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NEB Class 12 Physics Wave Motion Note Handwritten in PDF
Progressive (Travelling) Waves
A progressive wave is a disturbance that carries energy through a medium from one point to another without transferring matter.
Characteristics of a progressive wave:
- Amplitude (A): Maximum displacement of particles
- Frequency (f): Number of complete oscillations per second
- Time period (T): Time for one complete oscillation, T = 1/f
- Wavelength (Ξ»): Distance between two consecutive points in the same phase
- Wave speed (v): Speed of energy propagation, v = fΞ»
Mathematical Description of a Progressive Wave
The displacement of a particle at position x and time t for a wave moving in +x direction:
y = A sin(Οt β kx)
Where:
- Ο = 2Οf (angular frequency, rad/s)
- k = 2Ο/Ξ» (wave number or angular wave number, rad/m)
- Wave speed: v = Ο/k = fΞ»
For a wave moving in βx direction: y = A sin(Οt + kx)
Phase difference between two points separated by distance Ξx: ΞΟ = kΞx = (2Ο/Ξ»)Ξx
How to extract parameters from a wave equation:
- If y = 5 sin(6Οt β 2Οx):
- A = 5 m, Ο = 6Ο rad/s, k = 2Ο rad/m
- f = Ο/2Ο = 3 Hz, Ξ» = 2Ο/k = 1 m, v = f Ξ» = 3 m/s
This type of question β extract all parameters from a given equation β appears regularly in NEB board exams.
Stationary (Standing) Waves
When two identical progressive waves travel in opposite directions:
- yβ = A sin(Οt β kx)
- yβ = A sin(Οt + kx)
Their superposition gives: y = 2A cos(kx) sin(Οt)
This is a stationary wave. The amplitude at each point is 2A|cos(kx)| β it varies with position but not with time.
Nodes: Points where cos(kx) = 0 β displacement always zero β no movement ever
- Positions: x = Ξ»/4, 3Ξ»/4, 5Ξ»/4…
- Spacing between consecutive nodes = Ξ»/2
Antinodes: Points where |cos(kx)| = 1 β maximum amplitude 2A
- Positions: x = 0, Ξ»/2, Ξ», 3Ξ»/2…
- Antinodes lie midway between nodes
Comparison: Progressive vs Stationary Waves
| Feature | Progressive Wave | Stationary Wave |
|---|---|---|
| Energy transfer | Yes energy flows | No β energy stored |
| Amplitude | Same for all particles | Varies (0 at nodes, max at antinodes) |
| Phase | Different for each particle | Same for all particles between two nodes |
| Waveform | Moves forward | Appears stationary |
| Nodes | None | Present at fixed positions |
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Frequently Asked Questions
What is progressive wave in Class 12 Physics?
A progressive wave transfers energy through a medium without transferring matter. Key parameters: amplitude (A), frequency (f), wavelength (Ξ»), time period (T=1/f), and wave speed (v=fΞ»). Sound waves in air, water ripples, and seismic waves are all examples of progressive mechanical waves.
What is the equation of progressive wave Class 12?
Progressive wave moving in +x direction: y = A sin(Οt β kx). Here Ο = 2Οf is angular frequency and k = 2Ο/Ξ» is wave number. Wave speed v = Ο/k = fΞ». For βx direction: y = A sin(Οt + kx). Extracting all parameters from a given wave equation is a regular NEB exam question.
What is a stationary wave and how is it formed?
Stationary wave forms when two identical progressive waves travel in opposite directions and superpose. The equation is y = 2A cos(kx) sin(Οt). No energy is transferred energy is stored between nodes and antinodes. Stationary waves form in musical instruments including strings, flutes, and organ pipes.
What is the difference between nodes and antinodes?
Nodes are points where displacement is always zero β the two waves cancel completely at these points. Antinodes are points of maximum displacement 2A where the waves reinforce completely. Adjacent nodes are separated by Ξ»/2. Each antinode lies exactly midway between two consecutive nodes in a stationary wave.
What is phase difference between two points in a wave?
Phase difference ΞΟ = (2Ο/Ξ») Γ path difference = k Γ Ξx. Two points separated by one full wavelength Ξ» are completely in phase (ΞΟ = 2Ο). Points separated by Ξ»/2 are in anti-phase (ΞΟ = Ο). In a stationary wave all particles between two nodes are always in phase with each other.
What is the difference between progressive and stationary waves?
Progressive wave: all particles have same amplitude, different phases, energy transfers forward. Stationary wave: amplitude varies from zero at nodes to 2A at antinodes, all particles between nodes are in phase, no energy transfer. Progressive waves travel; stationary waves appear fixed in position.
How do you find wave speed from wave equation Class 12?
From y = A sin(Οt β kx): wave speed v = Ο/k. Alternatively v = fΞ», where f = Ο/2Ο and Ξ» = 2Ο/k. If equation is y = A sin(2Οt/T β 2Οx/Ξ»), then v = Ξ»/T = fΞ». Always identify Ο and k values first, then divide to get wave speed for NEB numerical problems.
Which wave motion topics are most important for NEB 2082?
Most important: mathematical equation of progressive wave and extracting parameters (4 marks), formation of stationary waves (2 marks), differences between progressive and stationary waves (2 marks), and phase difference calculation. Wave equation numericals appear regularly in NEB Class 12 Physics board exam papers.
