{3}$$
  • $$3\pi$$
  • $$\cfrac{\pi\sqrt{3}}{2}$$
  • $$\pi$$
A particle performs simple harmonic motion with amplitude $$A$$. Its speed is trebled at the instant that it is at a distance $$\dfrac { 2A }{ 3 }$$ from equilibrium position. The new amplitude of the motion is:
  • $$3A$$
  • $$A\sqrt { 3 }$$
  • $$\dfrac { 7A }{ 3 }$$
  • $$\dfrac { A }{ 3 }\sqrt { 41 }$$
A $$1000$$ m long rod of density $$10.0 \times 10^4\, kg/m^3$$ and having Young's modulus $$Y=10^{11} \, Pa$$, is clamped at one end. It is hammered at the other free end as shown in the figure. The longitudinal pulse goes to the right end, gets reflected and again returns to the left end. How much time (in sec) the pulse will take to go to initial point?

1327464_5e050065c9774e1e99691abe4a044eb0.PNG
  • $$0.1\ sec$$
  • $$0.2\ sec$$
  • $$0.3\ sec$$
  • $$2\ sec$$
Two uniform strings $$A$$ and $$B$$ made of steel are made to vibrate under the same tension. If the first overtone of $$A$$ is equal to the second overtone of $$B$$ and if the radius of $$A$$ is twice that of $$B$$, the ratio of the length of the strings is
  • $$2:1$$
  • $$3:2$$
  • $$3:4$$
  • $$1:3$$
A particle is executing SHM with amplitude $$A$$ has maximum velocity $${v}_{0}$$. Its speed at displacement $$\cfrac{3A}{4}$$ will be
  • $$\cfrac{\sqrt{7}}{4}{v}_{0}$$
  • $$\cfrac{{v}_{0}}{\sqrt{2}}$$
  • $${v}_{0}$$
  • $$\cfrac{\sqrt{3}}{2}{v}_{0}$$
A particle moves with simple harmonic motion in a straight line. In first $$t \, s$$, after starting from rest it travels a distance $$a$$, and in next $$t \, s$$ it travels $$2a$$, in the same direction, then: 
  • amplitude of motion is $$4a$$
  • time period of oscillations is $$6 t$$
  • amplitude of motion is $$3a$$
  • time period of oscillations is $$8 t$$
One end of a spring of force constant K is attached to the ceiling of a lift. A body of mass m is attached to another end of the spring. If the cable of the lift suddenly breaks, then the amplitude of oscillation of the body in the freely falling lift will be : 
  • $$\dfrac{mg}{k}$$
  • $$\dfrac{3mg}{2k}$$
  • $$\dfrac{7mg}{5k}$$
  • $$\dfrac{4mg}{3k}$$
If two waves, each of intensity $$I_0$$ , having the frequency but differing by a constant phase angle of $$60^o$$ , superimposing at a certain point in space then the intensity of the resultant wave is
  • $$2I_0$$
  • $$3I_0$$
  • $$\sqrt{3}I_0$$
  • $$4I_0$$
A $$4\ kg$$ particle is moving along the x-axis under the action of the force which varies with distance $$'x'$$ given by $$F = -\left (\dfrac {\pi^{2}}{16}\right )x$$ newton. 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
  • $$\dfrac {32\sqrt {2}}{\pi}m$$
  • $$\dfrac {16}{\pi}m$$
  • $$\dfrac {4}{\pi}m$$
  • $$\dfrac {16\sqrt {2}}{\pi}m$$
If the frequency of ac is $$60\ Hz$$ the time difference corresponding to a phase difference of $${ 60 }^{ \circ  }$$ is 
  • $$60\ s$$
  • $$1\ s$$
  • $$\dfrac { 1 }{ 60 } s$$
  • $$\dfrac { 1 }{ 360 } s$$
The distance between two particles in a wave motion vibrating out of phase of $$\pi $$ radians is:
  • $$\lambda /4$$
  • $$\lambda/2$$
  • $$3\lambda/4$$
  • $$\lambda $$
A particle is performing SHM with its position given as X=2+5 $$sin\left( \pi t\dfrac { \pi  }{ 6 }  \right) $$ where x (in m) & t (in sec). Which of the following is/ are correct :-
  • Equilibrium position is at X=2 m
  • Maximum speed of particle is $$5\pi m/s$$
  • Att=0 particle is 2.5 m away from position moving in negative direction
  • Att=0, X=4.5 m; acceleration of particle is $${ \pi }^{ 2 }\left( 4.5 \right) { m/s }^{ 2 }$$
Elastic waves in solids are
  • Only transverse
  • Only longitudinal
  • Neither transverse nor longitudinal
  • Either transverse or longitudinal
The path difference two waves $${ y }_{ 1 }={ a }_{ 1 }$$ sin $$\left( \omega t-\dfrac { 2\pi x }{ \lambda  }  \right) $$ and $${ y }_{ 2 }={ a }_{ 2 }$$ cos$$\left( \omega t=\dfrac { 2xy }{ \lambda  }  \right) is$$
  • $$\dfrac { y }{ 2\pi } \left( \phi \right) $$
  • $$\dfrac { y }{ 2\pi } \left( \phi +\dfrac { \pi }{ 2 } \right) $$
  • $$\dfrac { 2\pi }{ y } \left( \phi -\dfrac { \pi }{ 2 } \right) $$
  • $$\dfrac { 2\pi }{ \gamma } \left( \phi \right) $$
Two particle execute $$SHM$$ of the same amplitude and frequency along the same straight line. If they pass one another when going in opposite direction, each time displacement is $${ 1 }/{ \sqrt { 2 }  }$$ times their amplitude, the phase difference between them is
  • $$\pi/3$$
  • $$\pi/2$$
  • $$\pi/6$$
  • $$2\pi/3$$
In the equation $$y = \sin \pi (20t + 2x)$$
  • $$T= 1 s , \lambda = 1m$$
  • $$n= 10 Hz , \lambda = 1m$$
  • $$ a= 1m , T= 0.05 s$$
  • $$a= 1m , \lambda = 1m$$
A particle executes simple harmonic motion with an amplitude of $$4cm$$. At the mean position the velocity of the particle of the particle is $$10cm/s$$. The distance of the particle from the mean position when its speed becomes $$5cm/s$$ is:
  • $$\sqrt{3}cm$$
  • $$\sqrt{5}cm$$
  • $$2(\sqrt{3})cm$$
  • $$2(\sqrt{5})cm$$
Creating wind breaks means 
  • Cutting terraces on steep slopes
  • Cutting trees to increase the speed of wind
  • Planting a row of trees to reduce the speed of wind
  • Cutting plants in the direction of wind blow
The resultant amplitude of a vibrating particle by the superposition of the two waves $$  y_{1}=a \sin \left[\omega t+\frac{\pi}{3}\right] $$ and $$y_{2}=a \sin \omega t  $$ is :
  • $$a$$
  • $$\sqrt{2} a$$
  • $$2a$$
  • $$

    \sqrt{3} a

    $$
Two waves are represented by the equations $$y_{1} = a sin (\omega t+kx+0.57)m$$,  $$y_{2} = a cos (\omega t+kx)m$$, where $$x$$ in meter and $$t$$ in sec. The phase difference between them is 
  • $$0.57$$ radian
  • $$1.0$$ radian
  • $$1.25$$ radian
  • $$1.57$$ radian
A travelling wave in a string is represented by $$y=3sin\left( \dfrac { \pi  }{ 2 } t - \dfrac { \pi  }{ 4 } x \right) $$. The phase difference between two particles separated by a distance $$4cm$$ is (Take x and y in cm and t in seconds)
  • $$\dfrac{\pi}{2}\ rad$$
  • $$\dfrac{\pi}{4}\ rad$$
  • $$\pi\ rad$$
  • $$0$$
Three coherent waves of equal frequencies having amplitude $$  10 \mu m, 4 \mu m,  $$ and $$7  \mu m  $$ respectively, arrive at a given point with successive phase difference of $$  \pi / 2  $$ . the amplitude of the resulting wave in $$  \mu m  $$ is given by
  • $$5$$
  • $$6$$
  • $$3$$
  • $$4$$
A wave of frequency 500$$\mathrm { Hz }$$ travels between $$\mathrm { X }$$and $$\mathrm { Y }$$ and travel a distance of 600$$\mathrm { m }$$ in 2$$\mathrm { sec }$$ . between $$X$$ and $$Y .$$ How many wavelength are there in distance $$X Y$$ :
  • 1000
  • 300
  • 180
  • 2000
The amplitude of a wave disturbance propagating along positive $$x$$ -axis is given bY $$y = \frac { 1 } { 1 + x ^ { 2 } }$$ at $$t = 0 s ;$$ and $$y = \frac { 1 } { 1 + ( x - 2 ) ^ { 2 } }$$ at $$t = 4$$ s. Where $$x$$ and $$y$$ are in meters. The shape of wave disturbance does not change with time. The velocity of the wave is: 
  • 60$$\pi \mathrm { m } / \mathrm { s }$$
  • 30$$\pi \mathrm { cm } / \mathrm { s }$$
  • 30$$\mathrm { cm } / \mathrm { s }$$
  • 0.5$$\mathrm { m } / \mathrm { s }$$
Two wave of the same amplitude and frequency arrive at a point simultaneously. If the amplitude of resultant wave is the same as that of the cach wave, then the initial phase difference of the waveis 
  • $$( \sqrt { 2 } / 2 )$$ radian
  • $$( 2 \pi / 3 )$$radian
  • $$( 3 \pi / 4 )$$ radian
  • $$( \pi / 6 )$$ radian
From a line source, if amplitude of a wave at a distance $$r$$ is $$A$$ , then the amplitude at a distance 4$$\mathrm { f }$$ will be -
  • $$2A$$
  • $$A$$
  • $$\mathrm { A } / 2$$
  • $$\mathrm { A } / 4$$
A plane progressive wave is shown in the adjoining phase diagram. The wave equation of this wave, if its position is shown at $$t = 0 ,$$ is:
1429864_ea1c4ba310004031b7b00cdb70ada327.jpg
  • $$y = 0.05 \sin 2 \pi ( 300 t - x )$$
  • $$y = 0.05 \sin 2 \pi ( 300 t + x )$$
  • $$y = 0.05 \sin 8 \pi ( 300 t + x )$$
  • $$y = 0.05 \sin 8 \pi ( 300 t - x )$$
A particle executes SHM with a time period of 16 s. At time $$t = 2 s ,$$ the particle crosses the mean position while at $$t = 4 s ,$$ its velocity is 4$$m s ^ { - 1 } .$$ The amplitude of motion in metre is
  • $$\sqrt { 2 } \pi$$
  • 16$$\sqrt { 2 } \pi$$
  • 32$$\sqrt { 2 } / \pi$$
  • 4$$/ \pi$$
Two particies are oscillating along two close parallel straight  lines side by side, with the same frequen? amplindes. They pass each other, moving in opposite moving in opposite directions when their displacement is bif of amplitude. The mean positions of two particles lie on a particles lie on a straight line perpendicular to the paths of the paricles. The phase difference is:
  • $$\frac { \pi } { 6 }$$
  • 0
  • $$\frac { 2 \pi } { 3 }$$
  • $$\pi$$
25 waves pass through a point in 5 seconds. If the distance between one compression and one rarefaction is 0.05 m, the frequency and wavelength of the wave is : 
  • $$f=5Hz;\lambda =0.20m$$
  • $$f=4Hz;\lambda =0.1m$$
  • $$f=5Hz;\lambda =0.1m$$
  • $$f=5Hz;\lambda =0.15m$$
The wavelength and frequency of a sound wave in medium A is 20 cm and 1650 Hz. Keeping the medium same, if wavelength is changed to 16 cm, then new frequency is : 
  • 2060 Hz
  • 2062.5 Hz
  • 2061 Hz
  • 2063.0 Hz
Waves from two sources superpose on each other at a particular point, the amplitude, and frequency of both the waves are equal. The ratio of intensities when both waves reach in the same phase and they reach with the phase difference of $${ 90 }^{ \circ  }$$ will be 
  • $$1:1$$
  • $$\sqrt 2:1$$
  • $$2:1$$
  • $$4:1$$
Small amplitude progressive wave in a stretched string has a speed of $$100cm/s$$, and frequency $$100HZ$$. The phase difference between two points $$2.75cm$$ apart on the string in radiant is
  • $$0$$
  • $$\frac{{11\pi }}{2}$$
  • $$\frac{\pi }{4}$$
  • $$\frac{{3\pi }}{8}$$
Two waves are given by $$  y_{1}=\cos (4 t-2 x)  $$ and $$ y_{2}=\sin \left(4 t-2 x+\frac{\pi}{4}\right) \cdot  $$ The phase difference between the two waves is
  • $$ \pi / 4 $$
  • $$- \pi / 4 $$
  • $$3 \pi / 4 $$
  • $$ \pi / 2 $$
Two waves of the same amplitude and frequency arrive at a point simultaneously. The resultant amplitude is the same as that of the amplitude of each wave. So the initial phase difference of the two waves is:  
  • $$\pi/4$$
  • $$\pi/2$$
  • $$2\pi/3$$
  • $$3\pi/4$$
Two waves in a string ( all in SI units) are $$y_1 = 0.6 sin ( 10t  - 20 x)$$ and  $$y_2 = 0.4 sin (10 t +20 x)$$
 Statement-1: Stationary waves can be formed by their superposition but net energy transfer through any section will be non - zero.
Statement-2: Their amplitudes are unequal.
  • Both the statements are true and statement-2 is the correct explanation of statement-1
  • Both the statements are true but statement-2 is not the correct explanation of statement-1
  • Statement-1 is true and statement-2 is false
  • Statement-1 is false and statement-2 is true
A : If a wave moving in a rarer medium , gets reflected at the boundary of the denser medium , then it accounts a sudden change in phase of $$\pi $$.
R : If a wave propagating in a denser medium , gets reflected from rarer medium , then their will be no abrupt phase change .
  • Both assertion and reason are correct and reason explains the assertion
  • Both assertion and reason are correct and reason does not explains the assertion
  • Assertion is correct and reason is wrong
  • Assertion is wrong and reason is correct
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