Superposition, standing waves and harmonics - One Line Questions
1.
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? —
π
2.
A wave pulse traveling on a string reflects off a fixed end. What is the phase change of the reflected pulse? —
180 degrees (π radians)
3.
A wave pulse traveling on a string reflects off a free end. What is the phase change of the reflected pulse? —
0 degrees (no phase change)
4.
When a string fixed at both ends vibrates in its third harmonic, how many nodes are present along the string (excluding the fixed ends)? —
2
5.
When a string fixed at both ends vibrates in its fundamental mode, how many antinodes are present along the string? —
1
6.
In an open organ pipe, the second harmonic has a frequency that is how many times the fundamental frequency? —
2 times
7.
In a closed organ pipe, the third harmonic has a frequency that is how many times the fundamental frequency? —
3 times
8.
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? —
2:1
9.
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? —
4L
10.
When two waves with amplitudes A1 and A2 interfere constructively, what is the maximum possible resultant amplitude? —
A1 + A2
11.
When two waves with amplitudes A1 and A2 interfere destructively, what is the minimum possible resultant amplitude? —
A1 - A2
12.
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? —
13.
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? —
Increase
14.
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? —
f, 2f, 3f, ...
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? —
f, 2f, 3f, ...
16.
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? —
f, 3f, 5f, ...
17.
The frequency of the nth harmonic for a string fixed at both ends is given by fn. If the fundamental frequency is f1, then: —
fn = n f1
18.
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? —
Third harmonic (second overtone)
19.
If a string vibrates in 5 segments (loops), what is the mode of vibration? —
Fifth harmonic
20.
If a closed organ pipe resonates at frequencies f, 3f, 5f, ..., what are these frequencies called? —
Overtones
21.
If an open organ pipe resonates at frequencies f, 2f, 3f, ..., what are these frequencies called? —
Harmonics
22.
If two waves of the same frequency and amplitude travel in opposite directions, what phenomenon occurs? —
Stationary waves
23.
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? —
2L/3
24.
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? —
L = nλ/2
25.
For a closed organ pipe of length L, what is the condition for producing stationary waves (resonance)? —
L = (2n-1)λ/4
26.
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)? —
L = λ/4
27.
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? —
Length L = nλ/2
28.
What happens to the amplitude of oscillation of particles at nodes in a stationary wave? —
Minimum (zero)
29.
What happens to the amplitude of oscillation of particles at antinodes in a stationary wave? —
Maximum
30.
When two identical waves travel in opposite directions, they form stationary waves. What is the net displacement of particles at the nodes? —
Minimum (zero)
31.
In a stationary wave, what is the point called where the amplitude of oscillation is maximum? —
Antinode
32.
In a stationary wave, what is the point called where the amplitude of oscillation is minimum (ideally zero)? —
Node
33.
In a stationary wave, energy is stored in the medium. Where is the energy concentrated? —
Antinodes
34.
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: —
Linear
35.
The second harmonic for a string fixed at both ends corresponds to a vibration pattern with how many antinodes? —
Two
36.
The third harmonic for a string fixed at both ends corresponds to a vibration pattern with how many nodes (excluding the fixed ends)? —
Two
37.
What is the condition for destructive interference between two waves of the same frequency? —
Phase difference = (2n+1)π, where n is an integer
38.
What is the condition for constructive interference between two waves of the same frequency? —
Path difference = nλ, where n is an integer
39.
The phenomenon where the vibration of one body causes another body to vibrate with a large amplitude is called: —
Resonance
40.
For a string fixed at both ends, what is the condition for producing stationary waves? —
The length of the string must be an integer multiple of λ/2
41.
The phenomenon of superposition applies to which type of waves? —
Both transverse and longitudinal waves
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? —
v/(2L)
43.
What is the distance between two consecutive nodes in a stationary wave? —
Half wavelength (λ/2)
44.
What is the distance between two consecutive antinodes in a stationary wave? —
Half wavelength (λ/2)
45.
What is the distance between a node and an adjacent antinode in a stationary wave? —
Quarter wavelength (λ/4)
46.
Consider the superposition of two waves y1 = A sin(ωt) and y2 = A sin(ωt + π/2). The resultant wave is: —
y = √2 A sin(ωt + π/4)
47.
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? —
Twice the amplitude of one wave
48.
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? —
Zero
49.
For a string of length L fixed at both ends, the wavelength of the nth harmonic is given by: —
λn = 2L/n
50.
The relationship between phase difference (φ) and path difference (Δx) for two waves is given by: —
φ = (2π/λ) Δx