CBSE Class 11 Physics Oscillations And Waves Worksheet

OSCILLATIONS & WAVES WORK SHEET

Question. Lissajous figure obtained by combining x = a sin wt and y = a sin (ωt + π/4) will be a/an
(a) ellipse
(b) straight line
(c) circle
(d) parabola

Answer: A

Question. A circular hoop of radius R is hung over a knife edge. The period of oscillation is equal to that of a simple pendulum of length
(a) R
(b) 2R
(c) 3R
(d) 3R/2

Answer: B

Question. A Second’s pendulum is placed in a space laboratory orbiting around the earth at a height 3 R from the earth’s surface where R is earth’s radius. The time period of the pendulum will be
(a) zero
(b) 2√3
(c) 4 sec
(d) infinite

Answer: D

Question. A block rests on a horizontal table which is executing SHM in the horizontal plane with an amplitude 'a'. If the coefficient of friction is 'μ', then the block just starts to slip when the frequency of oscillation is 

Answer: A

Question. The displacement of a particle is represented by the equation y = 3 cos(π/4 - 2ωt). The motion of the particle is
(a) simple harmonic with period 2p/w
(b) simple harmonic with period p/w
(c) periodic but not simple harmonic
(d) non-periodic

Answer: B

Question. A particle undergoes simple harmonic motion having time period T. The time taken in 3/8th oscillation is
(a) 3/8 T
(b) 5/8 T
(c) 5/12 T
(d) 7/12 T

Answer: C

Question. The time period of a simple pendulum of infinite length is (R_e = radius of Earth) 
(a) T = 2π√Re/g
(b) T = 2π√2Re/g
(c) T = 2π√Re/2g
(d) T = ∞

Answer: A

Question. Which, one of the particle is exempting simple harmonic motion?
Motion of an oscillating liquid column in a U-tube is
(a) periodic but not simple harmonic
(b) non-periodic
(c) simple harmonic and time period is independent of the density of the liquid
(d) simple harmonic and time period is directly proportional to the density of the liquid

Answer: C

Question. A particle is acted simultaneously by mutually perpendicular simple harmonic motion x = a cos wt and y = a sin ωt. The trajectory of motion of the particle will be
(a) an ellipse
(b) a parabola
(c) a circle
(d) a straight line

Answer: C

Question. The displacement of a particle varies with time according to the relation y = asinwt + bcoswt.
(a) The motion is oscillatory but not SHM
(b) The motion is SHM with amplitude a + b
(c) The motion is SHM with amplitude a² + b²
(d) The motion is SHM with amplitude √a² + b2

Answer: D

Question. The spring constant from the adjoining combination of springs is
(a) K
(b) 2 K
(c) 4 K
(d) 5 K/2

Answer: C

Question. On Earth, a body suspended on a spring of negligible mass causes extension L and undergoes oscillations along length of the spring with frequency f. On the Moon, the same quantities are L/n and f ' respectively. The ratio f '/f is
(a) n
(b) 1/n
(c) n^–1/2
(d) 1

Answer: D

Question. Which one of the following equations of motion represents simple harmonic motion?
(a) Acceleration = – k(x + a)
(b) Acceleration = k(x + a)
(c) Acceleration = kx
(d) Acceleration = – k₀x + k₁x²
where k, k₀, k₁ and a are all postive.

Answer: A

Question. The displacement of a particle is represented by the equation y = sin³ ωt. The motion is
(a) non-periodic
(b) periodic but not simple harmonic
(c) simple harmonic with period 2π/ω
(d) simple harmonic with period π/ω

Answer: B

Question. A particle of mass m oscillates along x-axis according to equation x = a sin wt. The nature of the graph between momentum and displacement of the particle is
(a) straight line passing through origin
(b) circle
(c) hyperbola
(d) ellipse

Answer: D

Question. The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos (ωt)
where X = displacement at time t
w = frequency of oscillation
Which one of the following graphs shows correctly the variation of ‘a’ with ‘t’? (12 ex 3)

Answer: C

Question. When two displacements represented by y₁ = asin(wt) and y₂ = b cos(wt) are superimposed the motion is:
(a) simple harmonic with amplitude a/b
(b) simple harmonic with amplitude √a² + b²
(c) simple harmonic with amplitude (a+b)/2
(d) not a simple harmonic

Answer: B

Question. A forced oscillator is acted upon by a force F = F₀ sin ωt. The amplitude of oscillation is given by 55/√2ω² - 360ω + 9 The resonant angular frequency is
(a) 2 unit
(b) 9 unit
(c) 18 unit
(d) 36 unit

Answer: B

Question. The relation between acceleration and displacement of four particles are given below
(a) a_x = +2x
(b) a_x = +2x²
(c) a_x = –2x²
(d) a_x = –2x

Answer: D

Question. The equation of motion of a particle is x = a cos(at)₂. The motion is
(a) periodic but not oscillatory
(b) periodic and oscillatory
(c) oscillatory but not periodic
(d) neither periodic nor oscillatory

Answer: C

Question. A particle executing SHM maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s². The period of oscillation is
(a) π sec
(b) π/2 sec
(c) 2π sec
(d) π/t sec

Answer: A

Question. Four pendulums A, B, C and D are suspended from the same elastic support as shown in figure. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,
(a) D will vibrate with maximum amplitude
(b) C will vibrate with maximum amplitude
(c) B will vibrate with maximum amplitude
(d) All the four will oscillate with equal amplitude

Answer: B

Question. A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
(a) √5/2π
(b) 4π/√5
(c) 2π/√3
(d) √5/π

Answer: B

DIRECTIONS for Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer (ONLY ONE option is correct ) from the following-
(a) Statement -1 is false, Statement-2 is true
(b) Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -1 is true, Statement-2 is false

Question. Statement 1 : The graph between velocity and displacement for a harmonic oscillator is an ellipse.
Statement -2 : Velocity does not change uniformly with displacement in harmonic motion.

Answer: C

Question. Statement -1 : If the amplitude of a simple harmonic oscillator is doubled, its total energy becomes four times.
Statement -2 : The total energy is directly proportional to the square of the amplitude of vibration of the harmonic oscillator.

Answer: B
 

SECTION-A CONCEPTUAL & APPLICATION TYPE QUESTIONS

1. list any two characteristics of simple harmonic motion.

2. On what factors does the energy of a harmonic oscillator depends ?

3. A simple pendulum is inside a space-craft. What should be its time period of vibration?

4. What is the main difference between forced oscillations & resonance?

5. Glass windows may be broken by a far away explosion. Explain why.

6. Name two important properties of a material responsible for the propagation of waves through it .

7. If the pressure of a gas at constant temperature is increased four times, how the velocity of sound in the gas will be affected?

8. What are harmonics?

9. What is difference between a tone & note?

10. What is beat frequency?

SECTION-B NUMERICAL QUESTIONS

1. The acceleration of a particle performing S.H.M. is 12 c/m² at a distance of 3cm from the mean position. Calculate its time-period.

2. The displacement equation for a particle executing simple harmonic motion is
y = 0.2 sin 50π (t + 0.01) metre, where y is the displacement at the instant t. Calculate the amplitude, time period , maximum velocity and the displacement at the start of motion.

3. A block whose mass is 1 kg is fastened to a spring The spring has a spring constant of 50 N/m. The block is pulled to a distance x=10cm from its equilibrium position at x=0 on a
frictionless surface from rest at t=0. Calculate kinetic, potential & total energies of the block when it is 5 cm away from mean position.

4. A spring of force constant 1200 N /m is mounted horizontally on a horizontal table. A mass of 3.0 kg is attached to the free end of the spring, pulled sideways to a distance of
2.0 cm & released. (i) What is the frequency of oscillation of the mass ? (ii) What is the maximum acceleration of the mass ? (iii) What is the maximum speed of the mass ?

5. At what temperature will the velocity of sound in hydrogen be the same as in oxygen at 100⁰ C ? Density of oxygen is 16 times the density of hydrogen.

6. A simple harmonic wave is expressed by equation , y = 7x 10 ^-6 sin ( 800 π t – π x/42.5 ) where y & x are in cm & t in seconds. Calculate the following : (i) amplitude(ii) frequency (iii) wave length (iv) wave velocity , & (v) phase difference between two particles separated by 17.0 cm.

7. A metal wire of linear mass density of 9.8g/m is stretched with a tension of 10 kgwt into between two rigid supports 1m apart. The wire passes at its middle point between the poles of a permanent magnet & it vibrates in resonance, when carrying an alternating current of frequency ν . Find the frequency of the alternating source.

8. A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source? Will this same source be in resonance with the pipe if both ends are open ? Speed of sound =340 m/s.

9. A tuning fork arrangement (pair) produces 4 beats/s with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it sounded again then produces 2 beats/s.What is the frequency of the unknown fork?

10. A railway engine & a car are moving on parallel tracks in opposite directions with speed of 144 kmph 72 kmph , respectively. The engine is continuously sounding a whistle of frequency 500 Hz. The velocity of sound is 340 m/s. Calculates the frequency of sound heard in the car when (i) the car & the engine are approaching each other, (ii) the two are moving away from each other.

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