Waves 1.3 Flashcards
(25 cards)
Principle of Superposition
When two or more waves meet travelling in the same medium, the resultant displacement of the particles in the medium is the algebraic sum of the displacements due to the separate waves
After pulses passed through each other they continue unaffected
Interference
The interaction of waves undergoing superposition
Constructive Interference
Occurs when waves meet and have displacements in the same direction
Results in a net increase in the amplitude (energy content) of the wave
Destructive Interference
Occurs when waves with opposite displacements merge
Results in a net decrease in the amplitude (energy content) of the way
Beats
When waves with slightly different frequencies superpose the resultant interference gives rise to periodic variations in amplitude or loudness (beats)
In phase –> constructively interfere
Out of phase –> destructively interfere
Beat Frequency
The number of beats that occur each second
- The difference between the frequencies of the component waves
Standing Waves
Formed by the interference of two coherent waves travelling in opposite directions
Coherent Waves
Waves that remain in phase both in time and space
Characteristics of a Standing Wave
- Resulting standing wave does not progress in either direction
- Are an interference pattern
- Positions occur where there is no movement and particles are at rest –> Nodes
- Particle amplitude increases away from nodes and is at a max midway between nodes –> Antinodes
- Distance between successive nodes/antinodes is 𝜆/2
- Movement of particles and energy of wave are confined to regions between successive nodes
- Phase of all particles between adjacent nodes is the same
- Particles in adjacent segments are 180 out of phase
Interference from Two Coherent Point Sources
Superposition of the circular wave front results in the formation of lines along which constructive interference occurs (Antinodal lines)
Midway between antinodal lines destructive interference occurs resulting in the formation of nodal lines
Path Difference (Definition)
The difference in the distances travelled by the two waves from their sources to a certain point
Path Difference
For any point on the antinodal line (A1) - PD = 𝜆
- Interfering waves are always in phase
For all point on antinodal line (A0) - PD = 0
- Interfering waves are also in phase for all points on this line
For any point of maximum amplitude: P.D = n 𝜆
For any point on a nodal line
- Interfering waves are 180 out of phase
- Annulment occurs
For any point of minimum amplitude : P.D = (n-0.5) 𝜆
Free Vibrations
When particles oscillate freely
Damping: Amplitude of waves will decrease as it lose energy to its surroundings
- Unless supplied with energy from external source
Forces Vibrations
Occurs when a body or system is set into vibration by impulses received from another external vibrating force
Resonance
Occurs when the driver frequency is equal to the natural frequency of the system
Closer the frequencies –> Greater the amplitude of forced vibration
Transfer of energy between driver and system most efficient when resonance occurs
- Energy of system increase to a max
- System acquires high amplitude of vibration
Examples of Resonance
- Push given to child’s swing must be equal to its natural frequency
- Glasses may break if frequency of sound equals natural frequency
- Soldiers normally break step when crossing suspension bridge
- Resonance in strings and open pipes
Overtones and Harmonics
Oscillating systems have one or more modes of vibration
- Resonant frequencies depend on physical nature and dimensions of the system (boundary conditions)
Fundamental Frequency
The lowest frequency at which a system will resonate
- Will be vibrating in its first/fundamental mode of vibration
Overtones
The allowed resonant modes of vibration above the fundamental
For stringed instrument resonant frequencies occur at integral multiples of the fundamental (harmonics)
Harmonics
The integral multiples of the fundamental frequency
Resonant Modes of Vibration
- For strings an open pipes - overtones occur at all harmonics
- For closed pipes - overtones occur only at odd armonics
Organ Pipes - Resonating Air Columns
Open pipes
Pressure waves reflected 180 out of phase with incident waves –> pressure node at each end
Antinodes –> Max pressure variation
Maximum particle vibrations occur at open ends (antinodes)
Zero displacement midway between (nodes)
Resonant Modes of Vibration
Boundary conditions for closed pipe is that particle node forms at one end and antinode forms at other
Open pipe has particle antinode at both ends
Resonant Modes of Vibration (Closed Pipe)
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