Shri Datta KASHID CLASSES

Science Academy, Kurundwad

MH-CET CELL
Physics
Class - 12th Science. Subject- Physics
Total Questions : 150 Total Marks : 150
Roll No.
20-Sep-2021
XII - A Div
Superposition of wave 10:00 AM To 12:00 PM
This is to certify that, the entry of Roll No. has been correctly written and verified.

Candidate’s Signature MH-CET Physics Invigilator’s Signature

Note :
i) All Questions are compulsory
ii) Darken ( ) the appropriate circle(#) of the most correct option/response with black ball point pen.

Superposition of Waves

1) Mechanical waves require ______ medium for

A) Waves are called progressive waves, if they
their propagation.
travel in same straight line
A) elastic B) inelastic
B) Waves are called progressive waves, if they
travel without change the form
C) rigid D) liquid

2) Progressive wave with doubly periodic motion C) Waves are called progressive waves, if they
means travel in opposite direction

A) form of the wave repeats itself and travel D) Waves are called progressive waves, if they
equal distance in equal interval of time . are not transverse or longitudinal .

4) Which of the following is NOT the characteristic

B) repetiton at equal distance .
of the progressive wave ?

C) repetition after equal intervals of time .

A) All the vibrating particles of the medium
have different amplitudes and frequency .
D) repetition in medium without inertia .

3) Choose the WRONG statement . B) State of oscillation changes from particle to

particle .

C) For its propagation , medium has elasticity

and inertia.

D) The form of wave repeats itself at equal

intervals.
2π
5) The equation y − a sin (vt − x) is the
λ
equations .
 10) A wave undergoes reflection at a rigid wall. The
A) stationary wave of single frequency along x
parameter changed during this reflection is
- axis
A) frequency B) wavelength
B) a simple harmonic motion
C) amplitude D) velocity
C) a progressive wave of single frequency
along x-axis 11) A wave shown by the equation y = A cos
(ωt − ϕ) is totally reflected by a closed end.
D) the resultant of two S.H.M"s of slightly After reflection,
different frequencies
A) ϕ does not change.
6) A sine wave is travelling in a medium . The
minimum distance between two particles
B) only ϕ changes.
always having same speed is ( λ is the
wavellenght of wave )
C) ω changes.
λ λ λ
A) B) C) D) λ
4 3 2 D) both ω and ϕ change.
7) In a plane progressive harmonic wave, particle
12) A wave is reflected by a rigid support, the
speed is always less than the wave speed, if
change in phase due to reflection will be
λ
A) amplitude o f wave is less than
2π A) π/4 B) π/2 C) π D) 2π
λ
B) amplitude o f wave is greater than 13) After reflection from the open end, a transverse
2π
progressive wave y! = A sin 2π(t/T − x/λ)
λ travels along the direction of negative X-axis.
C) amplitude of wave is less than
4π The equation of the reflected wave will be
λ
D) amplitude of wave is greater than
π A) y2 = A sin 2π(t/T − λ/x)
8) A pulse on the string is inverted, when it is
reflected from B) y2 = −A sin 2π(t/T + x/λ)

A) a fixed end. C) y2 = A sin 2π(t/T + x/λ)

B) a free end. D) y2 = A sin 2π(t/T − x/λ)

14) When a wave is reflected at a rarer surface, the

C) both free as well as fixed ends.
change in phase is
D) neither a fixed nor a free end.
A) 0 B) π/2 . C) π D) 3π/2
9) The production of echo is due to
15) A phase reversal of π means
A) rarefaction of sound waves

B) interference of sound waves.

C) reflection o f sound waves.

D) refraction of sound waves.

 A) reversal of wave velocity. A) 0C
πC
B) there is a reversal of particle velocity. B)
2
C) there is a reversal of particle as well as the C) πC
wave velocity.
D) 2πC
D) there is reversal of medium.
19) When a longitudinal wave is incident on a rigid
16) Not only a change in direction but also a phase wall,
change of n radian is suffered by a sound wave,
when it suffers A) compression is reflected as rarefaction with
phase change of 0◦
A) reflection from a denser medium.
B) compression is reflected as rarefaction with
B) reflection from a rarer medium. phase change of 180◦

C) refraction in a denser medium. C) compression is reflected as compression

with no phase change.
D) refraction in a rarer medium
D) compression is reflected as compression
17) The given figure shows an incident pulse P
with phase change of 180◦
reflected from a rigid support. Which one of A,
B, C, D represents the reflected pulse correctly 20) Which two of the following waves are in the
same phase? y = A sin(kx − ωt)
y = A sin(kx − ωt + π)
y = A sin(kx − ωt + π/2)y = A sin(kx − ωt + π2)

A) I and II B) II and III

C) II and IV D) I and IV

21) The phenomenon of interference is observed

when two sources have

A) nearly same frequency.

B) exactly same wavelength.

C) same frequency and constant phase

difference.

D) same frequency and varying phase

difference.

22) Two waves

y1 = A1 sin(ωt − β1 ), y2 = A2 sin(ωt − β2 )
superimpose to form a resultant wave whose
amplitude is
18) What is phase difference, when longitudinal
wave is reflected from rigid wall?
 q
A) A21 + A22 + 2A1 A2 cos (β1 − β2 ) A) strain is maximum at antinodes.
q
B) A21 + A22 + 2A1 A2 sin (β1 − β2 ) B) strain is maximum at nodes.

C) |A1 − A2 | C) strain is minimum at nodes.

D) |A1 + A2 | D) amplitude is zero at all points

23) If stationary waves are being generated, then 27) At nodes, the velocity of stationary wave is
particles of medium
A) zero.
A) remain stationary.
B) maximum.
B) do not execute oscillatory motion.
C) minimum but not zero.
C) execute simple harmonic motion and at
some places amplitude is maximum. D) depends on amplitude.

28) In a stationary wave, at the antinodes, there is a

D) execute simple harmonic motion of equal
change in
amplitude

24) Stationary waves are produced A) density.

A) when two waves o f equal frequency B) pressure.

superpose while travelling in opposite
directions. C) both pressure and density.

B) due to diffraction. D) neither pressure nor density

C) due to superposition of two waves of equal 29) In a stationary wave, the particle velocity at the
frequency while travelling in the same nodal points is
direction.
A) zero.
D) due to constructive interference.
B) maximum and finite.
25) When the stationary waves, are formed, then
C) minimum but non zero.
A) transfer of energy is double of the energy of
component waves. D) infinite.

B) transfer of energy is zero. 30) Select the WRONG statement for a stationary
wave.
C) no energy is present in the medium.

D) value of energy density at each point of the

path is infinite.

26) In a stationary wave,

 A) The particles o f the medium perform S.H.M. A) the amplitudes are same but the time
of same period. periods are different.

B) Amplitude of oscillation for each particle is B) the amplitudes are different but the time
different. periods are same.

C) There is no transport of energy. C) the amplitudes and the time periods both
are same.
D) The wave does not travel along positive or
negative x-direction D) the amplitudes and the time periods both
are different.
31) In an air column, stationary waves can be
produced even if the superposing waves 35) When a body oscillates with its natural
frequency, then its vibration is called
A) have different quality.
A) free vibration.
B) have different pitch.
B) forced vibration.
C) have different amplitude.
C) resonance.
D) have different velocities.
D) phenomenon of beats.
32) When stationary waves are set up in a medium,
which of the following is a true statement? 36) If a body is set into vibrations with a strong
external force, the vibrations are
A) All the particles in the medium are in the
same phase of vibration at all times. A) free vibrations.

B) There is a continuous phase lag along the B) resonant vibrations.

wave.
C) forced vibrations.
C) There is a continuous phase lead along the
wave. D) damped vibrations.

D) The particles between two successive nodes 37) The example of forced vibration is
are in same phase but the particle just
opposite to a node are in opposite phase A) resonance. B) beats.

33) In stationary waves, all particles in between two C) interference. D) diffraction.

nodes pass through the mean position
38) In forced vibration, amplitude
A) simultaneously with equal velocity.
A) changes continuously.
B) at different times but with equal velocity.
B) remains constant.
C) at different times with different velocities.
C) first decreases gradually and finally
D) simultaneously but with different velocities. becomes zero.

34) In any stationary wave, for vibrating particles, D) changes irregularly.

39) In forced vibration, the body vibrates with 44) Pleasing sounds are produced

A) same frequency as that of external periodic A) in open organ pipe.

force.
B) in closed organ pipe.
B) any frequency having value between natural
and external periodic force. C) in both closed and open pipes.

C) natural frequency. D) in string instruments.

D) both (A) and (C) 45) The frequency of vibration of open organ pipe is
v v
40) Resonant vibration is a special case of A) B)
4l 2l + 1.2d
A) forced vibrations. v v
C) D)
l 8l
B) free vibrations. 46) A pipe open at both ends gives frequencies
which are
C) natural vibrations.
A) only even multiples of fundamental
D) damped vibrations. frequency.

41) In resonance, B) only odd multiples of fundamental

frequency.
A) the energy released by the vibrating body is
maximum. C) all integral multiples of fundamental
frequency.
B) energy absorbed by the vibrating body is
maximum. D) all fractional multiple of fundamental
frequency.
C) neither energy is absorbed by the vibrating
body nor energy is released. 47) In open organ pipe, if fundamental frequency is
n, then the other frequencies are
D) energy form does not evolve.
A) n, 2n, 3n, 4n B) n, 3n, 5n
42) Stationary waves in closed pipe will produce
C) n, 2n, 4n, 8n D) n, n2 , n3 , ......
A) all the harmonics.
48) In the case of an open organ pipe, which
B) all the even harmonics. harmonic will be denoted by the pth overtone?

C) all the odd harmonics. A) 2p + 1 B) 2 p - l

D) no harmonics. C) p + 1 D) p -1‘

43) Which of the pipes loses more energy? 49) An open pipe of length I vibrates in fundamental
mode. The pressure variation is maximum at
A) Wider B) Thinner

C) Both (A) and (B) D) Thick walled pipe

 A) l/4 from ends. A) Assertion is True, Reason is True; Reason is
a correct explanation for Assertion
B) the middle of pipe.
B) Assertion is True, Reason is True; Reason is
C) the ends of pipe. not a correct explanation for Assertion

D) l/8 from ends of pipe. C) Assertion is True, Reason is False

50) The harmonics which are present in a pipe D) Assertion is False but, Reason is True.
open at one end are
54) If the length of the vibrating string is kept
A) odd harmonics. constant, then frequency of the string will be
directly proportional to
B) even harmonics. √ 1
r
1
A) T B) T C) D)
T T
C) even as well as odd harmonics.
55) The harmonics produced in a vibrating string
are
D) fractional harmonics.

51) An empty vessel is partially filled with water, A) not related to each other.
then the frequency of vibration of air column in
the vessel B) of same frequency

A) remains same. C) in the ratio 1 : 2 : 3.

B) decreases. D) in the ratio 1 : 3 : 5.

C) increases. 56) In a stretched string,

D) first increases then decreases. A) only even harmonics are produced,

52) The fundamental note produced by a closed B) only odd harmonics are produced,
organ pipe is of frequency n. The fundamental
note produced by an open organ pipe of same C) even as well as odd harmonics are
length will be of frequency produced.
n
A) B) n C) 2n D) 4n D) neither even nor odd harmonics are
2
produced
53) Assertion: The fundamental frequency of
vibration of an open organ pipe remains same if 57) The string of a sonometer is plucked so as to
the radius o f the pipe is doubled. Reason: make it vibrate in one segment. The sound
Frequency of vibration of an open organ pipe is produced is called
independent o f the radius of pipe.
A) first harmonic. B) first overtone.

C) second harmonic. D) second overtone.

58) The beats are produced by sounding the two

tuning forks together. If wax is put on any one
of the forks, then the beat period
 A) increases. A) two times that corresponding to each wave.

B) decreases. B) same as that corresponding to each wave.

C) remain same. C) four times that corresponding to each wave.

D) may decrease, increase or remain the same. D) eight times that corresponding to each
wave.
59) To demonstrate the phenomenon of beats, we
need two sources which emit sound of 63) When the beats are produced by vibrations of
two tuning forks of nearly equal frequencies,
A) nearly the same frequency. then the velocity of propagation of beats

B) exactly the same frequency. A) is less than the velocity of sound.

C) exactly the same frequency and have a B) is equal to the velocity of sound.
definite phase relationship.
C) is more than the velocity of sound.
D) exactly the same wavelength
D) depends on the relative frequency.
60) Phenomenon of beats is audible if the
difference in the frequencies of the sound 64) At a place, due to beats obtained from two
waves is sources o f sound,

A) very large B) zero A) waves will always superpose in same phase.

C) more than 20 D) less than B) waves will always superpose in opposite

phase.
61) Waxing and waning of sound is noticeable if
waxing and waning repeats at an interval
C) the phase difference between waves
changes with time.
A) less than 1/10 s
D) the phase difference between waves
B) more than 1/10 s remains constant

C) between 1/10 sec and 1/3 s 65) A note is ____ .

D) between 1/3 sec and 1 s A) pure sine vibration

62) When beats are produced by progressive waves B) pure tan vibration
having the same amplitude and nearly the same
frequency, the maximum loudness heard is
C) straight motion

D) irregular disturbance

66) Loudness of the sound depends upon

 A) square of the amplitude. A) melody B) harmony

B) amplitude. C) overtone D) musical interval

72) A series of notes separated by fixed musical

C) reciprocal of the amplitude.
intervals constitute________ .
D) square root of the amplitude
A) melody B) overtone
67) Loudness can be increased by
C) musical scale D) note scale
A) increasing distance.
73) The pleasant sensation produced when two
notes simultaneously sounded together is
B) resonance.
A) consonance B) dissonant notes
C) decreasing intensity.
C) dischord D) dissonance
D) decreasing amplitude.
74) Two waves of same amplitude superimpose to
68) Every musical sound can be regarded as
produce two beats per second. What is the ratio
combination of_______ .
of minimum loudness to that of one of the
waves?
A) nodes B) antinodes
A) ∞ B) 0 C) 1 D) -1
C) notes D) noises
75) A stringed instrument is provided with hollow
69) Quality of a musical note depends on boxes. This helps to increase loudness of
sound by _______ .
A) harmonics present.
A) setting string into natural vibrations
B) length of the wave.
B) setting string into forced vibrations
C) velocity of sound in the medium.
C) setting hollow boxes into natural vibrations
D) fundamental frequency. along with the stringes
70) Pitch of a note depends up o n_______ .
D) setting hollow boxes into forced vibrations
along with the stringes
A) fundamental frequency
76) A travelling wave passes through a point of
B) harmonics observation. At this point, the time interval
between successive crests is 0.2 s, then,
C) source
A) wavelength is 5 m.
D) amplitude
B) frequency is 5 Hz.
71) When two or more notes are sounded together,
they produce pleasant effect due to conchord.
C) velocity of propagation is 5 m/s
It is called a s _______ .

D) wavelength is 0.2 m.
77) When a wave travels in a medium, displacement
A) 4 cm, 32 cm, 16 cm/s, 0.5 Hz
of a particle is given by, y (x, t) = 0.03 sin π (2t -
O.Olx) where y and x are in metres and t in
B) 4 cm, 16 cm, 32 cm/s, 1.0 Hz
seconds. The phase difference at a given
instant of time between two particles 25 m apart
in the medium is C) 4 cm, 32 cm, 19 cm/s, 0.6 Hz

A) π /8 B) π /4 C) π /2 D) π D) 4 cm, 24 cm, 16 cm/s, 1.0 Hz

78) If the wave equation of a particle is represented 81) The equation o f a wave is
 π π x
by, y = 0.8 sin 20πt − 5πx + , where x and y y = 4 sin 2t + where y, x are in cm and
4 2 8
are measured in metre and t is measured in time is in second. The phase difference
seconds, then the wave equation represents a between two positions of the same particle
wave travelling in which are occupied at time interval of 0.4 s is

A) the positive x-direction with velocity 4 m/s A) 0.2π B) 0.4π C) 0.6 π D) 0.8 π
and wavelength 0.1 m.
82) The equation of a wave of amplitude 0.02 m and
period 0.04 s travelling along a stretched string
B) the positive x-direction with velocity 4 m/s with a velocity of 25 m/s will be
and wavelength 0.4 m.
A) y = 0.02 sin 2π (0.04t - 0.5x)
C) the negative x-direction with velocity 1 m/s
and wavelength 0.4 m.
B) y = 0.02 sin 2π (25t - 2x )

D) the negative x-direction with velocity 4 m/s

C) y = 0.02 sin 2π (0.04t - x )
and wavelength 0.1 m.

79) A transverse wave of amplitude wavelength 1 m D) y = 0.02 sin 2π (25t - x)

and frequency 2 propagating in a string in the
83) The path difference between the two waves,
negative x direction. The equation of this wave 
2πx

is y1 = A1 sin ωt − and
 λ 
2πx
A) y = 0.5 sin (4 π t - 2π x) y2 = A2 cos ωt − + ϕ is
λ

B) y = 0.5 cos ( π t - 2 π x) λ λ  π
A) ϕ B) ϕ+
2π 2π 2
C) y = 0.5 sin (4 π t + 2π x) 2π  π 2π
C) ϕ− D) ϕ
λ 2 λ
D) y = 0.5 sin ( π t + 2π x) 84) The equation of a transverse wave travelling on
π x a rope is given by y = 10 sin π (0.01 x - 2.00 t)
80) The equation of a wave is y = 4 sin 2t + where y and x are in cm and t is in seconds.
2 8
, where y, x are in cm and time is in second. The The maximum transverse speed of a particle in
amplitude, wavelength, velocity and frequency the rope is about
of the wave are respectively
A) 63 cm/s B) 75 cm/s

C) 100 cm/s D) 121 cm/s

  
t x
85) The equation o f a wave is x = 5 sin −
0.04 4
cm. The maximum velocity of the particles of
the medium is

A) 1 m/s B) 1.5 m/s

C) 1.25 m/s D) 2 m/s

86) The equation o f sound wave travelling along

negative X-direction is given by, y = 0.04 sin π
(500t + 1.5x) m. The shortest distance between A) y = 0.05 sin 2π (40001 -12.5 x)
two particles having phase difference of π at
the same instant is B) y = 0.05sin2π (4000t -122.5 x)

A) 0.66 m B) 0.5 m C) 0.33 m D) 0.2 m C) y = 0.05sin2π (3300t - 10x)

87) A progressive wave is represented by the
equation, y = 0.5 sin (314 t - 12.56 x), where y D) y = 0.05sin2π (3300x -10t)
and x are in metre and t is in second. Its 91) A wave is expressed by the equation, y = 0.5 sin
wavelength is [ π (0.01x - 3t)], where y and x are in metre and t
is in second. The speed of propagation of the
A) 0.5 m B) 0.2 m C) 1 m D) 2 m wave is
88) A wave of frequency 400 Hz has a phase
velocity of 300 m/s. The phase difference A) 100 m/s B) 150 m/s
between two displacements at a certain point at
time t = 10−3 s is C) 200 m/s D) 300 m/s

92) The wave described by y = 0.25 sin (10 π x-27 π

A) 72◦ B) 102◦ C) 144◦ D) 180◦ nt) where x and y are in meters and t in
89) A progressive wave of frequency 500 Hz is seconds, is a wave travelling along the
travelling with a speed of 350 m/s. A
compressional maximum appears at a given A) positive x direction with frequency 1 Hz and
instant. The minimum time interval after which wavelengthλ = 0.2 m.
a rarefactional maximum occurs at the same
point is B) negative x direction with amplitude 0.25 m
and wavelengthλ = 0.2 m.
A) 1/250 s B) 1/500 s
C) negative x direction with frequency 1 Hz.
C) 1/1000 s D) 1/350 s
D) positive x direction with frequency π Hz and
90) If the speed of the wave shown in the figure is wavelength λ = 0.2 m.
330 m/s in the given medium, then the equation 
2π

of the wave propagating in the positive 93) Given that y = A sin (ct − x) 6 and x are
λ
x-direction will be (all quantities are in M.K.S. measured in metres. Which of the following
units ) statements is true?
 2π 99) The equations of displacement of two waves
A) The unit of λ−1 is same as that of  π
λ are given as y1 = 10 sin 3πt +
 √  3
B) The unit of λ is same as that o f x but not of y2 = 5 sin 3πt + 3 cos 3πt Then what is the
A. ratio of their amplitudes?
2π
C) The unit of c is same as that of A) 1:2 B) 2:1 C) 1:1 D) 2:3
λ
2π 100)A wave in a string has an amplitude of 2 cm.
D) The unit of (ct - x) is same as that of
λ The wave travels in the +ve direction of X-axis
94) The equation of a plane with a speed of 128 m/s and it is noted that 5
 progressive wave is
complete waves fit in 4 m length of the string.

t x
given by, y = 3 sin π − . The The equation describing the wave is
0.02 20
frequency of the wave is
A) y = (0.02) m sin (7.85 x + 1005t)
A) 100 Hz B) 25 Hz C) 50 Hz D) 20 Hz
B) y = (0.02) m sin (15.7 x -2 0 1 0 t)
95) Progressive wave of sound is represented by
y = A sin [400πt − πx/6.85] where x is in m and t
C) y = (0.02) m sin (15.7 x + 201 Ot)
is in s. Frequency of the wave will be
D) y = (0.02) m sin (7.85 x - 1005t
A) 200 Hz B) 400 Hz C) 500 Hz D) 600 Hz
101)The electric field part of an electromagnetic
96) If the equation
 of a transverse wave is
t x
 wave in a medium is represented by Ex = 0;
y = 5 sin 2π − , where distance is in Ey =
0.04 40     
cm and time in second, then the wavelength of N 6 rad −2 rad
2.5 cos 2π × 10 t − π × 10 x
the wave is C m s
; Ey = 0. The wave is
A) 10 cm B) 25 cm C) 40 cm D) 60 cm
A) moving along y direction with frequency 2 π
97) The equation of a wave travelling in a string can x 106 Hz and wavelength 200 m.
be written as y = 3 cos π (100 t - x). Its
wavelength is B) moving along x direction with frequency 106
Hz and wavelength 100 m.
A) 100 cm B) 2 cm C) 5 cm D) 10 cm
C) moving along x direction with frequency 106
98) A plane progressivewave is represented
 by the Hz and wavelength 200 m.
20πx
equation y = 0.1 sin 200πt − where y is
17
displacement in m, t in second and x is D) moving along -x direction with frequency
distance from a fixed origin in metre. The 106 Hz and wavelength 200 m.
frequency, wavelength and speed of the wave 102)The diagram below shows the propagation of a
respectively are wave. Which points are in same phase?

A) 100 Hz, 1.7 m, 170 m/s

B) 150 Hz, 2.4 m, 200 m/

C) 80 Hz, 1.1 m, 90 m/s

D) 120 Hz, 1.25 m, 207 m/s

 A) F, G B) C and E A) y = 0.9 A sin (27 π nt + π )
A
C) B and G D) B and F B) y = sin (27π nt)
9
103)Equation of a simple harmonic progressive

t x
 C) y = 0.9 A sin (27π nt)
wave is y = 0.03 sin 8π − , where all
0.016 1.6
the quantities are in S.I. units. The velocity of D) y = 9 A sin (27π nt)
wave is
108)A bat flying above lake emits ultrasonic sound
of 100 kHz. When this wave falls on the water
A) 0.010 m/s B) 1.0 m/s
surface, it is partly reflected and partly
transmitted. The wavelengths o f the reflected
C) 10 m/s D) 100m/s and the transmitted waves are (The speed of
104)The phase difference between two points sound in air is 340 m/s and in water is 1450 m/s)
separated by 0.8 m in a wave of frequency 120
Hz is 90◦ . The wave velocity is A) 6.8 mm and 2.9 mm

A) 144 m/s B) 256 m/s B) 3.4 mm and 1.45 cm

C) 384 m/s D) 720 m/s C) 3.4 mm and 7.8 mm

105)The phase difference between two particles in a D) 6.8 mm and 1.45 cm

medium separated by a distance x is π /6 . If the
frequency of the oscillation is 50 Hz and the 109)Assertion: On reflection from a rigid boundary
velocity of propagation of the wave is 100 m/s, (denser medium), there is a complete reversal
then x = of phase. Reason: This is because on reflection
at a denser medium, both the particle velocity
A) 1/3 m B) 1/4 m C) 1/6 m D) 1/12 m and wave velocity are reversed in sign.

106)A wave travelling along the x-axis is described A) Assertion is True, Reason is True; Reason is
by the equation y(x, t) = 0.005 cos (αx − βt) . If a correct explanation for Assertion
the wavelength and the time period of the wave
are 0.08 m and 2.0 s, respectively, then a and P B) Assertion is True, Reason is True; Reason is
in appropriate units are not a correct explanation for Assertion
0.08 2.0 0.04 1.0
A) α = ,β = B) α = ,β = C) Assertion is True, Reason is False
π π π π

C) D) α = 25.00π, β = π D) Assertion is False but, Reason is True.

π
α = 12.50π, β =
2.0 110)When longitudinal waves are reflected from the
107)The equation of a wave is y = A sin (27 π nt). surface of a rarer medium,
When it is reflected at a free end, its amplitude
becomes 90%. The equation of the reflected
wave is
 √
A) compression is reflected as rarefaction A) 1 : 1 B) 2:1 C) 2 : 1 D) 4 : 1
without phase change.
116)Consider ten identical sources o f sound, all
giving the same frequency but having phase
B) compression is reflected as rarefaction with
angles which are random. If the average
a phase change of tt rad.
intensity of each source is I0 , the average of
resultant intensity I due to all these ten sources
C) rarefaction is reflected as rarefaction
will be
without phase change.
A) I = 100I0 B) I = 10 I0
D) rarefaction is reflected as rarefaction with a
phase change of π rad. √
C) I = I0 D) I = 10I0
111)Two waves are represented by
π 117)42. Equations of two progressive waves at a
y1 = A sin ωt + and y2 = A cos ωt . what certain point in a medium are given by,
6
will be their resultant amplitude? y1 = a1 sin (ωt + ϕ1 ) and y2 = a2 sin (ωt + ϕ2 ) .
If amplitude and time period of resultant wave
A) A B) A C) A D) 2A formed by the superposition of these two waves
is same as that of both the waves, then ϕ1 - ϕ2
112)The transverse displacement of a string fixed at
is
both ends isgiven
 by
2πx π 2π π π
y = 0.06 sin cos(120πt)y and x are in A) B) C) D)
3 3 3 6 4
metres and t in seconds. The wavelength and
118)The amplitude of a wave represented by
frequency of the two superposing waves are
displacement equation
respectively 1 1
y = √ sin ωt ± √ cos ωt will be
2 a b
A) 2m, 120 Hz B) m ,60Hz √ √
3 a+b a+ b
A) B)
3 ab
C) m ,120Hz D) 3m, 60 Hz √ √ r √ab √
2 a± b a+ b
C) D)
113)Two waves represented by the following ab ab
equations are travelling in the same medium y1 119)If two waves x1 = A sin (ωt − 0.1x) and
= 5 sin 2 π (75t - 0.25x), y2 = 10 sin 2 π (150t - x2 = A sin (ωt − 0.1x − ϕ/2) are combined with
0.50x). The intensity ratio I1 I2 of the two waves each other, then resultant amplitude of the
is combined wave is
r
A) 1 :2 B) 1 :4 C) 1 :8 D) 1 : 16 ϕ ϕ
A) 2A cos B) A 2 cos
4 2
114)The superposition takes place between two r 
ϕ ϕ
waves of frequency f and amplitude a. The total C) 2A cos D) A 2 1 + cos
2 2
intensity is directly proportional to
120)The equations of two sound waves are given by,
A) A B) 2A C) 2A2 D) 4A2 y1 = 3 sin (100πt) and y2 = 4 sin (150πt) . The
ratio of intensities of sound produced in the
115)Waves from two different sources overlap near medium is
a particular point. The amplitude and the
frequency of the two waves are the same. The A) 1:4 B) 2:3 C) 3:4 D) 9:16
ratio of the intensity, when the two waves arrive
in the phase to that when they arrive 90◦ out of
phase is
121)Two waves of same frequency have amplitudes √
A) 2A cos θ B) 2A cos θ
5 cm and 3 cm. These waves are made to
superpose in the same direction. The ratio of √ θ
C) 4A cos θ/2 D) 2A cos
maximum intensity to minimum intensity at 2
various places will be
127)In a stationary wave,

A) 3 : 5 B) 9 : 25 C) 9 : 4 D) 16: 1
A) in each time period all particles come to rest
122)If two interfering waves have intensities in the twice simultaneously.
ratio 9 : 1, then the ratio of maximum to
minimum amplitude is B) in each time period, all particles come to
rest once simultaneously.
A) 10:8 B) 4 : 2
C) all the particles never remain at rest
C) 100: 64 D) 16 :4 simultaneously.

123)Two sources of sound A and B produce the D) all the particles never remain at rest.
wave of 350 Hz, they vibrate in the same phase.
The particle P is vibrating under the influence 128)Which of the properties makes difference
of these two waves. If the amplitudes at the between progressive and stationary waves?
point P produced by the two waves is 0.3 mm
and 0.4 mm, then the resultant amplitude o f the A) Amplitude
point P will be [Given AP - BP = 25 cm and the
velocity of sound is 350 m/s] B) Frequency

A) 0.7 mm B) 0.1mm C) 0.2 mm D) 0.5 C) Propagation of energy

124)When two sound waves with a phase difference

D) Phase of the wave
of π /2 and each having amplitude A and
frequency co are superimposed on each other, 129)Consider three waves z1 , z2 and z3 as
then the maximum amplitude and frequency of z1 = A sin (kx − ωt) , z2 = A sin (kx + ωt) and
resultant wave is z3 = A sin (kx − ωt) Which of the following,
A ω A represents a standing wave?
A) √ : B) √ : ω
2 2 2
A) z1 + z2 B) z2 + z3 C) z3 + z1 D) z1 .z2
√ ω √
C) 2A : D) 2A : ω
2 130)The energy is not transformed in the following
125)Two periodic waves of intensities I1 and I2 pass
through a region at the same time in the same A) Sound waves B) Visible waves
direction. The sum of the maximum and
minimum intensities is C) Progressive waves D) Stationary waves

√ √
2 131)Amplitude of vibration in stationary wave is

A) I1 − I2 B) 2 (I1 + I2 )
√ √
2 A) maximum at nodes.
C) I1 + I2 D) I1 + I2

126)Equation of motion in the same direction are B) zero at nodes.

given by y1 = 2A sin (ωt − kx) and
y2 = 2A sin (ωt − kx − θ) . The amplitude of the C) maximum at nodes and antinodes.
medium particle will be
D) equal at all the points.
132)Node is that point in longitudinal stationary 137)Two travelling waves, y1 = A sin [k (x + ct)] and
waves where pressure y2 = A sin [k (x − ct)] are superposed on a string.
The distance between adjacent nodes is
A) difference is maximum.
ct ct π π
A) B) C) D)
π 2π 2k k
B) is maximum. πx
138)y = 6 sin represents a stationary wave. The
6
C) is minimum. distance between two consecutive nodes is

D) difference is minimum. A) 2 B) 3 C) 6 D) 12

133)What is nature of waves on stretched 139)Energy is not carried by which of the following
sonometer wire? waves?

A) Transverse progressive polarised. A) Stationary waves.

B) Longitudinal progressive polarised. B) Progressive waves.

C) Transverse stationary polarised. C) Transverse waves.

D) Unpolarised. D) Electromagnetic waves.

πx 140)The equation of a 
wave travelling on a string is
134)y = 6 sin cos 8πt represents a stationary
6 π x
wave. The frequency of the stationary wave in y = 4 sin 8t − . If x and y are in cm, then
2 8
cycles/s is velocity o f wave is

A) 2 B) 4 C) 6 D) 8 A) 64 cm/s in -x direction.

135)The stationary wave, y = 2 A sin kx cos ωt in a B) 32 cm/s in - x direction.

closed organ pipe is the result of the
superposition of y = A sin ( ωt - kx) and and
C) 32 cm/s in +x direction.

A) y = -A cos( ωt + kx)
D) 64 cm/s in +x direction

B) y = -A sin( ωt + kx) 141)A standing wave is represented by, y = A sin

(lOOt) cos (0.0 lx), where x, y and A are in
C) y = A sin( ωt + kx) millimetre and t in second. The velocity of the
wave is
D) y = A cos( ωt + kx)
A) 104 m/s B) 10 m/s
136)A standing wave results from sum of two
transverse travelling waves given by, C) 10−4 m/s D) 103 m/s
y1 = 0.050 cos(πx − 4πt) and
y2 = 0.050 cos(πx + 4πt) , where x, y1 , y2 are in 142)Resonance occurs when
metre and t in seconds. The smallest positive
value of x that corresponds to a node is

A) 0 m B) 0.5 m C) 1.5 m D) 1 m
 146)A student determines the velocity of sound with
A) a body vibrates at a frequency lower than its
the help of a closed organ pipe. If the observed
normal frequency.
length for fundamental frequency is 24.7 m, the
length for third harmonic will be
B) a body vibrates at a frequency higher than
its normal frequency.
A) 74.1cm B) 72.7 cm

C) a body is set into vibrations with its natural

C) 75.4 cm D) 73.1cm
frequency by another body vibrating with
the same frequency. 147)In a closed organ pipe, the frequency of the
fundamental note is 50 Hz. The note of which of
D) a body is made of the same material as the the following frequencies will not be emitted by
sound source. it?

143)Above the resonant frequency,

A) 50 Hz B) 100 Hz C) 150 Hz D) 250 Hz

A) the frequency of the body is less than the 148)The fundamental frequency of a closed organ
frequency of the external periodic force. pipe is 50 Hz. The frequency of the second
overtone is
B) the frequency of the body is greater than the
frequency of the external periodic force. A) 100 Hz B) 150 Hz C) 200 Hz D) 250 Hz

149)Find the fundamental frequency of a closed

C) the frequency of the body is exactly equal to
pipe, if the length o f the air column is 42 m.
the frequency of the external periodic force.
(speed of sound in air = 332 m/sec)
D) both (A) and (B)
A) 2 Hz B) 4 Hz C) 7 Hz D) 9 Hz
144)There is a large difference between the
150)Two closed pipes produce 10 beats per second
frequencies of external periodic force and
when emitting their fundamental notes. If their
natural frequency of a body. The body will
lengths are in ratio of 25 : 26, then their
fundamental frequencies in Hz, are
A) vibrate with large amplitude and frequency
of force.
A) 270,280 B) 260,270 C) 260,250 D) 260,280
B) not vibrate.

C) vibrate with small amplitude with its own

frequency.

D) vibrate with small amplitude and with

frequency of force.

145)The frequency of the fundamental note

produced by a closed organ pipe is n. If the
diameter of the pipe is doubled, then the
frequency of the fundamental note produced by
it will be (Neglect end correction)

A) 4n B) 2n C) n D) n/2
 Answer Sheet

Physics : Superposition of Waves

Total Questions : 150 Total Marks : 150

1 A 2 A 3 B 4 A 5 C 6 C 7 A 8 A 9 C 10 D 11 B
12 C 13 C 14 A 15 B 16 A 17 D 18 C 19 D 20 D 21 C 22 A
23 C 24 A 25 B 26 B 27 A 28 D 29 A 30 A 31 C 32 D 33 D
34 B 35 A 36 C 37 B 38 B 39 A 40 A 41 B 42 C 43 A 44 A
45 B 46 C 47 A 48 C 49 B 50 A 51 C 52 C 53 A 54 A 55 C
56 C 57 A 58 D 59 A 60 D 61 B 62 C 63 B 64 C 65 A 66 A
67 B 68 C 69 D 70 A 71 B 72 C 73 A 74 B 75 D 76 B 77 B
78 B 79 C 80 A 81 B 82 D 83 B 84 A 85 A 86 A 87 A 88 C
89 C 90 C 91 D 92 A 93 A 94 B 95 A 96 C 97 B 98 A 99 C
100 D 101 C 102 D 103 D 104 C 105 C 106 D 107 C 108 B 109 A 110 A
111 C 112 D 113 B 114 D 115 C 116 B 117 B 118 D 119 A 120 A 121 D
122 B 123 D 124 D 125 B 126 C 127 A 128 C 129 A 130 D 131 B 132 A
133 C 134 B 135 B 136 B 137 D 138 C 139 A 140 D 141 B 142 C 143 A
144 D 145 C 146 A 147 B 148 D 149 A 150 C