Superposition, standing waves and harmonics - Question Bank
1. If a string vibrates in 5 segments (loops), what is the mode of vibration?
2. Consider the superposition of two waves y1 = A sin(ωt) and y2 = A sin(ωt + π/2). The resultant wave is:
3. 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?
4. The frequency of the nth harmonic for a string fixed at both ends is given by fn. If the fundamental frequency is f1, then:
5. For a string of length L fixed at both ends, the wavelength of the nth harmonic is given by:
6. The phenomenon where the vibration of one body causes another body to vibrate with a large amplitude is called:
7. When two identical waves travel in opposite directions, they form stationary waves. What is the net displacement of particles at the nodes?
8. 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?
9. 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?
10. What happens to the amplitude of oscillation of particles at antinodes in a stationary wave?
11. What happens to the amplitude of oscillation of particles at nodes in a stationary wave?
12. In a stationary wave, energy is stored in the medium. Where is the energy concentrated?
13. When a string fixed at both ends vibrates in its fundamental mode, how many antinodes are present along the string?
14. When a string fixed at both ends vibrates in its third harmonic, how many nodes are present along the string (excluding the fixed ends)?
15. 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?
16. If an open organ pipe resonates at frequencies f, 2f, 3f, ..., what are these frequencies called?
17. If a closed organ pipe resonates at frequencies f, 3f, 5f, ..., what are these frequencies called?
18. 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)?
19. 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?
20. The relationship between phase difference (φ) and path difference (Δx) for two waves is given by:
21. What is the condition for constructive interference between two waves of the same frequency?
22. What is the condition for destructive interference between two waves of the same frequency?
23. When two waves with amplitudes A1 and A2 interfere destructively, what is the minimum possible resultant amplitude?
24. When two waves with amplitudes A1 and A2 interfere constructively, what is the maximum possible resultant amplitude?
25. 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:
26. A wave pulse traveling on a string reflects off a free end. What is the phase change of the reflected pulse?
27. A wave pulse traveling on a string reflects off a fixed end. What is the phase change of the reflected pulse?
28. The phenomenon of superposition applies to which type of waves?
29. 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?
30. 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?
31. In a closed organ pipe, the third harmonic has a frequency that is how many times the fundamental frequency?
32. 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?
33. For a closed organ pipe of length L, what is the condition for producing stationary waves (resonance)?
34. 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?
35. In an open organ pipe, the second harmonic has a frequency that is how many times the fundamental frequency?
36. 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?
37. 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?
38. 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?
39. The third harmonic for a string fixed at both ends corresponds to a vibration pattern with how many nodes (excluding the fixed ends)?
40. The second harmonic for a string fixed at both ends corresponds to a vibration pattern with how many antinodes?
41. 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?
42. 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?
43. For a string fixed at both ends, what is the condition for producing stationary waves?
44. What is the distance between a node and an adjacent antinode in a stationary wave?
45. What is the distance between two consecutive antinodes in a stationary wave?
46. What is the distance between two consecutive nodes in a stationary wave?
47. In a stationary wave, what is the point called where the amplitude of oscillation is minimum (ideally zero)?
48. In a stationary wave, what is the point called where the amplitude of oscillation is maximum?
49. If two waves of the same frequency and amplitude travel in opposite directions, what phenomenon occurs?
50. 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?