Oscillations And Waves : Physics

 

Q.1.  A particle is executing simple harmonic motion . Its displacement is given by x = 5 sin  t. Where x is in cm and t in seconds. How long will the particle taken to move from the position of equilibrium to the position of maximum displacement ?

 A) 0.5 s

 B) 1.0 s

 C) 1.5 s

 D) 2.0 s

Explanation- 

Maximum displacement = amplitude = 5 cm At time t = 0 , x = 0 ( equilibrium position ) . Hence time t taken by the particle to move from x = 0 to x = 5 cm is given by   

Q.2. The displacement at an instant 't', of particle executing a linear S.H.M. is given by

 x = 5 sin 31.4(t + 0.1). Its periodic time is 

A) 2 sec 

B) 0.2 sec 

C) 0.5 sec 

D) 1 sec 

Explanation-

 

Q.3. A particle is in UCM. From its every position a perpendicular is dropped. The point of intersection of the perpendicular and a diameter is called foot of the perpendicular and its motion is SHM...

A) Only on horizontal diameter

B) Only on vertical diameter

C) On only horizontal and vertical diameters

D) On any diameter

Explanation-

The motion on any diameter is SHM.

Q.4. The potential energy of a particle executing simple harmonic motion at a distance x from the equilibrium position is proportional to  

A) 

B)  x 

C) 

D)  

Explanation-

The potential energy of a particle of mass m executing simple harmonic motion of angular frequency  at a distance x from the equilibrium position is given by   is constant.

Q.5. A wave represented by the equation y=a cos( kx - )b is superposed with another wave to form a stationary wave such that the point x=0 is a node. The equation of the other waves is

A) 

B) 

C) 

D)  

Explanation-

To from a stationary wave, waves y and y' must travel in opposite directions. Wave y = a cos ( kx = t ) travels along the position x - direction. Waves y' = - a cos ( kx -  t ) and y' = - a sin ( kx - t ) in choices ( b ) and ( d ) are not possible. Choice ( a ) is also incorrect because at x = 0

y' = a sin t and y = a cos ( - t ) = a cos t Therefore, the resultant displacement at x = 0 which  is y + y' = a sin t +a cos t is not zero, i.e. these waves do not produce a node at x = 0. 

Q.6. Three sound waves of equal amplitudes have frequencies (v-1), (v) and (v+1). They superpose to give beats. The number of beats produced per second will be

A) v

B) 

C) 2

D) 1

Explanation-

When the three waves superpose at a point, then from the superposition principle, the resultant particle displacement at that point is given by 

is the resultant amplitude . Now , the resultant intensity   will be maximum when cos 2  t = +1 

or 2  t = 0, 2 , 4, …. etc.

or t = 0 , 1 s , 2 s , … etc. . 

 Time period of beats = time interval between two consecutive maxima = 1 s . Hence the beat frequency is 1 Hz.

Q.7. The differential equation of SHM of a seconds pendulum oscillating along  x axis is

A)  = 

B) 

C) 

D)  

Explanation-

For seconds pendulum

T = 2 sec              

The diff. eqn. off SHM is

 

Q.8. Two SHMs of same period and amplitudes  and  act parallel to each other on a particle and have resultant amplitude  when the phase difference between them is  the resultant amplitude is . The amplitudes  and  respectively are...

A) 

B) 

C) 

D)  

Explanation-

When phase diff. 

 

Q.9.  A travelling wave in a stretched string is described by the equation  The maximum particle velocity is 

A) 

B) 

C) 

D)  

Explanation-

Particle velocity V =  

Q.10.  A simple pendulum attached to the ceiling of a stationary lift has a time period T. Te distance y covered the lift moving upwards varies with time t as y =  where y is in meter and t in second. If g = 10 ms, the time period of the pendulum will be 

A)  T

B)  T

C)  T

D)  T

Explanation-

Given y = t. The velocity of the lift varies with t as 

 Acceleration a =  , directed upwards , Hence