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#phase shift

9 public questions tagged with this topic.

Damped Oscillations

A particle’s displacement is \( x = 3 \cos (2\pi t - \frac{\pi}{4}) \) (in m). What is its velocity at \( t = 0.25 \, \t

**Effect of damping** is gradual amplitude reduction while period remains nearly constant for light damping. Mechanical energy decreases as work done against damping force, E(t) = ½ k A(t)² decaying exponentially, and motion ceases without external energy input, distinguishing from ideal undamped SHM. Velocity: v = -ω A sin (ω t + Φ) . A = 3 m, ω = 2π s⁻¹, Φ = -(π/4) . At t = 0.25 : 2π × 0.25 - (π/4) = (π/2) - (π/4) = (π/4) . v = -2π × 3 sin (π/4) = -6π × (√(2)/2) ≈ -13.32 m/s . Applying x = A cos(ωt + φ),

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

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Energy in SHM - Kinetic, Potential and Total

A particle’s displacement is \( x = 4 \cos (3\pi t + \frac{\pi}{6}) \) (in m). What is its velocity at \( t = 0 \, \text

**Conservation of mechanical energy** in undamped SHM implies total energy proportional to amplitude squared A² and spring constant k. E = ½ k A² allows amplitude determination from known E and k via A = √(2E/k), with k = m ω² linking dynamical and energetic descriptions for spring-mass system. Velocity: v = -ω A sin (ω t + Φ) . A = 4 m, ω = 3π s⁻¹, Φ = (π/6) . At t = 0 : v = -3π × 4 sin (π/6) = -12π × 0.5 ≈ -18.84 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ),

Ref: NCERT > Physics Book > Oscillations > Energy in SHM - Kinetic, Potential and Total

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Doppler Effect

Two waves \( y_1 = 3 \sin (8x - 16t) \) and \( y_2 = 3 \sin (8x - 16t + \frac{2\pi}{3}) \) interfere. What is the amplit

**Doppler effect** describes apparent frequency shift due to relative motion between source and observer, f' = f·v/(v ∓ v_s) for source motion, f' = f·(v ± v_o)/v for observer motion, upper signs for approach increasing observed frequency. Motion towards observer compresses wavelength raising f'. Amplitude: A = 2a cos (Φ/2) , a = 3 m , Φ = (2π/3) . A = 2 × 3 cos (π/3) = 6 × (1/2) = 3 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Superposition and Interference of Waves

Two waves \( y_1 = 5 \sin (7x - 14t) \) and \( y_2 = 5 \sin (7x - 14t + \frac{\pi}{2}) \) interfere. What is the amplitu

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. Amplitude: A = 2a cos (Φ/2) , a = 5 m , Φ = (π/2) . A = 2 × 5 cos (π/4) = 10 × (1/√(2)) ≈ 7.07 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 7 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Superposition and Interference of Waves

Two waves \( y_1 = 5 \sin (6x - 12t) \) and \( y_2 = 5 \sin (6x - 12t + \frac{\pi}{3}) \) interfere. What is the amplitu

**Interference of waves** produces enhancement or cancellation based on phase. Two equal amplitude waves out of phase by π cancel completely, A = 0, while in-phase superposition doubles amplitude to 2a, demonstrating energy redistribution without violation of conservation. Amplitude: A = 2a cos (Φ/2) , a = 5 m , Φ = (π/3) . A = 2 × 5 cos (π/6) = 10 × (√(3)/2) = 5√(3) ≈ 8.66 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 8.7 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Superposition and Interference of Waves

Two waves \( y_1 = 6 \sin (4x - 12t) \) and \( y_2 = 6 \sin (4x - 12t + \pi) \) interfere. What is the amplitude of the

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. Amplitude: A = 2a cos (Φ/2) , a = 6 m , Φ = π . A = 2 × 6 cos (π/2) = 12 × 0 = 0 m (destructive interference). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Sound Waves, Reflection and Characteristics

A wave \( y = 0.08 \sin (10x - 30t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

**Reflection at boundaries** follows phase change rules: rigid boundary (fixed end) introduces π phase shift, inverting displacement y → -y, while free boundary reflects without phase change. Reflected wave derived by reversing propagation direction kx → -kx and applying phase shift, preserving k = 2π/λ and ω = 2πf. At rigid boundary, phase changes by π . Incident: y_i = 0.08 sin (10x - 30t) . Reflected: y_r = -0.08 sin (10x + 30t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.08 sin (10x + 30t), illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

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PHYSICS

In a purely inductive AC circuit, the current lags the voltage by what phase angle?

For a pure inductor, i = i_m sin (omega t - π/2), while v = v_m sin omega t . Phase difference: phi = -π/2, meaning current lags voltage by π/2 or 90° .

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Wave Optics, Topic: Interference, phase difference φ = (2π/λ)Δ, path difference 7λ/4 and double-slit experiment. The section explains definitions, governing laws, formulas like μ₀ = 4π × 10⁻⁷ T·m/A, units and illustrative examples.

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PHYSICS

What is the phase difference corresponding to a path difference of 7lambda/4 in a double-slit experiment?

Given: What is the phase difference corresponding to a path difference of 7lambda/4 in a double-slit experiment? These values define the system as per NCERT data. Formula: Phase difference phi = 2π/lambda Δ. This is standard NCERT relation. Substitution & Calculation: For Δ = 7lambda/4, phi = 2π/lambda · 7lambda/4 = 7π/2 . Result: The computed value matches expected outcome and confirms correct choice as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Wave Optics, Topic: Interference, phase difference φ = (2π/λ)Δ, path difference 7λ/4 and double-slit experiment. The section explains definitions, governing laws, formulas like μ₀ = 4π × 10⁻⁷ T·m/A, units and illustrative examples.

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