Waves Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. When a wave travel in a medium, the particle displacement is given by
the equation y = a sin 2p (bt– cx) where a, b and c are constants. The
maximum particle velocity will be twice the wave velocity if
(a)
(b) c = pa
(c) b = ac
(d)
2. A thick uniform rope of length L is hanging from a
rigid support. A transverse wave of wavelength ?
0
 is
set up at the middle of rope as shown in figure. The
wavelength of the wave as it reaches to the topmost
point is
(a) 2?
0
Page 2


PART-I (Single Correct MCQs)
1. When a wave travel in a medium, the particle displacement is given by
the equation y = a sin 2p (bt– cx) where a, b and c are constants. The
maximum particle velocity will be twice the wave velocity if
(a)
(b) c = pa
(c) b = ac
(d)
2. A thick uniform rope of length L is hanging from a
rigid support. A transverse wave of wavelength ?
0
 is
set up at the middle of rope as shown in figure. The
wavelength of the wave as it reaches to the topmost
point is
(a) 2?
0
(b)
(c)
(d) ?
0
3. The fundamental frequency of a sonometer wire of length l is f
0
. A
bridge is now introduced at a distance of ? l from  the centre of the
wire (? l << l). The number of beats heard if both sides of the bridges
are set into vibration in their fundamental modes are –
(a)
(b)
(c)
(d)
4. A source of sound S emitting waves of
frequency 100 Hz and an observor O are
located at some distance from each other. The
source is moving with a speed of 19.4 ms
–1
 at
an angle of 60° with the source observer
line as shown in the figure. The observor is at rest.
The apparent frequency observed by the observer is (velocity of sound
in air is 330 ms
–1
)
(a) 103 Hz
(b) 106 Hz
(c) 97 Hz
(d) 100 Hz
5. Two identical piano wires kept under the same tension T have a
fundamental frequency of 600 Hz. The fractional increase in the tension
of one of the wires which will lead to occurrence of 6 beats/s when both
the wires oscillate together would be
(a) 0.02
Page 3


PART-I (Single Correct MCQs)
1. When a wave travel in a medium, the particle displacement is given by
the equation y = a sin 2p (bt– cx) where a, b and c are constants. The
maximum particle velocity will be twice the wave velocity if
(a)
(b) c = pa
(c) b = ac
(d)
2. A thick uniform rope of length L is hanging from a
rigid support. A transverse wave of wavelength ?
0
 is
set up at the middle of rope as shown in figure. The
wavelength of the wave as it reaches to the topmost
point is
(a) 2?
0
(b)
(c)
(d) ?
0
3. The fundamental frequency of a sonometer wire of length l is f
0
. A
bridge is now introduced at a distance of ? l from  the centre of the
wire (? l << l). The number of beats heard if both sides of the bridges
are set into vibration in their fundamental modes are –
(a)
(b)
(c)
(d)
4. A source of sound S emitting waves of
frequency 100 Hz and an observor O are
located at some distance from each other. The
source is moving with a speed of 19.4 ms
–1
 at
an angle of 60° with the source observer
line as shown in the figure. The observor is at rest.
The apparent frequency observed by the observer is (velocity of sound
in air is 330 ms
–1
)
(a) 103 Hz
(b) 106 Hz
(c) 97 Hz
(d) 100 Hz
5. Two identical piano wires kept under the same tension T have a
fundamental frequency of 600 Hz. The fractional increase in the tension
of one of the wires which will lead to occurrence of 6 beats/s when both
the wires oscillate together would be
(a) 0.02
(b) 0.03
(c) 0.04
(d) 0.01
6. Two sound sources emitting sound each of wavelength ? are fixed at a
given distance apart. A listener moves with a velocity u along the line
joining the two sources. The number of beats heard by him per second
is
(a)
(b)
(c)
(d)
7. A star, which is emitting radiation at a wavelength of 5000 Å, is
approaching the earth with a velocity of 1.50 × 10
6
 m/s. The change in
wavelength of the radiation as received on the earth is
(a) 0.25 Å
(b) 2.5 Å
(c) 25 Å
(d) 250 Å
8. An object of specific gravity ? is hung from a thin steel wire. The
fundamental frequency for transverse standing waves in the wire is 300
Hz. The object is immersed in water so that one half of its volume is
submerged. The new fundamental frequency in Hz is
(a)
(b)
(c)
Page 4


PART-I (Single Correct MCQs)
1. When a wave travel in a medium, the particle displacement is given by
the equation y = a sin 2p (bt– cx) where a, b and c are constants. The
maximum particle velocity will be twice the wave velocity if
(a)
(b) c = pa
(c) b = ac
(d)
2. A thick uniform rope of length L is hanging from a
rigid support. A transverse wave of wavelength ?
0
 is
set up at the middle of rope as shown in figure. The
wavelength of the wave as it reaches to the topmost
point is
(a) 2?
0
(b)
(c)
(d) ?
0
3. The fundamental frequency of a sonometer wire of length l is f
0
. A
bridge is now introduced at a distance of ? l from  the centre of the
wire (? l << l). The number of beats heard if both sides of the bridges
are set into vibration in their fundamental modes are –
(a)
(b)
(c)
(d)
4. A source of sound S emitting waves of
frequency 100 Hz and an observor O are
located at some distance from each other. The
source is moving with a speed of 19.4 ms
–1
 at
an angle of 60° with the source observer
line as shown in the figure. The observor is at rest.
The apparent frequency observed by the observer is (velocity of sound
in air is 330 ms
–1
)
(a) 103 Hz
(b) 106 Hz
(c) 97 Hz
(d) 100 Hz
5. Two identical piano wires kept under the same tension T have a
fundamental frequency of 600 Hz. The fractional increase in the tension
of one of the wires which will lead to occurrence of 6 beats/s when both
the wires oscillate together would be
(a) 0.02
(b) 0.03
(c) 0.04
(d) 0.01
6. Two sound sources emitting sound each of wavelength ? are fixed at a
given distance apart. A listener moves with a velocity u along the line
joining the two sources. The number of beats heard by him per second
is
(a)
(b)
(c)
(d)
7. A star, which is emitting radiation at a wavelength of 5000 Å, is
approaching the earth with a velocity of 1.50 × 10
6
 m/s. The change in
wavelength of the radiation as received on the earth is
(a) 0.25 Å
(b) 2.5 Å
(c) 25 Å
(d) 250 Å
8. An object of specific gravity ? is hung from a thin steel wire. The
fundamental frequency for transverse standing waves in the wire is 300
Hz. The object is immersed in water so that one half of its volume is
submerged. The new fundamental frequency in Hz is
(a)
(b)
(c)
(d)
9. The transverse displacement y (x, t) of a wave on  a string is given by 
. 
This represents a:
(a) wave moving in –x direction with speed 
(b) standing wave of frequency 
(c) standing wave of frequency 
(d) wave moving in + x direction with speed 
10. A source of sound A emitting waves of frequency 1800 Hz is falling
towards ground with a terminal speed v. The observer B on the ground
directly beneath the source receives waves of frequency 2150 Hz. The
source A receives waves, reflected from ground of frequency nearly:
(Speed of sound = 343 m/s)
(a) 2150 Hz
(b) 2500 Hz
(c) 1800 Hz
(d) 2400 Hz
11. In the figure shown the wave speed is v. The velocity of car is v
0
. The
beat frequency for the observer will be
(a)
(b)
(c)
Page 5


PART-I (Single Correct MCQs)
1. When a wave travel in a medium, the particle displacement is given by
the equation y = a sin 2p (bt– cx) where a, b and c are constants. The
maximum particle velocity will be twice the wave velocity if
(a)
(b) c = pa
(c) b = ac
(d)
2. A thick uniform rope of length L is hanging from a
rigid support. A transverse wave of wavelength ?
0
 is
set up at the middle of rope as shown in figure. The
wavelength of the wave as it reaches to the topmost
point is
(a) 2?
0
(b)
(c)
(d) ?
0
3. The fundamental frequency of a sonometer wire of length l is f
0
. A
bridge is now introduced at a distance of ? l from  the centre of the
wire (? l << l). The number of beats heard if both sides of the bridges
are set into vibration in their fundamental modes are –
(a)
(b)
(c)
(d)
4. A source of sound S emitting waves of
frequency 100 Hz and an observor O are
located at some distance from each other. The
source is moving with a speed of 19.4 ms
–1
 at
an angle of 60° with the source observer
line as shown in the figure. The observor is at rest.
The apparent frequency observed by the observer is (velocity of sound
in air is 330 ms
–1
)
(a) 103 Hz
(b) 106 Hz
(c) 97 Hz
(d) 100 Hz
5. Two identical piano wires kept under the same tension T have a
fundamental frequency of 600 Hz. The fractional increase in the tension
of one of the wires which will lead to occurrence of 6 beats/s when both
the wires oscillate together would be
(a) 0.02
(b) 0.03
(c) 0.04
(d) 0.01
6. Two sound sources emitting sound each of wavelength ? are fixed at a
given distance apart. A listener moves with a velocity u along the line
joining the two sources. The number of beats heard by him per second
is
(a)
(b)
(c)
(d)
7. A star, which is emitting radiation at a wavelength of 5000 Å, is
approaching the earth with a velocity of 1.50 × 10
6
 m/s. The change in
wavelength of the radiation as received on the earth is
(a) 0.25 Å
(b) 2.5 Å
(c) 25 Å
(d) 250 Å
8. An object of specific gravity ? is hung from a thin steel wire. The
fundamental frequency for transverse standing waves in the wire is 300
Hz. The object is immersed in water so that one half of its volume is
submerged. The new fundamental frequency in Hz is
(a)
(b)
(c)
(d)
9. The transverse displacement y (x, t) of a wave on  a string is given by 
. 
This represents a:
(a) wave moving in –x direction with speed 
(b) standing wave of frequency 
(c) standing wave of frequency 
(d) wave moving in + x direction with speed 
10. A source of sound A emitting waves of frequency 1800 Hz is falling
towards ground with a terminal speed v. The observer B on the ground
directly beneath the source receives waves of frequency 2150 Hz. The
source A receives waves, reflected from ground of frequency nearly:
(Speed of sound = 343 m/s)
(a) 2150 Hz
(b) 2500 Hz
(c) 1800 Hz
(d) 2400 Hz
11. In the figure shown the wave speed is v. The velocity of car is v
0
. The
beat frequency for the observer will be
(a)
(b)
(c)
(d)
12. The equation of a wave on a string of linear mass density 0.04 kg m
–1
 is
given by
y =0.02(m)  .
The tension in the string is
(a) 4.0 N
(b) 12.5 N
(c) 0.5 N
(d) 6.25 N
13. 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?
(a)
(b)
(c) p
(d)
14. A massless rod of length L is suspended
by two identical strings AB and CD of
equal length. A block of mass m is
suspended from point O such that BO is
equal to ‘x’. Further it is observed that
the frequency of 1st harmonic in AB is
equal to 2nd harmonic frequency in CD.
‘x’ is