


TARGET : PRE-MEDICAL 2026 NURTURE COURSE
WAVE MOTION (FUNDAMENTAL) # 01
1. Let speed of sound waves in O2 gas at certain 5. Two small boats are 20m apart on a lake. Each
temperature is v0. What will be the speed of pops up and down with a period of 2.0 seconds
sound waves in a room which contains an due to wave motion on the surface of water.
When one boat is at its highest point, the other
equimolar mixture of O2 and 'He' at same
boat is at its lowest point. Both boats are always
temperature :-
within a single cycle of the waves. The speed of
20 40 the waves is :-
(1) v0 (2) v0
3 21 (1) 2.5 m/s (2) 20 m/s
(3) 14 m/s (4) 40 m/s
21
(3) v0 (4) None 6. A uniform rope of mass M = 0.1kg and length
30
L = 10m hangs from the celling. [g=10m/s2] :-
2. A sound absorber attenuates (decreases) the
(1) Speed of the transverse wave in the rope

®
sound level by 20 dB. The intensity decreases by increases linearly from top to the bottom
a factor of : (2) Speed of the transverse wave in the rope
(1) 100 (2) 1000 decreases linearly from bottom to the top
(3) Speed of the transverse wave in the rope
(3) 10000 (4) 10
remain constant along the length of the rope
0.8 (4) Time taken by the transverse wave to travel
3. y(x,t) = represents a moving pulse,
(4x + 5t)2 + 5 the full length of the rope is 2 sec
where x,y, are in metre and t in second. Then : 7. A thick uniform rope of length L is hanging from
(i) pulse is moving in +x-direction a rigid support. A transverse wave of wavelength
λ0 is set up in the middle of the rope. The
(ii) in 2 second it will travel a distance of 2.5 m
wavelength of the wave as it reaches the topmost
(iii) its maximum displacement is 0.16 m
point is :-
(iv) it is travelling wave pulse

(1) (i,iv) (2) (ii,iii,iv)

L
(3) (i,ii,iv) (4) (i,iii)

4. Two particles of medium disturbed by the wave

(1) 2λ0 (2) 2 λ0 (3) λ0/ 2 (4) λ0
propagation are at x1 = 0 and x2 = 2cm. The 8. A wave travelling along the x-axis is described by
respective displacements (in cm) of the particles the equation y (x, t ) = 0.005 cos ( αx − βt ). If the
can be given by the equations :-
wavelength and the time period of the wave are
y1 = 2sin3πt 0.08m and 2.0 s respectively then α and β in

y2 = 2sin(3πt – π/8) appropriate units are

(1) α = 25.00π, β = π
The wave velocity is :
0.08 2.0
=
(2) α = ,β
(1) 16 cm/sec π π
(2) 48 cm/sec 0.04 1.0
=
(3) α = ,β
π π
(3) 12 cm/sec
π
(4) 8 cm/sec =
(4) α 12.50=
π, β
2.0

E Your Target is to secure Good Rank in Pre-Medical 2026 [ 105 ]




NURTURE COURSE TARGET : PRE-MEDICAL 2026
9. A sinusoidal wave propagates along a string. In 12. The transverse displacement of a stretched string

figure (a) and (b) 'y' represents displacement of which is connected between two rigid supports is

particle from the mean position. 'x' & 't' have given by

usual meanings. Find :-  2πx 

y = 0.06 sin  − 80πt 
y(in mm)
 5 
for x=2m
+3
6 where x and y are in metre and t in sec. Length
(a) 2 4 t (in second)
0 –2
of string is 1.5 m and its mass is 3 × 10 kg.
–3 Then tension in string will be :-

(1) 600 N (2) 400 N

y (in mm) at t = 3s
(3) 800 N (4) 200 N
(b)
x (in m)

®
13. The figure shows four progressive waves A, B, C
& D. It can be concluded from the figure that
with respect to wave A :-
(a) wavelength, frequency and speed of the wave
y
(b) maximum velocity and maximum B A C
acceleration of the particles
ωt
10. For a given medium find intensity ratio I1:I2 for

the shown waves :- ωt=π/2 ωt=π ωt=3π/2

4
1 (1) the wave C is ahead by a phase angle of
2 π/2 & the wave B lags behind by a phase
y 1
t angle π/2

(2) the wave C lags behind by a phase angle of

π/2 & the wave B is ahead by a phase angle
(1) 4 : 5 (2) 5 : 4
of π/2
(3) 16:25 (4) 25:16
(3) the wave C is ahead by a phase angle of π &
11. The diagram below shows the propagation of a
the wave B lags behind by the phase angle of π
wave. Which points are in phase ?
(4) the wave C lags behind by a phase angle of
π & the wave B is ahead by a phase angle of π
C 14. When the temperature of an ideal gas is
O
B D E increased by 600 K, the velocity of sound in the
A
gas becomes 3 times the initial velocity in it.
(1) A, B (2) B, C The initial temperature of the gas is .

(3) B, D (4) E, B (1) –73° C (2) 27°C

(3) 127°C (4) 327°C

[ 106 ] Your Target is to secure Good Rank in Pre-Medical 2026 E




TARGET : PRE-MEDICAL 2026 NURTURE COURSE
15. Which of the following is/are correct :- 18. Ultrasonic, infrasonic and audio waves travel
through a medium with speeds Vu , Vi and Va
(Velocity of sound in
respectively then :-
(1) Vu, Vi and Va are equal
(1) (T=constant
(2) Vu > Va >Vi
(Parabola) (3) Vu < Va <Vi
O (4) Va < Vu and Vu ≈ Vi
(Pressure
19. Consider the wave represented by,
2
(Velocity of sound in air) y = 25 sin (20t + 5x) where y is in mm, x in m
and t in seconds. Which of the following is/are
(2)
true ?
O (1) the wave is a standing wave
(Temperature °C) (2) the speed of the wave is 4 ms
–1

®
(3) the frequency of oscillation is 500 × 2π Hz
(Velocity of transeverse
Wave in a string) (4) two nearest points in the same phase have
separation 40π cm
(3) 20. The frequency of man's voice is 150 Hz and its
wavelength is 1 m. If the wavelength of a child's
(Parabola)
O voice is 1.5 m, then the frequency of the child's
(tension)
voice in same medium is :-
(Fundamental freq. of an (1) 100 Hz (2) 150 Hz
organ pipe) (3) 400 Hz (4) 450 Hz
21. A light pointer fixed to one prong of a tuning
(4) (Exponential curve fork touches a vertical plate. The fork is set
vibrating and the plate is allowed to fall freely.
O Sixteen complete oscillations of fork are counted
(Length of organ pipe)
when the plate falls through 10 cm. What is the
16. The speed of sound in oxygen (O2) at a certain frequency of the tuning fork ?
(1) 112 Hz (2) 56 Hz
temperature is 460 ms–1. The speed of sound in
(3) 8/7 Hz (4) 7/8 Hz
helium (He) at the same temperature will be:
22.
3
If the density of air at NTP is 1.293kg/m and
(assume both gases to be ideal) γ = 1.41, then the velocity of sound in air at
NTP is :
(1) 460 10 ms–1 (2) 360 5 ms–1 (1) 102.3 m/s (2) 252.3 m/s
–1 –1
(3) 332.3m/s (4) 432.3 m/s
(3) 650 ms (4) 330 ms
23. Which of the following statements is correct ?
17. How far does the sound travel in air when a (1) Both sound and light waves in air are
tuning fork of frequency 560 Hz makes electromagnetic

30 vibrations ? Given speed of sound in (2) Both sound and light waves in air are
transverse
air = 336 m/s.
(3) Sound waves in air are faster while light
(1) 36 m (2) 18 m waves slower
(3) 72 m (4) 9 m (4) Sound waves in air are longitudinal while
light waves transverse

E Your Target is to secure Good Rank in Pre-Medical 2026 [ 107 ]




NURTURE COURSE TARGET : PRE-MEDICAL 2026
24. Two waves are represented by : 27. The phase difference between two points

 π separated by 0.8 m in a wave of frequency

y1 = a sin  ωt +  and y2 = a cos ωt
 6  120 Hz is 0.5π. The wave velocity is :-
What will be their resultant amplitude ? (1) 144 m/s (2) 256 m/s

(1) a (2) 2a (3) 3a (4) 2a (3) 384 m/s (4) 720 m/s
28. You have learnt that a travelling wave in one
25. A small piece of cork in a ripple tank oscillates
dimension is represented by a function
up and down as ripples pass it. If the ripples
y = f(x, t) where x and t must appear in the
travelling at 0.3 m/s have a wavelength of
combination x - vt or x + vt, i.e. y = F (x ± vt). Is
1.5π cm and the cork vibrates with an amplitude
the converse true? Examine if the following
of 5 mm, the maximum velocity of the cork is:-
functions for y can possibly represent a travelling
(1) 20 cm/sec (2) 20 m/sec
wave:

®
(3) 0.02 m/sec (4) 200 cm/sec 2
(1) (x - vt)
26. If the equation of a progressive wave is given by :
(2) log [(x + vt)/x0]
 t x π
y= 4 sin π  − + 
5 9 6  (3) exp [-(x + vt)/x0]

where x, y are in meter is t in second. (4) 1/(x + vt)

Then, which of the following is correct ?
(1) υ = 5 cm/sec (2) λ = 18 m
(3) A = 0.04 cm (4) f = 50 Hz

ANSWER KEY

1. 2 2. 1 3. 2 4. 2 5. 2 6. 4 7. 2

8. 1 9. (a) 6m, 0.25 Hz, 1.5 m/s , (b) 1.5π mm/s,0.75π2 mm/s 10. 3 11. 4

12. 3 13. 2 14. 2 15. 3 16. 1 17. 2 18. 1

19. 2,4 20. 1 21. 1 22. 3 23. 4 24. 3 25. 1

26. 2 27. 3 28. No, None

[ 108 ] Your Target is to secure Good Rank in Pre-Medical 2026 E




TARGET : PRE-MEDICAL 2026 NURTURE COURSE
WAVE MOTION (SUPERPOSITION OF WAVES INTERFERENCE, BEATS) # 02
1. Three tuning forks of frequencies 200, 202 and 6. When two progressive waves of intensity I1 and I2
204 Hz are sounded together. The beat but slightly different frequencies superpose, the
frequency will be :- resultant intensity fluctuates between :-
(1) 4 (2) 12
( ) ( )
2 2
(1) I1 + I2 and I1 − I2
(3) 15 (4) None of these
2. Two identical sources of sound are placed at (2) ( )
I1 + I2 and ( I1 − I2 )
separation 2λ. A detector D moves along a circle
as shown. Find number of maxima and minima (3) (I1 + I2) and ( I1 − I2 )
recorded by detector in one round along the
I1 I
circle. (given OS1 = OS2) :- (4) and 2
I2 I1

®
D
7. A vibrating tuning fork of frequency n is placed
near the open end of a long cylindrical tube. The
O
S1 S tube has a side opening and is also fitted with a
movable reflecting piston. As the piston is moved
(1) 8, 12 (2) 8, 8 (3) 12, 12 (4) 4, 4 through 8.75 cm, the intensity of sound changes
3. Three waves producing displacement in the same from a maximum to maximum. If the speed of
direction of same frequency and of amplitudes sound is 350 metre per second, then n is :-
12µm, 4µm and 9µm arrive at a point with
successive phase difference of π/2. The
amplitude of the resultant wave is :-
Ear
(1) 2µm (2) 7µm (3) 5µm (4) 1
(1) 500 Hz (2) 1000 Hz
I1 169
4. In interference of two waves if = then
I2 100 (3) 2000 Hz (4) 4000 Hz

I max 8. The path difference between the two waves

is :-
I min
y1 = a1 sin (ωt – kx)
23 13
(1) (2) and y2 = a2 cos (ωt – kx + φ/2),
10 10
2 is :-
 23  23
(3)   (4)
 3  7 (1) ( λ / 4π ) φ
5. On sounding tuning fork A with another tuning
φ+ π
fork B of frequency 384 Hz, 6 beats are (2)   λ
 4π 
produced per second. After loading the prongs
of A with some wax and then sounding it again 4π  π
(3)  φ− 
λ  2
with B, 4 beats are produced per second. What
is the frequency of the tuning fork A ? 4π
(4) φ
(1) 388 Hz (2) 378 Hz (3) 380 Hz (4) 390 Hz λ

E Your Target is to secure Good Rank in Pre-Medical 2026 [ 109 ]




NURTURE COURSE TARGET : PRE-MEDICAL 2026
9. Two pulses in a stretched string whose centres 12. Two sitar strings A and B playing the note 'Ga'

are initially 6 cm apart are moving towards each are slightly out of tune and produce beats of
frequency 6 Hz. The tension in the string A is
other as shown in the figure. The speed of each
slightly reduced and the beat frequency is found
pulse is 2 cm/s. After 1.5 seconds, the total
to reduce to 3 Hz. If the original frequency of A
energy of the pulses will be :-
is 324 Hz, what is the frequency of B :-
(1) 324 Hz (2) 360 Hz
(3) 330Hz (4) 318 Hz
6cm 13. If two waves of same frequency and same
amplitude respectively, on superposition,
(1) zero
produce a resultant disturbance of the same
(2) purely kinetic amplitude, the waves differ in phase by :-

®
(3) purely potential (1) π (2) 2π/3 (3) π/3 (4) 3π
14. Two waves are represented by: y1 = a sin 2000πt
(4) partly kinetic and partly potential
and y2 = a sin 2008πt. Then :
10. Frequencies of three tuning forks A, B and C (1) beat frequency is 4 Hz and the ratio of
have a relation nA > nB > nC. When the forks A maximum to individual wave intensity is
and B are sounded together, the number of beats 4:1
produced is n1. When A and C are sounded (2) beat frequency is 2 Hz and the ratio of
maximum to individual wave intensity is
together, the number of beats produced is n2.
4:1
Then the number of beats produced when B and
(3) beat frequency is 2 Hz and the ratio of
C are sounded together is :-
maximum to individual wave intensity is
n1 + n2 1:4
(1) n1 + n2 (2)
2 (4) beat frequency is 4 Hz and the ratio of
(3) n2 – n1 (4) n1 – n2 maximum to individual wave intensity is
1:4
11. Two loudspeakers L1 and L2, driven by a
15. 26 tuning forks are placed in a series such that
common oscillator and amplifier, are arranged as
each tuning fork produces 4 beats with its
shown in fig. The frequency of the oscillator is previous tuning fork. If the frequency of last
gradually increased from zero and the detector at tuning fork be three times the frequency of first
D records a series of maxima and minima. If tuning fork then frequency of first tuning fork will

speed of sound is 330 m/s, then the frequency be :-

(1) 25 (2) 50 (3) 75 (4) 76
at which the first maximum is observed is :-
16. A tuning fork is found to give five beats in three
40m
L1 D seconds when sounded in conjuction with a
stretched string vibrating transversely under a
9m
tension of either 10.2 kgf or 9.9 kgf. The
L2 frequency of the fork is approximately :-
(1) 237 Hz (2) 235 Hz
(1) 165 Hz (2) 330 Hz
(3) 210 Hz (4) 222 Hz
(3) 495 Hz (4) 660 Hz

[ 110 ] Your Target is to secure Good Rank in Pre-Medical 2026 E




TARGET : PRE-MEDICAL 2026 NURTURE COURSE
17. A thin open organ pipe and a thin closed organ
pipe are of equal lengths; the ratio of the
frequency of their third overtones will be :-
(1) 7 : 8 (2) 8 : 7
(3) 7 : 4 (4) 1 : 1

ANSWER KEY
Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans 1 2 3 3 4 1 3 2 2 3 2 4 2 1 2
Que. 16 17
Ans 4 2

E Your Target is to secure Good Rank in Pre-Medical 2026 [ 111 ]




NURTURE COURSE TARGET : PRE-MEDICAL 2026
WAVE MOTION (STATIONARY WAVES, BEATS) # 03
1. A rod of length 1.2 m is clamped at the mid 6. Equation of a standing wave is generally
point and its fundamental frequency is 2 MHz, expressed as y = 2A sin ωt coskx. In the
then find speed of wave inside the rod ? equation, quantity ω/k represents :-
(1) the transverse speed of the particles of the
string
(2) the speed of either of the component wave

6 6
(3) the speed of the standing wave
(1) 1.2 × 10 m/s (2) 2.4 × 10 m/s
(4) a quantity that is independent of the
6
(3) 3.6 × 10 m/s (4) 4.8 × 106 m/s
properties of the string.
2. A tuning fork and an air column whose 7. Two uniform strings A and B made of steel are
temperature is 51°C produce 4 beats in one made to vibrate under the same tension. If the

®
second, when sounded together. When the first overtone of A is equal to the second
temperature of air column decreases the number overtone of B and if the radius of A is twice that
of beats per second decreases. When the of B, the ratio of the lengths of the strings is :-
temperature remains 16ºC only one beat per (1) 2 : 1 (2) 3 : 4 (3) 3 : 2 (4) 1 : 3
second is produced. The frequency of the tuning 8. The wave function for a certain standing
fork is :- wave on a string fixed at both ends is
(1) 100 Hz (2) 75 Hz (3) 150 Hz (4) 50 Hz y(x,t) = 4 sin (15πx) cos 96 πt where x and y are

3. If in a stationary wave the amplitude in meters and t is in seconds. The shortest

possible length of the string is :-
corresponding to antinode is 4 cm, then the
(1) 2.3 cm (2) 6.66 cm
amplitude corresponding to a particle of medium
(3) 7.2 cm (4) 10.5 cm
located exactly midway between a node and an
9. A chord attached to a vibrating fork vibrates into
antinode is :-
6 loops, when its tension is 36 N. The tension at
(1) 2 cm (2) 2 2 cm which it will vibrate in 4 loops is :-
(3) 2 cm (4) 1.5 cm (1) 24 N (2) 36 N (3) 64 N (4) 81 N
4. What is the path difference between the 10. A 20 m long string with a linear mass density of
–1
displacement wave and pressure wave in sound 0.04 kg m and tension 16 N has both of its

wave :- ends fixed. It vibrates in a standing wave pattern

with four antinodes. Frequency of the vibration is:-
λ
(1) Zero (2) (1) 1.5 Hz (2) 2 Hz (3) 5 Hz (4) 10 Hz
4
λ 11. A wave is represented by the equation
(3) (4) λ
2 y = 10sin2π(100 t – 0.04x) +
5. A string vibrates with a frequency of 200 Hz. 10sin2π (100t+0.04x). The maximum amplitude
When its length is doubled and tension is altered, and loop length are respectively:-

it begins to vibrate with a frequency of 300 Hz. (1) 20 units and 30 units

The ratio of the new tension to the original (2) 20 units and 12.5 units
(3) 30 units and 20 units
tension is :-
(4) 25 units and 20 units
(1) 9 : 1 (2) 1 : 9 (3) 3 : 1 (4) 1 : 3

[ 112 ] Your Target is to secure Good Rank in Pre-Medical 2026 E




TARGET : PRE-MEDICAL 2026 NURTURE COURSE
12. For COP if fundamental freq. is 100 Hz then 5th 15. A sonometer wire supports a 4 kg load and
overtone is :- vibrates in fundamental mode with a tuning fork
of frequency 416 Hz. The length of the wire
(1) 1100 Hz (2) 900 Hz
between the bridges is now doubled. In order to
(3) 500 Hz (4) 600 Hz
maintain fundamental mode, the load should be
13. In a long cylindrical tube, the water level is changed to :-
adjusted and the air column above it is made to (1) 1 kg (2) 2 kg
vibrate in unison with a vibrating tuning fork kept (3) 4 kg (4) 16 kg
16. A long glass tube is held vertically in water. A
at the open end. If the wavelength of sound
tuning fork is struck and held over the tube.
produced by tuning fork is λ, then the maximum
Strong resonances are observed at two
sound is heard when the air column lengths are successive lengths 0.50 m and 0.84 m above the
equal to :- surface of water. If the velocity of sound is
λ λ 3λ λ 3λ 340 m/s, then the frequency of the tuning fork
(1) , , (2) , λ,

®
4 2 4 2 4 is:-
(1) 128 Hz (2) 256 Hz
λ 3λ 5λ λ 3λ 5λ
(3) , , (4) , , (3) 384 Hz (4) 500 Hz
2 4 2 4 4 4
14. The first resonance length of a resonance tube is
17 cm and the second resonance length is
53 cm. The third resonance length of the tube
will be :-
(1) 85 cm (2) 87 cm
(3) 88 cm (4) 89 cm

ANSWER KEY
Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans 4 4 3 2 1 2 4 2 4 2 2 1 4 4 4
Que. 16
Ans 4

E Your Target is to secure Good Rank in Pre-Medical 2026 [ 113 ]