Jee 2014 Booklet5 Hwt Shm and Waves

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [1]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

6.

A particle executing a simple harmonic motion has a period of 6 s. The time taken by the particle to move from the mean position of half the amplitude, starting from the mean position is : (A) 1/4s (B) 3/4s (C) 1/2s (D) 3/2s The amplitude of a particle executing SHM is 4 cm. At the mean position of the speed of the particle is

7.

16 cms 1 . The distance of the particle from the mean position at which the speed of the particle become

3.

5.

(B) (D)

3 cm 2 cm

8.

If a simple pendulum of length L has maximum angular displacement  , then the maximum kinetic energy of bob of mass M is: Mg 1 ML (A) (B) 2L 2 g (C)

4.

2 3cm 1 cm

MgL 1  cos 

(D)

MgL sin 2

Consider the following statements : The total energy of a particle executing simple harmonic motion depends on its I. amplitude II. period III. displacement (A) I and II are correct (B) II and III are correct (C) I and III are correct (D) I, II & III are correct A simple harmonic wave having an amplitude A and time period T is represented by the equation y  5 sin   t  4  m . Then the value of A in (metre) and T in (second) are : (A) A = 10, T = 2 (C) A = 10, T = 1

VMC/SHM & Wave Motion

(B) (D)

(A)

 p   

(C)

p 

2

(B)

 p   

(D)

p 

2/3

The equation of a simple harmonic progressive wave is given by y  A sin 100 t  3 x  . Find the distance between 2 particles having a phase difference of /3. (A) /9 m (B) /18 m (C) /6 m (D) /3 m

8 3 cms 1 , will be: (A) (C)

The speed of sound in gas of density  at a pressure p is proportional to :

The period of a wave is 360ms 1 and frequency is 500 Hz. Phase difference between two consecutive particles is 60 , then path difference between them will be : (A) 0.72 cm (B) 120 cm (C) 12 cm (D) 7.2 cm

9.

Two tuning forks, A produce note of frequencies 258 Hz and 262 Hz. An unknown note sounded with a produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is : (A) 256 Hz (B) 254 Hz (C) 300 Hz (D) 280 Hz

10.

A vibrating string of certain length l under a tension T resonates with a mode corresponding to the second overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats/s when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be

340ms 1 , the frequency n of the tuning fork in Hz is : (A) 344 (B) 336 (C) 117.3 (D) 109.3

A = 5, T = 1 A = 5, T = 2

103

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [2]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

1/ 2

The displacement of a particle in SHM varies according to the relation x = 4  cos  t  sin  t  . The amplitude of the particle is: (A) 4

(B)

4

(C)

(D)

8

4 2

(C) 6.

maximum acceleration equal to 24ms 2 and maximum

3.

4.

(D)

M Mm

Two Cu wires of radii R1 and R2 such that  R1  R2  . Then which of the following is true? (A) Transverse wave travels faster in thicker wire (B) Transverse wave travels faster in thinner wire (C) Travels with the same speed in both the wires (D) Does not travel

A body executing simple harmonic motion has a velocity of 16ms 1 , the amplitude harmonic motion is : 1024 (A) (B) m 9 64 (C) (D) m 9

M  m    M 

of the simple

7.

A wave equation is given by   t x 1  y  4 sin       where x in cm and t is in   5 9 6  second. Which of the following is true?

32 m 3 3 m 32

2 A particle performing SHM has time period and 3 path length 4 cm. The displacement from mean position at which magnitude acceleration is equal to magnitude of velocity is: (A) zero (B) 0.5 cm (C) 1 cm (D) 1.5 cm

8.

(A)

  18cm

(B)

v  4ms 1

(C)

a  0.4 cm

(D)

f  50 Hz

The equation of a transverse wave travelling along positive x-axis with amplitude 0.2m, velocity 360ms 1 and wavelength 60m be written as : (A)

For a particle executing SHM the displacement x is given x  A cos ωt . Identify the graph which represents the

x   y  0.2 sin  6t   60  

(B)

variation of potential energy (PE) as a function of time t and displacement x.

x   y  0.2 sin  6t   60  

(C)

x   y  0.2 sin 2 6t  60  

x   y  0.2 sin 2 6t  60   Two strings A and B are slightly out tune and produces beats of frequency 5 Hz. Increasing the tension in B reduces the beat frequency to 3 Hz. If the frequency of string A is 450 Hz, calculate the frequency of string B. (A) 460 Hz (B) 455 Hz\ (C) 445 Hz (D) 440 Hz A string vibrates with a frequency of 200 Hz. When its length is doubled and tension in altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is : (A) 9:1 (B) 1:9 \ (C) 3:1 (D) 1:3

(D) 9. (A) (C) 5.

I, III II, III

(B) (D)

II, IV I, IV

A mass M, attached to a horizontal spring, executes SHM with amplitude A1. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2. The  A  ratio of  1  is :  A2  (A)

M m M

VMC/SHM & Wave Motion

10.

1/ 2

(B)

 M    M  m

103

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [3]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Two simple harmonic motions are represented by y1  5  sin 2 t  3 cos 2 t   

  y2  5 sin  2 t   4  The ratio of their amplitudes is : (A) 1:1 (B)

6.

and

(C) 2.

1:3

2:1

3 1

(D)

7.

A particle executing simple harmonic motion along yaxis has the its motion described by the equation

y  A sin  ωt   B . The amplitude of the simple

3.

4.

harmonic motion is : (A) A

(B)

(C)

(D)

A+B

B

A B

0.10ms 1

(B)

0.15ms 1

(C)

0.8ms 1

(D)

0.26ms 1

The amplitude of two waves are in ratio 5 : 2. If all other conditions for the two waves are same, then what is the ratio of their energy densities? (A) 5:2 (B) 5:4 (C) 4:5 (D) 25 : 4

9.

Two sounding bodies producing progressive waves are given by

A wooden cube (density of wood d) of side l float in a liquid of density  with its upper and lower surfaces

y1  4 sin 400 t and y2  3 sin 404 t One situated very near to ears of a person who will hear (A) 2 beats/s with intensity ratio 4/3 between maxima and minima (B) 2 beats/s with intensity ratio 49/1 between maxima and minima (C) 4 beats/s with intensity ratio 7/2 between maxima and minima (D) 4 beats/s with intensity ratio 4/3 between maxima and minima

horizontal. If the cube is pushed slightly down and released, its performs simple harmonics motion of period T, then T is equal :

5.

(A)

2

(C)

2

l

  d  g l dg

(B)

2

ld g

(D)

2

ld    dg

The period of oscillation of a simple pendulum of length l suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination  is given by: (A)

2

1 g cos 

(B)

2

1 g sin 

(C)

2

l g

(D)

2

1 g tan 

VMC/SHM & Wave Motion

x t y  3 sin    represents an equation of a 2 4 progressive wave, where t is in second and x is in meter. The distance travelled by the wave in 5 s is : (A) 8m (B) 10 m (C) 5m (D) 32 m

8.

If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 s, then its maximum velocity is: (A)

A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distances of 2m and 3m respectively from the source. The ratio of the intensities of the waves at P and Q is: (A) 9:4 (B) 2:3 (C) 3:2 (D) 4:9

10.

103

A hollow cylinder with both sides open generates a frequency v in air. When the cylinder vertically immersed into water by half its length the frequency will be : (A) v (B) 2v (C) v/2 (D) v/4

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [4]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle is executing SHM with amplitude a. When the PE of a particle is one-fourth of its maximum value during the oscillation, its displacement from the equilibrium position will be : (A) a/4 (B) a/3 (C) a/2 (D) 2a/3

6.

The frequency and velocity of sound wave are 600 Hz and 360 m/s respectively. Phase difference between two particles of the medium are 60 , the minimum distance between these two particles will be : (A) 10 cm (B) 15 cm (C) 20 cm (D) 50 cm

2.

The SHM of a particle is given

7.

When a wave travels in a medium, the particle displacement is given by the equation y  a sin 2  bt  cx  where a, b and c are constants.

  x  t   5 cos  2 t   in MKS units 4 

The maximum particle velocity will be twice the wave velocity if : 1 (A) (B) c c  a a

Calculate the displacement and the magnitude of acceleration of the particle at t =1.5s:

(A)

3.0 m 100 m/s 2

(B)

 2.54 200 m/s 2

(C)

3.55m 120 m/s 2 (D)

 3.55m 120 m/s 2

3.

Ratio of kinetic energy at mean position to potential energy at A/2 of a particle performing SHM: (A) 2:1 (B) 4:1 (C) 8:1 (D) 1:1

4.

A particle of mass m is located in a one dimensional potential field where potential energy is given by

(C) 8.

9.

period of small oscillations of the particle is :

5.

(A)

2

m AP

(C)

2

m A

(B)

2

(D)

1 2

b

1 ac

20%

(D)

36%

Two tuning forks P and Q when set vibrating given 4 beats/s. If a prong of the fork P is filed the beats are reduced to 2s 1 . What is frequency of P, if that of Q is 250 Hz? (A) 246 Hz (B) 250 Hz (C) 254 Hz (D) 252 Hz

m Ap 2 AP m

10.

The graph between the time period and the length of a simple pendulum is : (A) straight line (B) curve (C) ellipse (D) parabola

VMC/SHM & Wave Motion

(D)

The intensity of sound gets reduced by 10% on passing through a slab. The reduction in intensity on passing through three consecutive slabs is: (A) (B) 30% 27.1% (C)

V  x   A 1  cos px  , where A and p are constants. The

b  ac

If L1 and L2 are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is :

103

(A)

2  L2  L1 

(B)

2  L2  L1 

(C)

L   2  L2  1  2  

(D)

L   2  L2  1  2  

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [5]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time? aT aT (A) (B) (C) (D) a 2T 2  4 2v 2 aT  2 v x v For a particle in SHM, if the amplitude of the displacement is a and the amplitude of velocity is v’ the amplitude of acceleration is: (A)

va

(B)

v2 a

(C)

v2 2a

(D)

v a

3.

A body is vibrating in simple harmonic motion. If its acceleration is 12cms 2 at a displacement 3cm, then time period is: (A) 6.28s (B) 3.14s (C) 1.57s (D) 2.57 s

4.

The displacement of an object attached to a spring and executing simple harmonic motion is given by x  2  102 cos  t metre. The time at which the maximum speed first occurs is : (A) 0.5 s (B) 0.75 s

(C)

0.125 s

(D)

0.25 s

5.

A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should the lift be accelerated upwards in order to reduce its period to T/2? (g is acceleration due to gravity) (A) 2g (B) 3g (C) 4g (D) g

6.

The angle between particle velocity and wave velocity in a transverse wave is: (A) zero (B) (C) /4 /2

7.

(D)



A transverse sinusoidal wave moves along a string in positive x – direction at a speed of 10 cms 1 . The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-short of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is :

3  1 3  3  1 3  1 (B) (C) (D) j ms  j ms 1 i ms  i ms 50 50 50 50 When a sound wave of frequency 300 Hz through a medium, the maximum displacement of a particle of the medium is 0.1 cm. The maximum velocity of the particle is equal to : (A) 60 cm/s (B) 30 cm/s (C) (D) 30 cm / s 60  cm / s (A)

8.

9.

When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats/s are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats/s are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2? (A) 200 Hz (B) 202 Hz (C) 196 Hz (D) 204 Hz

10.

An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is : (A)

200s 1

VMC/SHM & Wave Motion

(B)

100s 1

(C)

103

300s 1

(D)

250s 1

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [6]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Two particles A and B execute simple harmonic motion of period T and 5T/4. They start form mean position. The phase difference between them when the particle A complete an oscillation will be : (A) (B) zero (C) (D) /2 2 / 5 /4

2.

The average acceleration of a particle performing SHM over one complete oscillation is : (A)

ω2 A 2

(B)

ω2 A 2

(C)

zero

(D)

Aω2

3.

Two simple harmonic motions of angular frequency 100 and 1000 rad/s have the same displacement amplitude. The ratio of their maximum acceleration is: (A) 1 : 10 (B) 1 : 102 (C) 1 : 10 (D) 1 : 104

4.

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration. Then time period in second is : (A)

5.

6.

1 2 3

(B)

2 3

(C)

2 3

(D)

Two springs, of force constants k1 and k2, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes. (A) f/2 (B) f/4 (C) 4f (D)

3 2

2f

5  The ratio of the velocity of sound in hydrogen    7 / 5  to that in helium     at the same temperature is : 3 

42 5 5 21 (B) (C) (D) 5 42 21 5 When a sound wave of wavelength  is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of wave is : (A)

7.

(A) 8.



(B)

 2

(C)

 2

(D)

 4

The equation of a wave is given as y  0.007 sin 12 x  3000 t  Where x is in meter and t in second, then the correct statement is :

9.

10.

(A)

 1 / 6m v  250ms 1

(B)

a  0.07 m v  300ms 1

(C)

n  1500 v  200 ms 1

(D)

None of these

A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one*ninth the tension. Then the fundamental frequency will became. (A) 400 Hz (B) 600 Hz (C) 300 Hz (D) 200 Hz A string fixed at both ends oscillates in 5 segments, length 10 m and velocity of wave is 20ms 1 . What is the frequency? (A) 5Hz (B) 15 Hz (C) 10 Hz (D) 2 Hz

VMC/SHM & Wave Motion

103

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [7]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

6.

A particle executes simple harmonic motion with a time period of 16 s. At time t = 2s, the particle crosses the

modulus of elasticity of water is 2  109 Nm2 and mean

mean position while at t = 4 s, velocity is 4 ms 1 . The

temperature is 4C , the depth of the sea will be : (A) 1014 m (B) 1414 m (C) 2828 m (D) None of these

amplitude of motion in metre is : (A)

2

(B)

16 2

4 32 2 (D)   A particle of mass m is executing oscillations about the origin on the x-axis with amplitude A. Its potential (C)

2.

7.

energy ( U  x   ax 4 where a is positive constant. The xcoordinate of mass where potential energy is one-third of the kinetic energy of particle is :

8.

A A (B) 3 2 A A (C) (D) 3 2 A point mass oscillates along the axis according to the law x  x0 cos  ωt   / 4  . If the acceleration of the

A  x0      / 4 (B)

(C)

A  x0 2      / 4

(D) 4.

(B) (C) (D)

A  x0 2     / 4

9.

x   A and x   A . The time taken for it to go from

5.

T1  2T2

A spring (spring constant = k) is cut into 4 equal parts and two parts are connected in parallel. What is the effective spring constant? (A) 4K (B) 16 k (C) 8k (D) 6k

VMC/SHM & Wave Motion

A standing wave having nodes at

A wave travelling along +x direction A wave travelling along  x direction A standing wave having nodes at

n  n  0 1 2 2 A hollow pipe of length 0.8m is closed a one end. At its open end a 0.5m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. It the tension in the wire is 50 N and the speed of sound is 320ms 1 , the mass of the string is : (A) 5g (B) 10 g (C) 20g (D) 40g

0 to A/2 is T1 and to go from A/2 to A is T2. Then (A) (B) T1  T2 T1  T2 (D)

by

x

A  x0ω2    3 / 4

T1  T2

represented

1  x   n    n  0 1 2 2 2 

A particle executes simple harmonic motion between

(C)

A travelling wave represented by y  a sin  ωt  kx  is

(A)

particle is written as : a  Acos  ωt    , then : (A)

At a moment is a progressive wave, the phase of a particle executing SHM is /3. Then the phase of the particle 15 cm ahead and at the time T/2 will be, if the wavelength is 60 cm: (A) /2 (B) 2/3 (C) None (D) 5/6

superimposed on another wave y  a sin  ωt  kx  . The resultant is :

(A)

3.

Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after 2 s. If bulk

10.

103

A string vibrates according to the equation  2 x  y  5 sin   cos 20  t  3  Where x and y are in cm and t in second. The distance between two adjacent nodes is: (A) 3 cm (B) 4.5 cm (C) 6 cm (D) 1.5 cm

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [8]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The motion of a particle varies with time according to

6.

The speed of sound wave in a gas: (A) does not depend upon density of the gas (B) does not depend upon changes in pressure (C) does not depend upon temperature (D) depends upon density of the gas

7.

A

8.

When two progressive waves y1  4 sin  2 x  6t  and

the relation y  a  sin ωt  cos ωt  . (A) (B)

The motion is oscillatory but not SHM The motion is SHM with amplitude a

(C) (D)

The motion is SHM with amplitude a 2 The motion is SHM with amplitude 2a

2.

A particle starts oscillating simple harmonically from its equilibrium position with time period T. The ratio of KE and PE of the particle at the t = T / 12 is: (A) 1:4 (B) 2:1 (C) 3:1 (D) 4:1

3.

A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is: 1 (A) (B) ma 2v 2  2ma 2v 2 4 (C)

4.

(D)

(B) (C) (D)

2 2ma 2v 2

(A) (B) (C) (D)

A closed Prgan pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is : (A) 2 (B) 6 (C) 8 (D) 7

10.

A car sounding its horn at 480 Hz moves towards a high

a simple harmonic motion with a period  / ω

Two identical springs are connected in series and parallel as shown in the figure. If fs and fp are frequencies of

wall at a speed of 20ms 1 . If the speed of sound is

fs ? fp

340ms 1 , the frequency of the reflected sound heard by the girl sitting in the car will be closest to : (A) 540 Hz (B) 524 Hz (C) 568 Hz (D) 480 Hz

1:2 2:1 1:3 3:1

VMC/SHM & Wave Motion

the

9.

a periodic, but simple harmonic, motion with a period 2 / ω a periodic, but not simple harmonic, motion with a period  / ω a simple harmonic motion with a period 2 / ω

series and parallel arrangements, what is

wave is described by the x  equation y  y0 sin 2  ft   . The maximum particle   velocity is equal to four times the wave velocity is equal to four times the wave velocity, if : y y (A) (B)  0  0 4 2 (C) (D)    y0   2 y0

  are superimposed, y2  3 sin  2 x  6t   2  amplitude of the resultant wave is : (A) 5 (B) 6 (C) 5/6 (D) 1/2

The function sin 2  ωt  represents (A)

5.

4 2ma 2v 2

transverse

103

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [9]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

3.

4.

A particle of amplitude A is executing simple harmonic motion. When the potential energy of particle is half of its maximum potential energy, then displacement from its equilibrium position is: (A) A/4 (B) A/3 (C) A/3 (D) A 2

7.

If a simple harmonic is represented by

(C)

2

d 2x dt 2

8.

2 

(D)

2 

(B) (C) (D)

(B)

2 17

(C)

1 8

(D)

32 17

Two points on a travelling wave having frequency 500

The equation of a wave on a string of linear mass density

The tension in the string is : (A) 4.0 N (B) (C) 0.5 N (D) 9.

f 

1 D

10.

12.5 N 6.25 N

A uniform wire of length L, diameter D and density S is stretched under a tension T. The correct relation between its fundamental frequency f, the length L and the diameter D is: 1 1 (A) (B) f  f LD L D (C)

mg1g k m2 g k m  1  m2  g

2

(D)

f

1 LD 2

A bus is moving with a velocity of 5ms 1 towards a huge wall. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 335ms 1 , the number of beats heard per second by a passenger inside the bus will be: (A) 3 (B) 4 (C) 5 (D) 6

k

 m1  m2  g k

VMC/SHM & Wave Motion

8

   t x y  0.02  m  sin  2    .  0.04  s  0.50  m      

Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removed without disturbing the system. The amplitude of oscillations is : (A)

(A)

0.04kg m1 is given by :

  x  0 , is

(B)

Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is:

Hz and velocity 300ms 1 are 60 out of phase, then the minimum distance between the two point is : (A) 0.2 (B) 0.1 (C) 0.5 (D) 0.4

A particle is executing SHM at mid-point of mean position and extremely, What is the potential energy in terms of total energy (E)? (A) E/4 (B) E/16 (C) E/2 (D) E/8

time period is : 2 (A) 

5.

6.

Two particles execute SHM of the same amplitude and frequency along the same straight line. If they pass one another when going in opposite directions, each time their displacement is half their amplitude, the phase difference between them is: (A) /3 (B) /4 (C) /6 (D) 2/3

103

HWT/Physics

Vidyamandir Classes DATE :

TIME : 30 Minutes

MARKS : [ ___ /10]

TEST CODE : SHM WV [10]

START TIME :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The displacement-time graph of a particle executing SHM is as shown in the figure.

The corresponding force-time graph of the particle is :

(A) 2.

3.

(B)

(C)

(D)

4 The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t  s is: 3 (A)

3 2  cms 2 32

(B)



2 cms 2 32

(C)

2 cms 2 32

(D)



3 2  cms 2 32

The KE and PE of a particle executing SHM of amplitude a will be equal when displacement is : (A)

a 2

(B)

a 2

(C)

2a

(D)

a 2

4.

A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position ? (A) 0.5 (B) 1.0 s (C) 1.5 s (D) 2.0 s

5.

Two particles A and B of equal masses are suspended from two massless springs of spring constant k1 and k2, respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitudes of A and B is : (A)

6.

7.

k1 / k2

(B)

k1 / k2

The sound wave produced in a gas is always (A) longitudinal (B) transverse

(C)

k2 / k1

(D)

k2 / k1

(C)

stationary

(D)

electromagnetic

  Equation of progressive wave is : y  a sin 10 x  11 t   3 

(A) (C)

its wavelength is 0.2 units wave velocity is 1.5 units

VMC/SHM & Wave Motion

(B) (D)

103

it is travelling in the positive x-direction time period of SHM is 1 s

HWT/Physics

Vidyamandir Classes 8.

A progressive wave y  a sin  kx  ωt  is reflected by a rigid wall at x = 0. Then the reflected wave can be represented by: (A)

y  a sin  kx  ωt  (B)

y  a cos  kx  ωt  (C)

y   a sin  kx  ωt  (D)

y   a sin  kx  ωt 

9.

In a resonance pipe the first and second resonances are obtained at depth 22.7 cm and 70.2 cm respectively. What will be the end correction? (A) 1.05 cm (B) 115.5 cm (C) 92.5 cm (D) 113.5 cm

10.

A whistle of frequency 500 Hz, tied to the end of a string of length 1.2 m, revolves at 400 rev/min. A listener standing some distance away in the plane of rotation of whistle hears frequency in the range of (speed of sound = 340ms 1 ) (A) 436 to 386 Hz (B) 426 to 474 Hz (C) 426 to 586 Hz (D) 436 to 586 Hz

VMC/SHM & Wave Motion

103

HWT/Physics