Practice Test - Waves & Oscillations Mechanical Engineering Notes | EduRev

Created by: Anirudh Kumar Saddi

Mechanical Engineering : Practice Test - Waves & Oscillations Mechanical Engineering Notes | EduRev

 Page 1


                                   [1] 
 
 
 
(Waves & Oscillations) 
1. A particle of mass m g is executing S.H. M. about 
a point  with amplitude 10- cm. Its maximum 
velocity is 100 cms
–1
. Its velocity will be 50 cms
–1
 
at a distance  
(a) 5 cm  (b)  5 2 cm 
(c) 3 5 cm (d) 
2
10
cm 
2. A S.H.M. oscillator  has period of 0.1 sec and 
amplitude of 0.2 m. The  maximum velocity is 
given by  
(a) 100 ms
–1
 (b)  4 p ms
–1
 
(c) 100 p ms
–1
 (d) 20 p ms
–1
 
3. If a hole is drilled along the diameter of the earth 
and a stone is dropped into it. The stone 
(a) reaches  the centre of earth and stops  
(b) reaches the opposite end and stops  
(c) executes S.H.M. about the centre of earth 
(d) reaches  the opposite  side and escapes earth 
4. Total energy of the particles  executing S.H. M is 
proportional to  
(a) displacement of the particle   
(b)  frequency  of oscillation  
(c) square of the amplitude  
(d) velocity at the mean position 
5. A pendulum suspended to the celling of a train 
has  a period T when the train is at rest. If  the 
train is accelerated uniformly, the period will  
(a) Increase (b)  decrease 
(c) remain the same (d) become infinite 
6. A pendulum is first vibrated on the surface of 
earth. Its period is T. It is then taken to the surface 
of moon where acceleration due to gravity is 1/6
th
 
of that on earth. Its period will be  
(a) 
6
T
 (b)  
3
T
 
(c) 
3
T
 (d) 6 T 
7. The angular frequency  of a pendulum is ? rad s
–1
 
. If the length is made one fourth of the orginal 
length, the angular frequency becomes 
(a) 
2
?
 (b)  2 ? 
(c) 4 ? (d) ?/4 
8. A simple pendulum  has a bob which is given 
negative charge. It is then allowed to oscillate just 
above a uniformly positively charged plate, its 
period 
(a) remains the same   
(b)  decreases 
(c) increases   
(d) no vibration is possible 
9. A particle moves such that its motion is 
represented by a = kx, where ‘a’ is the acceleration 
and x is displacement and k is a constant. The 
period of oscillation is  
(a) 2 p k (b) 
k
2 p
  
(c) 
k
2 p
 (d) none of these 
10. A simple pendulum consists of a bob of radius r 
and mass m and its period is 2 sec. When its bob 
is replaced by a bob of mass 2m but same radius r, 
the time period of motion is 
(a) 4 sec  (b)  2 sec 
(c) 6 sec  (d) 8 sec 
11. A simple pendulum has a period T inside a lift 
when it is stationary. The lift is accelerated 
upwards with constant acceleration ‘a’ . The 
period 
(a) decreases   
(b)  increases 
(c) remains same  
(d) sometimes increases and sometimes 
decreases 
12. In  above question if lift is accelerated downwards 
with constant acceleration, the period 
(a) decreases   
b)  increases 
(c) remains same   
(d) none  
13. The angular velocities of three bodies in simple 
harmonic motion are ? 1
, ?
2
, ?
3
 with their 
respective amplitude as A
1
, A
2
, A
3
. If all the three 
bodies have same mass and maximum velocity, 
then : 
(a) A
2
1
?
2
1
 = A
2
2
?
2
2
 = A
2
3
?
2
3
 
(b) A
2
1
?
1
 = A
2
2
?
2
 = A
2
3
?
3
 
(c) A
1
?
2
1
 = A
2
?
2
2
 = A
3
?
2
3
 
(d) A
1
?
1
 = A
2
?
2
 = A
3
?
3
 
14. In arrangement shown in Fig., if the block of mass 
‘m’ is displaced and then released the frequency 
of oscillation  is given by :  
Page 2


                                   [1] 
 
 
 
(Waves & Oscillations) 
1. A particle of mass m g is executing S.H. M. about 
a point  with amplitude 10- cm. Its maximum 
velocity is 100 cms
–1
. Its velocity will be 50 cms
–1
 
at a distance  
(a) 5 cm  (b)  5 2 cm 
(c) 3 5 cm (d) 
2
10
cm 
2. A S.H.M. oscillator  has period of 0.1 sec and 
amplitude of 0.2 m. The  maximum velocity is 
given by  
(a) 100 ms
–1
 (b)  4 p ms
–1
 
(c) 100 p ms
–1
 (d) 20 p ms
–1
 
3. If a hole is drilled along the diameter of the earth 
and a stone is dropped into it. The stone 
(a) reaches  the centre of earth and stops  
(b) reaches the opposite end and stops  
(c) executes S.H.M. about the centre of earth 
(d) reaches  the opposite  side and escapes earth 
4. Total energy of the particles  executing S.H. M is 
proportional to  
(a) displacement of the particle   
(b)  frequency  of oscillation  
(c) square of the amplitude  
(d) velocity at the mean position 
5. A pendulum suspended to the celling of a train 
has  a period T when the train is at rest. If  the 
train is accelerated uniformly, the period will  
(a) Increase (b)  decrease 
(c) remain the same (d) become infinite 
6. A pendulum is first vibrated on the surface of 
earth. Its period is T. It is then taken to the surface 
of moon where acceleration due to gravity is 1/6
th
 
of that on earth. Its period will be  
(a) 
6
T
 (b)  
3
T
 
(c) 
3
T
 (d) 6 T 
7. The angular frequency  of a pendulum is ? rad s
–1
 
. If the length is made one fourth of the orginal 
length, the angular frequency becomes 
(a) 
2
?
 (b)  2 ? 
(c) 4 ? (d) ?/4 
8. A simple pendulum  has a bob which is given 
negative charge. It is then allowed to oscillate just 
above a uniformly positively charged plate, its 
period 
(a) remains the same   
(b)  decreases 
(c) increases   
(d) no vibration is possible 
9. A particle moves such that its motion is 
represented by a = kx, where ‘a’ is the acceleration 
and x is displacement and k is a constant. The 
period of oscillation is  
(a) 2 p k (b) 
k
2 p
  
(c) 
k
2 p
 (d) none of these 
10. A simple pendulum consists of a bob of radius r 
and mass m and its period is 2 sec. When its bob 
is replaced by a bob of mass 2m but same radius r, 
the time period of motion is 
(a) 4 sec  (b)  2 sec 
(c) 6 sec  (d) 8 sec 
11. A simple pendulum has a period T inside a lift 
when it is stationary. The lift is accelerated 
upwards with constant acceleration ‘a’ . The 
period 
(a) decreases   
(b)  increases 
(c) remains same  
(d) sometimes increases and sometimes 
decreases 
12. In  above question if lift is accelerated downwards 
with constant acceleration, the period 
(a) decreases   
b)  increases 
(c) remains same   
(d) none  
13. The angular velocities of three bodies in simple 
harmonic motion are ? 1
, ?
2
, ?
3
 with their 
respective amplitude as A
1
, A
2
, A
3
. If all the three 
bodies have same mass and maximum velocity, 
then : 
(a) A
2
1
?
2
1
 = A
2
2
?
2
2
 = A
2
3
?
2
3
 
(b) A
2
1
?
1
 = A
2
2
?
2
 = A
2
3
?
3
 
(c) A
1
?
2
1
 = A
2
?
2
2
 = A
3
?
2
3
 
(d) A
1
?
1
 = A
2
?
2
 = A
3
?
3
 
14. In arrangement shown in Fig., if the block of mass 
‘m’ is displaced and then released the frequency 
of oscillation  is given by :  
                                   [2] 
 
 
 
 
(a) v = 
m
k k
2
1
2 1
-
p
 (b) v = 
m
k k
2
1
2 1
+
p
  
(c) v = 
2 1
k k
m
2
1
- p
 (d) v = 
2 1
k k
m
2
1
+ p
 
15. A pendulum bob has a period 24 s. Its velocity 4 
sec after it has passed the mean position is 6.28 cm 
s
-
1
. The amplitude of its motion is :  
(a) 12 cm  (b) 24 cm   
(c) 48 cm  (d) 40 cm  
16. The ratio of intensities between two coherent 
sound sources is 4 : 1. The difference of loudness 
in decibels (dB) between maximum and minimum 
intensities when they interfere in space is :  
(a) 10 log (2)  (b) 20 log (3)  
(c) 10 log (3) (d) 10 log (2) 
17. A motorcyclist is moving towards a stationary car 
which is emitting a sound of 165 Hz, and a police 
car is chasing the motorcyclist blowing siren at 
frequency 172 Hz. If speed of police car is 22 m/s, 
then the speed of motorcyclist for which the 
motorcyclist hears no beats is : 
(a) 33 m/s   
(b) 22 m/s  
(c) 11 m/s  
(d) zero  
18. The vibrations of a string of length 60 cm fixed at 
both ends are represented by the equation  
 y = 4 sin ( px/15) cos (96 pt),  
where x and y are in cm and t in seconds. The  
maximum displacement at x = 5 cm is :  
(a) 2 3 cm  (b) 3 2 cm  
(c) 2 cm  (d) 3 cm  
19. In the above question, the nodes are located along 
the string at :  
(a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60  
(c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 
20. For production of beats the two sources must 
have :  
(a) different frequencies and same amplitude  
(b) different frequencies   
(c) different frequencies, same amplitude and 
same phase   
(d) different frequencies and same phase  
 
21.  The displacement versus time graph of SHM is 
given below :  
 
Which of the following is its acceleration versus 
time graph ? 
 
 
22. Velocity of sound in a gas is proportional to :  
(a) square root of isothermal elasticity   
(b) adiabatic elasticity   
(c) square root of adiabatic elasticity   
(d) isothermal elasticity  
23. Mechanical wave (sound wave) in a gas is :  
(a) transverse   
(b) longitudinal   
(c) neither transverse nor longitudinal   
(d) either transverse dependent 
24. A particle on the trough of a wave at any instant 
will come to the mean position after a time  
(T = time period) :  
(a) T/2  (b) T/4 
(c) T  (d) 2T  
25. The disc of a siren containing 60 holes rotates at a 
constant speed of 360 rpm. The emitted sound is 
in unison with a tuning fork of frequency :  
(a) 10 Hz  (b) 360 Hz  
(c) 216 Hz (d) 6 Hz 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices: 
Page 3


                                   [1] 
 
 
 
(Waves & Oscillations) 
1. A particle of mass m g is executing S.H. M. about 
a point  with amplitude 10- cm. Its maximum 
velocity is 100 cms
–1
. Its velocity will be 50 cms
–1
 
at a distance  
(a) 5 cm  (b)  5 2 cm 
(c) 3 5 cm (d) 
2
10
cm 
2. A S.H.M. oscillator  has period of 0.1 sec and 
amplitude of 0.2 m. The  maximum velocity is 
given by  
(a) 100 ms
–1
 (b)  4 p ms
–1
 
(c) 100 p ms
–1
 (d) 20 p ms
–1
 
3. If a hole is drilled along the diameter of the earth 
and a stone is dropped into it. The stone 
(a) reaches  the centre of earth and stops  
(b) reaches the opposite end and stops  
(c) executes S.H.M. about the centre of earth 
(d) reaches  the opposite  side and escapes earth 
4. Total energy of the particles  executing S.H. M is 
proportional to  
(a) displacement of the particle   
(b)  frequency  of oscillation  
(c) square of the amplitude  
(d) velocity at the mean position 
5. A pendulum suspended to the celling of a train 
has  a period T when the train is at rest. If  the 
train is accelerated uniformly, the period will  
(a) Increase (b)  decrease 
(c) remain the same (d) become infinite 
6. A pendulum is first vibrated on the surface of 
earth. Its period is T. It is then taken to the surface 
of moon where acceleration due to gravity is 1/6
th
 
of that on earth. Its period will be  
(a) 
6
T
 (b)  
3
T
 
(c) 
3
T
 (d) 6 T 
7. The angular frequency  of a pendulum is ? rad s
–1
 
. If the length is made one fourth of the orginal 
length, the angular frequency becomes 
(a) 
2
?
 (b)  2 ? 
(c) 4 ? (d) ?/4 
8. A simple pendulum  has a bob which is given 
negative charge. It is then allowed to oscillate just 
above a uniformly positively charged plate, its 
period 
(a) remains the same   
(b)  decreases 
(c) increases   
(d) no vibration is possible 
9. A particle moves such that its motion is 
represented by a = kx, where ‘a’ is the acceleration 
and x is displacement and k is a constant. The 
period of oscillation is  
(a) 2 p k (b) 
k
2 p
  
(c) 
k
2 p
 (d) none of these 
10. A simple pendulum consists of a bob of radius r 
and mass m and its period is 2 sec. When its bob 
is replaced by a bob of mass 2m but same radius r, 
the time period of motion is 
(a) 4 sec  (b)  2 sec 
(c) 6 sec  (d) 8 sec 
11. A simple pendulum has a period T inside a lift 
when it is stationary. The lift is accelerated 
upwards with constant acceleration ‘a’ . The 
period 
(a) decreases   
(b)  increases 
(c) remains same  
(d) sometimes increases and sometimes 
decreases 
12. In  above question if lift is accelerated downwards 
with constant acceleration, the period 
(a) decreases   
b)  increases 
(c) remains same   
(d) none  
13. The angular velocities of three bodies in simple 
harmonic motion are ? 1
, ?
2
, ?
3
 with their 
respective amplitude as A
1
, A
2
, A
3
. If all the three 
bodies have same mass and maximum velocity, 
then : 
(a) A
2
1
?
2
1
 = A
2
2
?
2
2
 = A
2
3
?
2
3
 
(b) A
2
1
?
1
 = A
2
2
?
2
 = A
2
3
?
3
 
(c) A
1
?
2
1
 = A
2
?
2
2
 = A
3
?
2
3
 
(d) A
1
?
1
 = A
2
?
2
 = A
3
?
3
 
14. In arrangement shown in Fig., if the block of mass 
‘m’ is displaced and then released the frequency 
of oscillation  is given by :  
                                   [2] 
 
 
 
 
(a) v = 
m
k k
2
1
2 1
-
p
 (b) v = 
m
k k
2
1
2 1
+
p
  
(c) v = 
2 1
k k
m
2
1
- p
 (d) v = 
2 1
k k
m
2
1
+ p
 
15. A pendulum bob has a period 24 s. Its velocity 4 
sec after it has passed the mean position is 6.28 cm 
s
-
1
. The amplitude of its motion is :  
(a) 12 cm  (b) 24 cm   
(c) 48 cm  (d) 40 cm  
16. The ratio of intensities between two coherent 
sound sources is 4 : 1. The difference of loudness 
in decibels (dB) between maximum and minimum 
intensities when they interfere in space is :  
(a) 10 log (2)  (b) 20 log (3)  
(c) 10 log (3) (d) 10 log (2) 
17. A motorcyclist is moving towards a stationary car 
which is emitting a sound of 165 Hz, and a police 
car is chasing the motorcyclist blowing siren at 
frequency 172 Hz. If speed of police car is 22 m/s, 
then the speed of motorcyclist for which the 
motorcyclist hears no beats is : 
(a) 33 m/s   
(b) 22 m/s  
(c) 11 m/s  
(d) zero  
18. The vibrations of a string of length 60 cm fixed at 
both ends are represented by the equation  
 y = 4 sin ( px/15) cos (96 pt),  
where x and y are in cm and t in seconds. The  
maximum displacement at x = 5 cm is :  
(a) 2 3 cm  (b) 3 2 cm  
(c) 2 cm  (d) 3 cm  
19. In the above question, the nodes are located along 
the string at :  
(a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60  
(c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 
20. For production of beats the two sources must 
have :  
(a) different frequencies and same amplitude  
(b) different frequencies   
(c) different frequencies, same amplitude and 
same phase   
(d) different frequencies and same phase  
 
21.  The displacement versus time graph of SHM is 
given below :  
 
Which of the following is its acceleration versus 
time graph ? 
 
 
22. Velocity of sound in a gas is proportional to :  
(a) square root of isothermal elasticity   
(b) adiabatic elasticity   
(c) square root of adiabatic elasticity   
(d) isothermal elasticity  
23. Mechanical wave (sound wave) in a gas is :  
(a) transverse   
(b) longitudinal   
(c) neither transverse nor longitudinal   
(d) either transverse dependent 
24. A particle on the trough of a wave at any instant 
will come to the mean position after a time  
(T = time period) :  
(a) T/2  (b) T/4 
(c) T  (d) 2T  
25. The disc of a siren containing 60 holes rotates at a 
constant speed of 360 rpm. The emitted sound is 
in unison with a tuning fork of frequency :  
(a) 10 Hz  (b) 360 Hz  
(c) 216 Hz (d) 6 Hz 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices: 
                                   [3] 
 
 
 
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: Sound travels slower on a rainy day 
than on a dry day  
 Reason: Moisture decreases the pressure 
27. Assertion: The coefficient of adiabatic elasticity is 
smaller than the coefficient of isothermal 
elasticity.  
Reason:  Heat is exchanged freely in an adiabatic 
change but not in an isothermal change. 
28. Assertion:  The amplitude of an oscillating 
pendulum decreases gradually with 
time.    
Reason:  The frequency of the pendulum 
decreases with time.    
29. Assertion:  The time period of a simple pendulum 
inside a lift falling freely is zero.   
Reason:  A body falling freely has infinite 
acceleration.  
30. Assertion:  When a spring is cut into 4 equal parts, 
the force constant becomes 4 times    
 Reason:     When two springs of spring constant 
k
1
 and k
2
 are connected in parallel, the force 
constant of combination become k
1
 + k
2
. 
 
 
 
 
Test- 05 (Waves & Oscillations)  
ANSWERS 
 
1 
C 
6 
D 
11 
A 
16 
B 
21 
B 
26 D 
2 
B 
7 
B 
12 
B 
17 
B 
22 C 27 D 
3 
C 
8 
B 
13 
D 
18 
A 
23 B 28 C 
4 
C 
9 
B 
14 
B 
19 
A 
24 B 29 D 
5 
B 
10 
B 
15 
C 
20 
C 
25 B 30 B 
 
SOLUTIONS 
1. v
max
 = r ?  ? 100 = 10. ?   ?   ? = 10 rad/s Now   v
2
 = ?
2
 (r
2
 - y
2
) ? 2500 = 100 (100 - y
2
) y
2
 = 100 - 25 = 75          
y = 5 3 cm 
2. w = 
T
2 p
 and v
max
 = r ?, v
max
 = 0.2 × 
1 . 0
2 p
= 4 p m/s 
3. A stone dropped in tunnel along the diameter of earth executes S.H.M. motion as acceleration is proportional 
to displacement from mean position is directed towards centre of earth. At depth d, g’ ?
?
?
?
?
?
-
R
d
1 , = g ?
?
?
?
?
? -
R
d R
  
4. E = 
2
1
mr
2
?
2
   ?  E ? r
2
 
5. When train accelerates, then net acceleration is a’ = 
2 2
a g +  ? a’ > g ?  T ?  
on accelerati
1
 ? Time period 
decreases 
6. 
2
1
1
2
a
a
T
T
= ? T
2
 = T  6 T
6 / g
g
= 
7. ? = 2 pv = 2 p × 
p 2
1
 
l
g
 = 
l
g
?   ?’ = 
l
g
2
l
g 4
4
l
g
= =  ?   ?’ = 2 ? 
8. Due to attractive force of electrostatic field of positive charge, time period will decreases. 
Page 4


                                   [1] 
 
 
 
(Waves & Oscillations) 
1. A particle of mass m g is executing S.H. M. about 
a point  with amplitude 10- cm. Its maximum 
velocity is 100 cms
–1
. Its velocity will be 50 cms
–1
 
at a distance  
(a) 5 cm  (b)  5 2 cm 
(c) 3 5 cm (d) 
2
10
cm 
2. A S.H.M. oscillator  has period of 0.1 sec and 
amplitude of 0.2 m. The  maximum velocity is 
given by  
(a) 100 ms
–1
 (b)  4 p ms
–1
 
(c) 100 p ms
–1
 (d) 20 p ms
–1
 
3. If a hole is drilled along the diameter of the earth 
and a stone is dropped into it. The stone 
(a) reaches  the centre of earth and stops  
(b) reaches the opposite end and stops  
(c) executes S.H.M. about the centre of earth 
(d) reaches  the opposite  side and escapes earth 
4. Total energy of the particles  executing S.H. M is 
proportional to  
(a) displacement of the particle   
(b)  frequency  of oscillation  
(c) square of the amplitude  
(d) velocity at the mean position 
5. A pendulum suspended to the celling of a train 
has  a period T when the train is at rest. If  the 
train is accelerated uniformly, the period will  
(a) Increase (b)  decrease 
(c) remain the same (d) become infinite 
6. A pendulum is first vibrated on the surface of 
earth. Its period is T. It is then taken to the surface 
of moon where acceleration due to gravity is 1/6
th
 
of that on earth. Its period will be  
(a) 
6
T
 (b)  
3
T
 
(c) 
3
T
 (d) 6 T 
7. The angular frequency  of a pendulum is ? rad s
–1
 
. If the length is made one fourth of the orginal 
length, the angular frequency becomes 
(a) 
2
?
 (b)  2 ? 
(c) 4 ? (d) ?/4 
8. A simple pendulum  has a bob which is given 
negative charge. It is then allowed to oscillate just 
above a uniformly positively charged plate, its 
period 
(a) remains the same   
(b)  decreases 
(c) increases   
(d) no vibration is possible 
9. A particle moves such that its motion is 
represented by a = kx, where ‘a’ is the acceleration 
and x is displacement and k is a constant. The 
period of oscillation is  
(a) 2 p k (b) 
k
2 p
  
(c) 
k
2 p
 (d) none of these 
10. A simple pendulum consists of a bob of radius r 
and mass m and its period is 2 sec. When its bob 
is replaced by a bob of mass 2m but same radius r, 
the time period of motion is 
(a) 4 sec  (b)  2 sec 
(c) 6 sec  (d) 8 sec 
11. A simple pendulum has a period T inside a lift 
when it is stationary. The lift is accelerated 
upwards with constant acceleration ‘a’ . The 
period 
(a) decreases   
(b)  increases 
(c) remains same  
(d) sometimes increases and sometimes 
decreases 
12. In  above question if lift is accelerated downwards 
with constant acceleration, the period 
(a) decreases   
b)  increases 
(c) remains same   
(d) none  
13. The angular velocities of three bodies in simple 
harmonic motion are ? 1
, ?
2
, ?
3
 with their 
respective amplitude as A
1
, A
2
, A
3
. If all the three 
bodies have same mass and maximum velocity, 
then : 
(a) A
2
1
?
2
1
 = A
2
2
?
2
2
 = A
2
3
?
2
3
 
(b) A
2
1
?
1
 = A
2
2
?
2
 = A
2
3
?
3
 
(c) A
1
?
2
1
 = A
2
?
2
2
 = A
3
?
2
3
 
(d) A
1
?
1
 = A
2
?
2
 = A
3
?
3
 
14. In arrangement shown in Fig., if the block of mass 
‘m’ is displaced and then released the frequency 
of oscillation  is given by :  
                                   [2] 
 
 
 
 
(a) v = 
m
k k
2
1
2 1
-
p
 (b) v = 
m
k k
2
1
2 1
+
p
  
(c) v = 
2 1
k k
m
2
1
- p
 (d) v = 
2 1
k k
m
2
1
+ p
 
15. A pendulum bob has a period 24 s. Its velocity 4 
sec after it has passed the mean position is 6.28 cm 
s
-
1
. The amplitude of its motion is :  
(a) 12 cm  (b) 24 cm   
(c) 48 cm  (d) 40 cm  
16. The ratio of intensities between two coherent 
sound sources is 4 : 1. The difference of loudness 
in decibels (dB) between maximum and minimum 
intensities when they interfere in space is :  
(a) 10 log (2)  (b) 20 log (3)  
(c) 10 log (3) (d) 10 log (2) 
17. A motorcyclist is moving towards a stationary car 
which is emitting a sound of 165 Hz, and a police 
car is chasing the motorcyclist blowing siren at 
frequency 172 Hz. If speed of police car is 22 m/s, 
then the speed of motorcyclist for which the 
motorcyclist hears no beats is : 
(a) 33 m/s   
(b) 22 m/s  
(c) 11 m/s  
(d) zero  
18. The vibrations of a string of length 60 cm fixed at 
both ends are represented by the equation  
 y = 4 sin ( px/15) cos (96 pt),  
where x and y are in cm and t in seconds. The  
maximum displacement at x = 5 cm is :  
(a) 2 3 cm  (b) 3 2 cm  
(c) 2 cm  (d) 3 cm  
19. In the above question, the nodes are located along 
the string at :  
(a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60  
(c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 
20. For production of beats the two sources must 
have :  
(a) different frequencies and same amplitude  
(b) different frequencies   
(c) different frequencies, same amplitude and 
same phase   
(d) different frequencies and same phase  
 
21.  The displacement versus time graph of SHM is 
given below :  
 
Which of the following is its acceleration versus 
time graph ? 
 
 
22. Velocity of sound in a gas is proportional to :  
(a) square root of isothermal elasticity   
(b) adiabatic elasticity   
(c) square root of adiabatic elasticity   
(d) isothermal elasticity  
23. Mechanical wave (sound wave) in a gas is :  
(a) transverse   
(b) longitudinal   
(c) neither transverse nor longitudinal   
(d) either transverse dependent 
24. A particle on the trough of a wave at any instant 
will come to the mean position after a time  
(T = time period) :  
(a) T/2  (b) T/4 
(c) T  (d) 2T  
25. The disc of a siren containing 60 holes rotates at a 
constant speed of 360 rpm. The emitted sound is 
in unison with a tuning fork of frequency :  
(a) 10 Hz  (b) 360 Hz  
(c) 216 Hz (d) 6 Hz 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices: 
                                   [3] 
 
 
 
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: Sound travels slower on a rainy day 
than on a dry day  
 Reason: Moisture decreases the pressure 
27. Assertion: The coefficient of adiabatic elasticity is 
smaller than the coefficient of isothermal 
elasticity.  
Reason:  Heat is exchanged freely in an adiabatic 
change but not in an isothermal change. 
28. Assertion:  The amplitude of an oscillating 
pendulum decreases gradually with 
time.    
Reason:  The frequency of the pendulum 
decreases with time.    
29. Assertion:  The time period of a simple pendulum 
inside a lift falling freely is zero.   
Reason:  A body falling freely has infinite 
acceleration.  
30. Assertion:  When a spring is cut into 4 equal parts, 
the force constant becomes 4 times    
 Reason:     When two springs of spring constant 
k
1
 and k
2
 are connected in parallel, the force 
constant of combination become k
1
 + k
2
. 
 
 
 
 
Test- 05 (Waves & Oscillations)  
ANSWERS 
 
1 
C 
6 
D 
11 
A 
16 
B 
21 
B 
26 D 
2 
B 
7 
B 
12 
B 
17 
B 
22 C 27 D 
3 
C 
8 
B 
13 
D 
18 
A 
23 B 28 C 
4 
C 
9 
B 
14 
B 
19 
A 
24 B 29 D 
5 
B 
10 
B 
15 
C 
20 
C 
25 B 30 B 
 
SOLUTIONS 
1. v
max
 = r ?  ? 100 = 10. ?   ?   ? = 10 rad/s Now   v
2
 = ?
2
 (r
2
 - y
2
) ? 2500 = 100 (100 - y
2
) y
2
 = 100 - 25 = 75          
y = 5 3 cm 
2. w = 
T
2 p
 and v
max
 = r ?, v
max
 = 0.2 × 
1 . 0
2 p
= 4 p m/s 
3. A stone dropped in tunnel along the diameter of earth executes S.H.M. motion as acceleration is proportional 
to displacement from mean position is directed towards centre of earth. At depth d, g’ ?
?
?
?
?
?
-
R
d
1 , = g ?
?
?
?
?
? -
R
d R
  
4. E = 
2
1
mr
2
?
2
   ?  E ? r
2
 
5. When train accelerates, then net acceleration is a’ = 
2 2
a g +  ? a’ > g ?  T ?  
on accelerati
1
 ? Time period 
decreases 
6. 
2
1
1
2
a
a
T
T
= ? T
2
 = T  6 T
6 / g
g
= 
7. ? = 2 pv = 2 p × 
p 2
1
 
l
g
 = 
l
g
?   ?’ = 
l
g
2
l
g 4
4
l
g
= =  ?   ?’ = 2 ? 
8. Due to attractive force of electrostatic field of positive charge, time period will decreases. 
                                   [4] 
 
 
 
9. Time period of S.H.M. is T = 2 p 
on accelerati
nt displaceme
?   T = 2 p
kx
x
      ?   T = 
k
2 p
 
10. Time period is independent of mass of bob so long as length remains constant. 
11. When the lift ascends with acceleration a then apparent value of acceleration due to gravity becomes (g + a) As 
T = 2 p 
g
?
. So the time period decreases. 
12. During downward motion apparent value of g becomes (g - a). As T ? 
g
1
? Time period increases 
13. The general equation for a body executing simple harmonic motion is given by :  y = A sin ?t.  Velocity is 
given by : ? = 
dt
d
dt
dy
= (A sin ?t)  = A ? cos ?t.  For maximum velocity, we put cos ?t = 1 
         Hence, ?
max.
 = A ?   Now, since the velocities of three bodies are same, therefore we have : ?
1
 = ?
2
 = ?
3
 
         A
1
?
1
 = A
2
?
2
 = A
2
?
3
 
14. In this case springs are in parallel.  ? k
p
 = k
1
 + k
2
 ? T = 2 p 
2 1
k k
m
+
 = ? = 
m
k k
2
1
2 1
+
p
 
15. Use v = r ? cos ?t,  6.28 = r ?
?
?
?
?
? p p
4 .
24
2
cos .
24
2
?   r = 48 cm 
16. 
1
4
I
I
2
1
= or  
2
1
l
l
= 
1
2
 ?  
2
2 1
2 1
min
max
1 I / I
1 I / I
I
I
?
?
?
?
?
?
?
?
-
+
= = 9
1 2
1 2
2
=
?
?
?
?
?
?
-
+
?L
1
 - L
2
 = 10 log 
0
min
0
max
I
I
log 10
I
I
- = 10 log 
min
max
I
I
 = 
10 log (9) = 20 log (3) 
17. Frequency recorded by motorcyclist from police car N”
motor
 = 
p
p
m
n
v c
v c
×
-
-
. Frequency recorded by 
motorcyclist from stationary car = 
c
m
n
v c
c
×
-
 For no beats 
c
m
p
p
m
n
v c
c
n
v c
v c
×
-
= ×
-
-
. Putting the given values, 
v
m
 = 22 m/s 
18. For x = 5,      y = 4 sin ?
?
?
?
?
? p
15
5
 cos (96 pt) = 2 3 cos (96 pt). So, y will be maximum when cos (96 pt) = max. = 1 
Y
max.
 = 2 3 cm   at   x = 5. 
19. At node amplitude of the wave is zero So 4 sin ( px/15) = 0 ? x = 0, 15, 30, 45, 60 
20. For the production of beats the two sources must have different frequencies, same amplitude and same phase. 
It should be remembered that different amplitude affect the maximum and minimum amplitude of beats and 
different phase affect the time of occurrence of minimum and maximum 
21. (b) Note that of y = A sin ?t    Then a = - ?
2
 A sin ?t    That a the y differ in phase by p 
Which is the case with option B 
22. (c) 
23. (b) 
24. The particle will come after a time T/4 to its mean position. 
25. Frequency = 60
60
360
× = 360 Hz. 
26. (d) The velocity of sound ? = .
P
?
?
 The presence of moisture in air on a rainy day decreases the density of air 
since ? ? 
?
1
, the velocity of sound increases. 
27. (d) The bulk’s modulus for adiabatic process is more than the bulk’s modulus for an isothermal process. 
I:\anmol\Anajana - Chemistry\Waves & Oscillations MCQ.doc 
Page 5


                                   [1] 
 
 
 
(Waves & Oscillations) 
1. A particle of mass m g is executing S.H. M. about 
a point  with amplitude 10- cm. Its maximum 
velocity is 100 cms
–1
. Its velocity will be 50 cms
–1
 
at a distance  
(a) 5 cm  (b)  5 2 cm 
(c) 3 5 cm (d) 
2
10
cm 
2. A S.H.M. oscillator  has period of 0.1 sec and 
amplitude of 0.2 m. The  maximum velocity is 
given by  
(a) 100 ms
–1
 (b)  4 p ms
–1
 
(c) 100 p ms
–1
 (d) 20 p ms
–1
 
3. If a hole is drilled along the diameter of the earth 
and a stone is dropped into it. The stone 
(a) reaches  the centre of earth and stops  
(b) reaches the opposite end and stops  
(c) executes S.H.M. about the centre of earth 
(d) reaches  the opposite  side and escapes earth 
4. Total energy of the particles  executing S.H. M is 
proportional to  
(a) displacement of the particle   
(b)  frequency  of oscillation  
(c) square of the amplitude  
(d) velocity at the mean position 
5. A pendulum suspended to the celling of a train 
has  a period T when the train is at rest. If  the 
train is accelerated uniformly, the period will  
(a) Increase (b)  decrease 
(c) remain the same (d) become infinite 
6. A pendulum is first vibrated on the surface of 
earth. Its period is T. It is then taken to the surface 
of moon where acceleration due to gravity is 1/6
th
 
of that on earth. Its period will be  
(a) 
6
T
 (b)  
3
T
 
(c) 
3
T
 (d) 6 T 
7. The angular frequency  of a pendulum is ? rad s
–1
 
. If the length is made one fourth of the orginal 
length, the angular frequency becomes 
(a) 
2
?
 (b)  2 ? 
(c) 4 ? (d) ?/4 
8. A simple pendulum  has a bob which is given 
negative charge. It is then allowed to oscillate just 
above a uniformly positively charged plate, its 
period 
(a) remains the same   
(b)  decreases 
(c) increases   
(d) no vibration is possible 
9. A particle moves such that its motion is 
represented by a = kx, where ‘a’ is the acceleration 
and x is displacement and k is a constant. The 
period of oscillation is  
(a) 2 p k (b) 
k
2 p
  
(c) 
k
2 p
 (d) none of these 
10. A simple pendulum consists of a bob of radius r 
and mass m and its period is 2 sec. When its bob 
is replaced by a bob of mass 2m but same radius r, 
the time period of motion is 
(a) 4 sec  (b)  2 sec 
(c) 6 sec  (d) 8 sec 
11. A simple pendulum has a period T inside a lift 
when it is stationary. The lift is accelerated 
upwards with constant acceleration ‘a’ . The 
period 
(a) decreases   
(b)  increases 
(c) remains same  
(d) sometimes increases and sometimes 
decreases 
12. In  above question if lift is accelerated downwards 
with constant acceleration, the period 
(a) decreases   
b)  increases 
(c) remains same   
(d) none  
13. The angular velocities of three bodies in simple 
harmonic motion are ? 1
, ?
2
, ?
3
 with their 
respective amplitude as A
1
, A
2
, A
3
. If all the three 
bodies have same mass and maximum velocity, 
then : 
(a) A
2
1
?
2
1
 = A
2
2
?
2
2
 = A
2
3
?
2
3
 
(b) A
2
1
?
1
 = A
2
2
?
2
 = A
2
3
?
3
 
(c) A
1
?
2
1
 = A
2
?
2
2
 = A
3
?
2
3
 
(d) A
1
?
1
 = A
2
?
2
 = A
3
?
3
 
14. In arrangement shown in Fig., if the block of mass 
‘m’ is displaced and then released the frequency 
of oscillation  is given by :  
                                   [2] 
 
 
 
 
(a) v = 
m
k k
2
1
2 1
-
p
 (b) v = 
m
k k
2
1
2 1
+
p
  
(c) v = 
2 1
k k
m
2
1
- p
 (d) v = 
2 1
k k
m
2
1
+ p
 
15. A pendulum bob has a period 24 s. Its velocity 4 
sec after it has passed the mean position is 6.28 cm 
s
-
1
. The amplitude of its motion is :  
(a) 12 cm  (b) 24 cm   
(c) 48 cm  (d) 40 cm  
16. The ratio of intensities between two coherent 
sound sources is 4 : 1. The difference of loudness 
in decibels (dB) between maximum and minimum 
intensities when they interfere in space is :  
(a) 10 log (2)  (b) 20 log (3)  
(c) 10 log (3) (d) 10 log (2) 
17. A motorcyclist is moving towards a stationary car 
which is emitting a sound of 165 Hz, and a police 
car is chasing the motorcyclist blowing siren at 
frequency 172 Hz. If speed of police car is 22 m/s, 
then the speed of motorcyclist for which the 
motorcyclist hears no beats is : 
(a) 33 m/s   
(b) 22 m/s  
(c) 11 m/s  
(d) zero  
18. The vibrations of a string of length 60 cm fixed at 
both ends are represented by the equation  
 y = 4 sin ( px/15) cos (96 pt),  
where x and y are in cm and t in seconds. The  
maximum displacement at x = 5 cm is :  
(a) 2 3 cm  (b) 3 2 cm  
(c) 2 cm  (d) 3 cm  
19. In the above question, the nodes are located along 
the string at :  
(a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60  
(c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 
20. For production of beats the two sources must 
have :  
(a) different frequencies and same amplitude  
(b) different frequencies   
(c) different frequencies, same amplitude and 
same phase   
(d) different frequencies and same phase  
 
21.  The displacement versus time graph of SHM is 
given below :  
 
Which of the following is its acceleration versus 
time graph ? 
 
 
22. Velocity of sound in a gas is proportional to :  
(a) square root of isothermal elasticity   
(b) adiabatic elasticity   
(c) square root of adiabatic elasticity   
(d) isothermal elasticity  
23. Mechanical wave (sound wave) in a gas is :  
(a) transverse   
(b) longitudinal   
(c) neither transverse nor longitudinal   
(d) either transverse dependent 
24. A particle on the trough of a wave at any instant 
will come to the mean position after a time  
(T = time period) :  
(a) T/2  (b) T/4 
(c) T  (d) 2T  
25. The disc of a siren containing 60 holes rotates at a 
constant speed of 360 rpm. The emitted sound is 
in unison with a tuning fork of frequency :  
(a) 10 Hz  (b) 360 Hz  
(c) 216 Hz (d) 6 Hz 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices: 
                                   [3] 
 
 
 
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: Sound travels slower on a rainy day 
than on a dry day  
 Reason: Moisture decreases the pressure 
27. Assertion: The coefficient of adiabatic elasticity is 
smaller than the coefficient of isothermal 
elasticity.  
Reason:  Heat is exchanged freely in an adiabatic 
change but not in an isothermal change. 
28. Assertion:  The amplitude of an oscillating 
pendulum decreases gradually with 
time.    
Reason:  The frequency of the pendulum 
decreases with time.    
29. Assertion:  The time period of a simple pendulum 
inside a lift falling freely is zero.   
Reason:  A body falling freely has infinite 
acceleration.  
30. Assertion:  When a spring is cut into 4 equal parts, 
the force constant becomes 4 times    
 Reason:     When two springs of spring constant 
k
1
 and k
2
 are connected in parallel, the force 
constant of combination become k
1
 + k
2
. 
 
 
 
 
Test- 05 (Waves & Oscillations)  
ANSWERS 
 
1 
C 
6 
D 
11 
A 
16 
B 
21 
B 
26 D 
2 
B 
7 
B 
12 
B 
17 
B 
22 C 27 D 
3 
C 
8 
B 
13 
D 
18 
A 
23 B 28 C 
4 
C 
9 
B 
14 
B 
19 
A 
24 B 29 D 
5 
B 
10 
B 
15 
C 
20 
C 
25 B 30 B 
 
SOLUTIONS 
1. v
max
 = r ?  ? 100 = 10. ?   ?   ? = 10 rad/s Now   v
2
 = ?
2
 (r
2
 - y
2
) ? 2500 = 100 (100 - y
2
) y
2
 = 100 - 25 = 75          
y = 5 3 cm 
2. w = 
T
2 p
 and v
max
 = r ?, v
max
 = 0.2 × 
1 . 0
2 p
= 4 p m/s 
3. A stone dropped in tunnel along the diameter of earth executes S.H.M. motion as acceleration is proportional 
to displacement from mean position is directed towards centre of earth. At depth d, g’ ?
?
?
?
?
?
-
R
d
1 , = g ?
?
?
?
?
? -
R
d R
  
4. E = 
2
1
mr
2
?
2
   ?  E ? r
2
 
5. When train accelerates, then net acceleration is a’ = 
2 2
a g +  ? a’ > g ?  T ?  
on accelerati
1
 ? Time period 
decreases 
6. 
2
1
1
2
a
a
T
T
= ? T
2
 = T  6 T
6 / g
g
= 
7. ? = 2 pv = 2 p × 
p 2
1
 
l
g
 = 
l
g
?   ?’ = 
l
g
2
l
g 4
4
l
g
= =  ?   ?’ = 2 ? 
8. Due to attractive force of electrostatic field of positive charge, time period will decreases. 
                                   [4] 
 
 
 
9. Time period of S.H.M. is T = 2 p 
on accelerati
nt displaceme
?   T = 2 p
kx
x
      ?   T = 
k
2 p
 
10. Time period is independent of mass of bob so long as length remains constant. 
11. When the lift ascends with acceleration a then apparent value of acceleration due to gravity becomes (g + a) As 
T = 2 p 
g
?
. So the time period decreases. 
12. During downward motion apparent value of g becomes (g - a). As T ? 
g
1
? Time period increases 
13. The general equation for a body executing simple harmonic motion is given by :  y = A sin ?t.  Velocity is 
given by : ? = 
dt
d
dt
dy
= (A sin ?t)  = A ? cos ?t.  For maximum velocity, we put cos ?t = 1 
         Hence, ?
max.
 = A ?   Now, since the velocities of three bodies are same, therefore we have : ?
1
 = ?
2
 = ?
3
 
         A
1
?
1
 = A
2
?
2
 = A
2
?
3
 
14. In this case springs are in parallel.  ? k
p
 = k
1
 + k
2
 ? T = 2 p 
2 1
k k
m
+
 = ? = 
m
k k
2
1
2 1
+
p
 
15. Use v = r ? cos ?t,  6.28 = r ?
?
?
?
?
? p p
4 .
24
2
cos .
24
2
?   r = 48 cm 
16. 
1
4
I
I
2
1
= or  
2
1
l
l
= 
1
2
 ?  
2
2 1
2 1
min
max
1 I / I
1 I / I
I
I
?
?
?
?
?
?
?
?
-
+
= = 9
1 2
1 2
2
=
?
?
?
?
?
?
-
+
?L
1
 - L
2
 = 10 log 
0
min
0
max
I
I
log 10
I
I
- = 10 log 
min
max
I
I
 = 
10 log (9) = 20 log (3) 
17. Frequency recorded by motorcyclist from police car N”
motor
 = 
p
p
m
n
v c
v c
×
-
-
. Frequency recorded by 
motorcyclist from stationary car = 
c
m
n
v c
c
×
-
 For no beats 
c
m
p
p
m
n
v c
c
n
v c
v c
×
-
= ×
-
-
. Putting the given values, 
v
m
 = 22 m/s 
18. For x = 5,      y = 4 sin ?
?
?
?
?
? p
15
5
 cos (96 pt) = 2 3 cos (96 pt). So, y will be maximum when cos (96 pt) = max. = 1 
Y
max.
 = 2 3 cm   at   x = 5. 
19. At node amplitude of the wave is zero So 4 sin ( px/15) = 0 ? x = 0, 15, 30, 45, 60 
20. For the production of beats the two sources must have different frequencies, same amplitude and same phase. 
It should be remembered that different amplitude affect the maximum and minimum amplitude of beats and 
different phase affect the time of occurrence of minimum and maximum 
21. (b) Note that of y = A sin ?t    Then a = - ?
2
 A sin ?t    That a the y differ in phase by p 
Which is the case with option B 
22. (c) 
23. (b) 
24. The particle will come after a time T/4 to its mean position. 
25. Frequency = 60
60
360
× = 360 Hz. 
26. (d) The velocity of sound ? = .
P
?
?
 The presence of moisture in air on a rainy day decreases the density of air 
since ? ? 
?
1
, the velocity of sound increases. 
27. (d) The bulk’s modulus for adiabatic process is more than the bulk’s modulus for an isothermal process. 
I:\anmol\Anajana - Chemistry\Waves & Oscillations MCQ.doc 
                                   [5] 
 
 
 
 K
a
 = ? K
i
 where ? = 1
C
C
v
p
> 
Hence K
a
 > K
i
 Heat is exchanged freely in isothermal process whereas in adiabatic process the heat remain 
constant. 
28. (c) Frequency, in case of simple pendulum, is given by ? = 
l
g
2
1
p
. The above expression shows that 
frequency is independent of amplitude. So, even if frequency remains same, amplitude constantly decreases 
due to friction of air and other factors. So, assertion and reason are not related to each other.  
29. (d) Time period of simple pendulum is given by T = 2 p
g
l
 when the lift is falling freely, then g = 0. 
Therefore T = 8     
30. (b) If K be the force constant of each of the part of spring when spring is cut into four parties, the 
K
1
K
1
K
1
K
1
k
1
+ + + =  or 
K
1
= 
K
4
 or K = 4k. Where k is the force constant of the spring initially.  
 
I:\anmol\Anajana - Chemistry\Waves & Oscillations MCQ.doc 
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