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Question
Answer briefly.
Explain what is meant by phase of a wave.
Solution
- The state of the oscillation of a particle is called the phase of the particle.
- The displacement, direction of velocity, and oscillation number of the particle describe the phase of the particle at a place.
Displacement as a function of distance along the wave - Particles r and t (q and u or v and s) have the same displacements but the directions of their velocities are opposite.
- Particles having same magnitude of displacements and the same direction of velocity are said to be in phase during their respective oscillations. Example: particles v and p.
- Separation between two particles which are in phase is wavelength (λ).
- The two successive particles differ by ‘1’ in their oscillation number i.e., if particle v is at its nth oscillation, particle p will be at its (n +1)th oscillation as the wave is travelling along + X direction.
- In the given graph, if the disturbance (energy) has just reached the particle w, the phase angle corresponding to particle is 0°. At this instant, particle v has completed quarter oscillation and reached its positive maximum (sin θ = +1). The phase angle θ of this particle v is `pi^"c"/2` = 90° at this instant.
- Phase angles of particles u and q are π c (180°) and 2πc (360°) respectively.
- Particle p has completed one oscillation and is at its positive maximum during its second oscillation.
∴ phase angle = 2πc + `pi^"c"/2 = (5pi^"c")/2`. - v and p are the successive particles in the same state (same displacement and the same direction of velocity) during their respective oscillations. Phase angle between these two differs by 2πc.
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