JEE Main - Superposition, standing waves and harmonics Online Test (MCQ Quiz)

1. When two waves of the same frequency and amplitude travel in the same direction in a medium, they interfere. What is the resultant amplitude if they are in phase?

A) Zero B) Equal to the amplitude of one wave C) Twice the amplitude of one wave D) Half the amplitude of one wave

2. If two waves of the same frequency and amplitude travel in opposite directions, what phenomenon occurs?

A) Interference B) Diffraction C) Polarization D) Stationary waves

3. In a stationary wave, what is the point called where the amplitude of oscillation is maximum?

A) Node B) Antinode C) Crest D) Trough

4. In a stationary wave, what is the point called where the amplitude of oscillation is minimum (ideally zero)?

A) Node B) Antinode C) Crest D) Trough

5. What is the distance between two consecutive nodes in a stationary wave?

A) Wavelength (λ) B) Half wavelength (λ/2) C) Quarter wavelength (λ/4) D) Twice the wavelength (2λ)

6. What is the distance between two consecutive antinodes in a stationary wave?

A) Wavelength (λ) B) Half wavelength (λ/2) C) Quarter wavelength (λ/4) D) Twice the wavelength (2λ)

7. What is the distance between a node and an adjacent antinode in a stationary wave?

A) Wavelength (λ) B) Half wavelength (λ/2) C) Quarter wavelength (λ/4) D) Twice the wavelength (2λ)

8. For a string fixed at both ends, what is the condition for producing stationary waves?

A) The length of the string must be an integer multiple of λ/4 B) The length of the string must be an integer multiple of λ/2 C) The length of the string must be an integer multiple of λ D) The length of the string must be an odd multiple of λ/4

9. The fundamental frequency of a string fixed at both ends is called the first harmonic. If its length is L and wave speed is v, what is the fundamental frequency?

A) v/L B) v/(2L) C) 2v/L D) v/(4L)

10. For a string fixed at both ends, the possible frequencies of vibration are called harmonics. If the fundamental frequency is f, what are the frequencies of the harmonics?

A) f, 2f, 3f, ... B) f, 3f, 5f, ... C) f, 4f, 9f, ... D) f, f/2, f/3, ...

11. The second harmonic for a string fixed at both ends corresponds to a vibration pattern with how many antinodes?

A) One B) Two C) Three D) Four

12. The third harmonic for a string fixed at both ends corresponds to a vibration pattern with how many nodes (excluding the fixed ends)?

A) One B) Two C) Three D) Four

13. What is the relationship between the wavelength (λ) of a stationary wave and the length (L) of a string fixed at both ends when it vibrates in its nth harmonic?

A) L = nλ/2 B) L = nλ C) L = nλ/4 D) L = 2nλ

14. In an open organ pipe (open at both ends), the fundamental frequency corresponds to a vibration pattern with an antinode at each open end. What is the condition for resonance?

A) Length L = nλ/4 B) Length L = nλ/2 C) Length L = (2n-1)λ/4 D) Length L = (2n-1)λ/2

15. For an open organ pipe, the possible frequencies of vibration are called harmonics. If the fundamental frequency is f, what are the frequencies of the harmonics?

A) f, 2f, 3f, ... B) f, 3f, 5f, ... C) f, 4f, 9f, ... D) f, f/2, f/3, ...

16. In an open organ pipe, the second harmonic has a frequency that is how many times the fundamental frequency?

A) 1 times B) 2 times C) 3 times D) 4 times

17. In a closed organ pipe (closed at one end and open at the other), what is the boundary condition at the closed end and the open end, respectively?

A) Antinode, Node B) Node, Antinode C) Node, Node D) Antinode, Antinode

18. For a closed organ pipe of length L, what is the condition for producing stationary waves (resonance)?

A) L = nλ/4 B) L = (2n-1)λ/4 C) L = nλ/2 D) L = (2n-1)λ/2

19. For a closed organ pipe, the possible frequencies of vibration are called harmonics. If the fundamental frequency is f, what are the frequencies of the harmonics?

A) f, 2f, 3f, ... B) f, 3f, 5f, ... C) f, 4f, 9f, ... D) f, f/2, f/3, ...

20. In a closed organ pipe, the third harmonic has a frequency that is how many times the fundamental frequency?

A) 1 times B) 2 times C) 3 times D) 5 times

21. What is the ratio of the fundamental frequency of an open organ pipe to that of a closed organ pipe of the same length, assuming the speed of sound is the same?

A) 1:1 B) 2:1 C) 1:2 D) 1:3

22. When two waves of the same frequency and amplitude but with a phase difference of π radians travel in the same direction, what is the resultant amplitude?

A) Zero B) Equal to the amplitude of one wave C) Twice the amplitude of one wave D) Half the amplitude of one wave

23. The phenomenon of superposition applies to which type of waves?

A) Transverse waves only B) Longitudinal waves only C) Both transverse and longitudinal waves D) Electromagnetic waves only

24. A wave pulse traveling on a string reflects off a fixed end. What is the phase change of the reflected pulse?

A) 0 degrees (no phase change) B) 90 degrees (π/2 radians) C) 180 degrees (π radians) D) 270 degrees (3π/2 radians)

25. A wave pulse traveling on a string reflects off a free end. What is the phase change of the reflected pulse?

A) 0 degrees (no phase change) B) 90 degrees (π/2 radians) C) 180 degrees (π radians) D) 270 degrees (3π/2 radians)

26. In the superposition principle, the displacement of any point at a given time is the algebraic sum of the displacements due to individual waves. This principle holds true as long as the medium's response is:

A) Non-linear B) Linear C) Damped D) Dispersive

27. When two waves with amplitudes A1 and A2 interfere constructively, what is the maximum possible resultant amplitude?

A) A1 + A2 B) A1 - A2 C) √(A1² + A2²) D) (A1 + A2)/2

28. When two waves with amplitudes A1 and A2 interfere destructively, what is the minimum possible resultant amplitude?

A) A1 + A2 B) A1 - A2 C) √(A1² + A2²) D) (A1 + A2)/2

29. What is the condition for destructive interference between two waves of the same frequency?

A) Phase difference = nπ, where n is an integer B) Phase difference = (2n+1)π, where n is an integer C) Path difference = nλ, where n is an integer D) Path difference = (2n+1)λ/2, where n is an integer

30. What is the condition for constructive interference between two waves of the same frequency?

A) Phase difference = nπ, where n is an integer B) Phase difference = (2n+1)π, where n is an integer C) Path difference = nλ, where n is an integer D) Path difference = (2n+1)λ/2, where n is an integer

31. The relationship between phase difference (φ) and path difference (Δx) for two waves is given by:

A) φ = (2π/λ) Δx B) φ = (λ/2π) Δx C) φ = λ Δx D) φ = Δx / λ

32. If a string is vibrated such that it forms a stationary wave with 3 loops, and its length is L, what is the wavelength of the wave?

A) L B) 2L C) 3L D) 2L/3

33. A sound wave in a tube closed at one end resonates at its fundamental frequency. What is the relationship between the length of the tube (L) and the wavelength (λ)?

A) L = λ/4 B) L = λ/2 C) L = 3λ/4 D) L = λ

34. If a closed organ pipe resonates at frequencies f, 3f, 5f, ..., what are these frequencies called?

A) Harmonics B) Octaves C) Overtones D) Fundamental frequencies

35. If an open organ pipe resonates at frequencies f, 2f, 3f, ..., what are these frequencies called?

A) Harmonics B) Octaves C) Overtones D) Fundamental frequencies

36. Consider a string fixed at both ends. If the tension is increased, what happens to the frequencies of the harmonics, assuming the length and mass per unit length remain constant?

A) Decrease B) Increase C) Remain the same D) First increase then decrease

37. When a string fixed at both ends vibrates in its third harmonic, how many nodes are present along the string (excluding the fixed ends)?

A) 1 B) 2 C) 3 D) 4

38. When a string fixed at both ends vibrates in its fundamental mode, how many antinodes are present along the string?

A) 1 B) 2 C) 3 D) 0

39. In a stationary wave, energy is stored in the medium. Where is the energy concentrated?

A) Nodes B) Antinodes C) Equally distributed D) Between nodes and antinodes

40. What happens to the amplitude of oscillation of particles at nodes in a stationary wave?

A) Maximum B) Minimum (zero) C) Varies sinusoidally D) Depends on the frequency

41. What happens to the amplitude of oscillation of particles at antinodes in a stationary wave?

A) Maximum B) Minimum (zero) C) Varies sinusoidally D) Depends on the frequency

42. A tuning fork of frequency 400 Hz is sounded near one end of a closed organ pipe of length 0.5 m. If the speed of sound is 320 m/s, at which harmonic will resonance occur?

A) Fundamental B) Second harmonic (first overtone) C) Third harmonic (second overtone) D) Fourth harmonic (third overtone)

43. Two waves are represented by y1 = A sin(ωt - kx) and y2 = A sin(ωt - kx + φ). For destructive interference, what is the value of φ?

A) 0 B) π/2 C) π D) 3π/2

44. When two identical waves travel in opposite directions, they form stationary waves. What is the net displacement of particles at the nodes?

A) Maximum B) Minimum (zero) C) Varies with time D) Depends on the wave speed

45. The phenomenon where the vibration of one body causes another body to vibrate with a large amplitude is called:

A) Superposition B) Interference C) Resonance D) Diffraction

46. For a string of length L fixed at both ends, the wavelength of the nth harmonic is given by:

A) λn = 2L/n B) λn = L/n C) λn = 4L/n D) λn = L/(2n)

47. The frequency of the nth harmonic for a string fixed at both ends is given by fn. If the fundamental frequency is f1, then:

A) fn = n f1 B) fn = (n+1) f1 C) fn = f1 / n D) fn = n² f1

48. In a closed organ pipe, resonance occurs when the length of the air column is (2n-1)λ/4, where n = 1, 2, 3, .... The first resonance (fundamental) occurs when n=1. What is the wavelength in this case?

A) 4L B) 2L C) 4L/3 D) 4L/5

49. Consider the superposition of two waves y1 = A sin(ωt) and y2 = A sin(ωt + π/2). The resultant wave is:

A) y = 2A sin(ωt) B) y = A sin(ωt + π/4) C) y = √2 A sin(ωt + π/4) D) y = 0

50. If a string vibrates in 5 segments (loops), what is the mode of vibration?

A) Fundamental B) Second harmonic C) Fifth harmonic D) Sixth harmonic

Superposition, standing waves and harmonics - Online Test

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