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Multiple Choice Questions (MCQ)

1. What is the time period of a simple pendulum of length \( l \) and acceleration due to gravity \( g \)?
a) \( 2\pi \sqrt{\frac{l}{g}} \)
b) \( 2\pi \sqrt{\frac{g}{l}} \)
c) \( 2\pi \sqrt{l} \)
d) \( 2\pi \sqrt{g} \)

2. Which of the following is the characteristic of a simple harmonic motion (SHM)?

a) Nonlinear restoring force
b) Constant amplitude
c) The force is proportional to the displacement but opposite in direction
d) No displacement from the equilibrium position

3. The angular frequency of a body executing SHM is given by:

a) \( \omega = \frac{2\pi}{T} \)
b) \( \omega = \frac{T}{2\pi} \)
c) \( \omega = 2\pi T \)
d) \( \omega = \pi T \)

4. The energy in a simple harmonic oscillator is:

a) Dependent on the amplitude only
b) Dependent on the frequency only
c) Constant and independent of time
d) Zero at maximum displacement

5. Which of the following is a property of a damped oscillator?

a) The amplitude increases with time
b) The amplitude decreases with time
c) The energy of the system increases
d) The frequency of the system remains constant

6. In the case of a forced oscillation, resonance occurs when:

a) The driving frequency is much lower than the natural frequency
b) The driving frequency equals the natural frequency
c) The driving frequency is higher than the natural frequency
d) The amplitude of oscillation is zero

7. The displacement equation for a damped harmonic oscillator is given by \( x(t) = Ae^{-\gamma t} \cos(\omega t) \). What does \( \gamma \)
represent?
a) The angular frequency
b) The amplitude of the oscillations
c) The damping coefficient
d) The time period of the oscillations

8. The period of a mass-spring system depends on:

a) The mass and the spring constant
b) The mass and the amplitude
c) The amplitude and the spring constant
d) The mass only
9. A wave with frequency \( f \) and wavelength \( \lambda \) is propagating with speed \( v \). The relationship between these quantities is:
a) \( v = f + \lambda \)
b) \( v = f \lambda \)
c) \( v = \frac{f}{\lambda} \)
d) \( v = f - \lambda \)

10. In a standing wave, nodes are the points where:

a) Displacement is maximum
b) Displacement is minimum
c) The wave oscillates
d) The wave does not oscillate

11. The frequency of a wave in a string is doubled. The speed of the wave will:
a) Double
b) Decrease by half
c) Remain the same
d) Be quadrupled

12. The intensity of a sound wave is proportional to:

a) The square of the amplitude
b) The frequency
c) The square of the frequency
d) The amplitude

13. A sound wave in air has a wavelength of 2 m. If the frequency of the wave is 343 Hz, what is the speed of sound in air?
a) 171.5 m/s
b) 343 m/s
c) 686 m/s
d) 2 m/s
14. The frequency of a harmonic wave is:
a) The number of oscillations per unit time
b) The distance between two consecutive crests
c) The time for one complete wave to pass a point
d) The speed of the wave

15. The principle of superposition of waves applies to:

a) Only transverse waves
b) Only longitudinal waves
c) Both transverse and longitudinal waves
d) Neither transverse nor longitudinal waves

16. The phase difference between two points on a wave is:

a) The difference in the amplitudes
b) The difference in the frequencies
c) The difference in the wave's displacements
d) The difference in their positions relative to the wave

17. The wave equation is given by \( y(x, t) = A \cos(kx - \omega t) \). What does \( k \) represent?
a) The angular frequency
b) The wave speed
c) The wave number
d) The amplitude

18. The Doppler effect refers to:

a) The change in amplitude of a wave as it moves through different media
b) The change in frequency of a wave as the source or observer moves
c) The change in wave speed with temperature
d) The reflection of sound waves from surfaces

19. In resonance, the amplitude of oscillation is:

a) Minimum
b) Maximum
c) Zero
d) Decreasing

20. The fundamental frequency of a vibrating string is:

a) The first harmonic frequency
b) The second harmonic frequency
c) The third harmonic frequency
d) Zero frequency

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Assertion-Reason Type Questions

21. Assertion: The time period of a simple pendulum is independent of its amplitude for small oscillations.
Reason: For small displacements, the restoring force is proportional to the displacement.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

22. Assertion: In a damped harmonic oscillator, the amplitude decreases with time.
Reason: The energy is dissipated in the form of heat due to friction.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

23. Assertion: The frequency of a sound wave does not change if the observer is moving towards or away from the source.
Reason: The Doppler effect only affects the wavelength of the wave, not the frequency.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

24. Assertion: The phase of a wave determines the displacement of the wave at a given point in space.
Reason: Phase difference between two waves results in constructive or destructive interference.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

25. Assertion: The amplitude of oscillations in forced oscillation decreases as the damping increases.
Reason: Damping removes energy from the system and reduces the amplitude of oscillation.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

26. Assertion: The velocity of a wave in a string is independent of the frequency.

Reason: The velocity of the wave depends on the tension and mass per unit length of the string.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

27. Assertion: In a longitudinal wave, the particles of the medium move parallel to the direction of wave propagation.
Reason: A longitudinal wave has compressions and rarefactions in the direction of the wave.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

28. Assertion: The intensity of sound is inversely proportional to the square of the distance from the source.
Reason: The energy spread over a larger area diminishes the intensity.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

29. Assertion: A standing wave is formed by the superposition of two waves traveling in opposite directions.
Reason: Standing waves have no net energy transfer.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

30. Assertion: In a transverse wave, the displacement is perpendicular to the direction of wave propagation.
Reason: In transverse waves, the energy propagates without a net movement of particles in the medium.
a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c) Assertion is correct, but Reason is incorrect
d) Assertion is incorrect, but Reason is correct

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Answers

MCQs
1. a) \( 2\pi \sqrt{\frac{l}{g}} \)
2. c) The force is proportional to the displacement but opposite in direction
3. a) \( \omega = \frac{2\pi}{T} \)
4. a) Dependent on the amplitude only
5. b) The amplitude decreases with time
6. b) The driving frequency equals the natural frequency
7. c) The damping coefficient
8. a) The mass and the spring constant
9. b) \( v = f \lambda \)
10. b) Displacement is minimum
11. c) Remain the same
12. a) The square of the amplitude
13. b) 343 m/s
14. a) The number of oscillations per unit time
15. c) Both transverse and longitudinal waves
16. c) The difference in the wave's displacements
17. c) The wave number
18. b) The change in frequency of a wave as the source or observer moves
19. b) Maximum
20. a) The first harmonic frequency
Assertion-Reason
21. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
22. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
23. b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
24. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
25. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
26. b) Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
27. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
28. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
29. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion
30. a) Both Assertion and Reason are correct, and Reason is the correct explanation of Assertion

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