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#phase relationship

2 public questions tagged with this topic.

Periodic Motion and SHM Basic Concepts

In SHM, what is the phase relationship between displacement and acceleration?

**Periodic motion** repeats after fixed period T, x(t+T)=x(t), while oscillatory motion involves to-and-fro about equilibrium. SHM is special periodic motion where restoring force proportional to displacement, F = -k x, acceleration a = -ω² x, leading to sinusoidal displacement x = A cos(ωt + φ). Displacement ( x = A cos (ω t + Φ) ) and acceleration ( a = -ω² A cos (ω t + Φ) ) are 180° ( π radians) out of phase, as acceleration is the negative of displacement. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² =

Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts

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Transverse and Longitudinal Waves

In a progressive wave, what is the phase relationship between two points separated by one full wavelength?

**Wave classification** depends on particle vibration relative to propagation. Longitudinal waves have particle oscillation parallel to propagation, creating compressions and rarefactions as in sound in air; transverse have perpendicular oscillation. Tuning fork generates longitudinal sound because air cannot sustain shear. For a progressive wave, phase difference Δ Φ = k Δ x , where k = (2π/λ) . If Δ x = λ , then Δ Φ = (2π/λ) × λ = 2π , meaning they are in phase. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields In phase, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Transverse and Longitudinal Waves

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