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#amplitude

48 public questions tagged with this topic.

What determines the intensity of light in the wave picture?

**Refractive index** n = c/v, c=3×10⁸ m/s vacuum, v speed in medium, for v=2.25×10⁸ m/s n=3/2.25=1.33, for v=1.8×10⁸ n=1.67, for n=1.3 v=3×10⁸/1.3=2.31×10⁸ m/s, for n=1.6 v=1.875×10⁸ m/s, for n=1.2 λ_medium = λ_vacuum/n =600/1.2=500 nm, for n=1.75 λ=700/1.75=400 nm, for n=1.5 λ=750/1.5=500 nm, wavelength in medium λ' = λ/n. In the wave picture, intensity is proportional to the square of the amplitude of the wave. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives Square of the amplitude, illustrating interference, dif

Ref: NCERT > Physics Book > Wave Optics > Refraction, Refractive Index and Critical Angle

What is the resultant amplitude when two coherent waves of amplitude \( a \) interfere with a phase difference of \( \pi

**Superposition principle** resultant displacement sum of individual, for two coherent waves amplitude a each, resultant amplitude A = √(a² + a² +2a² cosφ)=2a|cos(φ/2)|, phase difference φ, path difference Δ = (φ/2π)λ, for φ=π/2 A=√2 a, for φ=6π cos3π=-1? Actually φ=6π cos3π? A=2a|cos3π|=2a, for φ=4π A=2a, intensity I ∝ A², maximum I_max=4I₀ when φ=0, I=2I₀(1+cosφ)=4I₀ cos²(φ/2). Resultant amplitude A = 2a cos(Φ/2) . For Φ = π , A = 2a cos(π/2) = 2a × 0 = 0 . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' =

Ref: NCERT > Physics Book > Wave Optics > Superposition, Resultant Amplitude and Intensity

What is the resultant amplitude of two coherent waves of amplitude \( a \) with a phase difference of \( 3\pi \)?

**Phase difference** corresponding to path difference Δ, φ =2π Δ/λ, for Δ=5λ/8 φ=5π/4, for Δ=9λ/4 φ=9π/2, for Δ=λ path difference φ=2π constructive, but for destructive condition path difference λ can be destructive if one reflection introduces π phase shift, resultant amplitude zero when φ=(2n+1)π. Resultant amplitude A = 2a cos(Φ/2) . For Φ = 3π , A = 2a cos((3π/2)) = 2a × 0 = 0 . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives 0, illustrating interference, diffraction and polarization principles.

Ref: NCERT > Physics Book > Wave Optics > Superposition, Resultant Amplitude and Intensity

What is the resultant amplitude of two coherent waves of amplitude \( a \) with a phase difference of \( 6\pi \)?

**Phase difference** corresponding to path difference Δ, φ =2π Δ/λ, for Δ=5λ/8 φ=5π/4, for Δ=9λ/4 φ=9π/2, for Δ=λ path difference φ=2π constructive, but for destructive condition path difference λ can be destructive if one reflection introduces π phase shift, resultant amplitude zero when φ=(2n+1)π. Resultant amplitude A = 2a cos(Φ/2) . For Φ = 6π , A = 2a cos(3π) = 2a × (-1) = -2a , magnitude 2a . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives

Ref: NCERT > Physics Book > Wave Optics > Superposition, Resultant Amplitude and Intensity

What is the amplitude of the resultant wave when two coherent waves of amplitude \( a \) interfere with a phase differen

**Phase difference** corresponding to path difference Δ, φ =2π Δ/λ, for Δ=5λ/8 φ=5π/4, for Δ=9λ/4 φ=9π/2, for Δ=λ path difference φ=2π constructive, but for destructive condition path difference λ can be destructive if one reflection introduces π phase shift, resultant amplitude zero when φ=(2n+1)π. Resultant amplitude A = 2a cos(Φ/2) . For Φ = π/2 , A = 2a cos(π/4) = 2a × (√(2)/2) = a√(2) . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives a√(2), illustrating interference, diffraction and polarization principles.

Ref: NCERT > Physics Book > Wave Optics > Superposition, Resultant Amplitude and Intensity

A coil is placed in a magnetic field that oscillates rapidly. The induced emf is higher when what property of the field

**Flux change example** coil 150 turns area 0.06 m² B 0.14 T drops to zero in 0.3 s, ΔΦ = B A =0.14×0.06=0.0084 Wb per turn, ΔΦ/Δt=0.028 Wb/s, e=150×0.028=4.2 V, illustrating calculation from B and area. The induced emf depends on the rate of change of magnetic flux ( ε = -(dΦ/dt) ), which increases with the frequency of oscillation of the magnetic field. Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt) and U = ½ L I², result Frequency of oscillation

Ref: NCERT > Physics Book > Electromagnetic Induction > Magnetic Flux and Faraday's Laws of Induction

An electromagnetic wave in vacuum has a magnetic field amplitude of \( B_0 = 2 \times 10^{-8} \, \text{T} \). What is th

**Energy in EM wave** equally divided between electric and magnetic fields, energy density u = ½ ε₀ E² + B²/(2μ₀) = ε₀ E² = B²/μ₀, average u_avg = ½ ε₀ E₀², intensity I = c u_avg = ½ c ε₀ E₀² = E₀ B₀/(2μ₀) = c B₀²/(2μ₀), radiation pressure p = I/c for absorption, 2I/c for reflection. Using E₀ = B₀ c , we have E₀ = (2 × 10⁻⁸) × (3 × 10⁸) = 6 V/m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 6 V/m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Energy, Intensity and Momentum of EM Waves

A spring system has \( m = 1.0 \, \text{kg}, k = 400 \, \text{N/m}, A = 6 \, \text{cm} \). What is the potential energy

**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. Potential energy: U = (1/2) k x² . k = 400 N/m, x = 0.03 m . U = 0.5 × 400 × (0.03)² = 0.5 × 400 × 0.0009 = 0.18 J . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.18 J follows, reflecting SHM

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

A mass of \( 2.0 \, \text{kg} \) on a spring with \( k = 800 \, \text{N/m} \) has \( A = 5 \, \text{cm} \). What is the

**Damped oscillations** occur when resistive forces dissipate energy, amplitude decays exponentially as A(t) = A₀ e^(-b t/2m), b damping coefficient (kg/s), frequency slightly reduced ω' = √(ω₀² - (b/2m)²). Damping arises from friction or viscosity, energy loss per cycle proportional to velocity squared, motion eventually stops. Total energy: E = (1/2) k A² = 0.5 × 800 × (0.05)² = 1 J . Potential energy: U = (1/2) k x² = 0.5 × 800 × (0.025)² = 0.25 J . Kinetic energy: K = E - U = 1 - 0.25 = 0.75 J . Applying x = A cos(ωt + φ), v = -ωA

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

A mass of \( 0.5 \, \text{kg} \) on a spring has \( E = 2 \, \text{J} \) at \( A = 20 \, \text{cm} \). What is the sprin

**Damped oscillations** occur when resistive forces dissipate energy, amplitude decays exponentially as A(t) = A₀ e^(-b t/2m), b damping coefficient (kg/s), frequency slightly reduced ω' = √(ω₀² - (b/2m)²). Damping arises from friction or viscosity, energy loss per cycle proportional to velocity squared, motion eventually stops. Total energy: E = (1/2) k A² . 2 = (1/2) k (0.2)² ⇒ 2 = 0.02 k ⇒ k = (2/0.02) = 100 N/m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 100 N/m follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

A spring of \( k = 200 \, \text{N/m} \) has a \( 0.5 \, \text{kg} \) mass. If \( E = 1 \, \text{J} \), what is the ampli

**Real oscillators** experience damping, amplitude decreasing with time. Critical damping returns to equilibrium fastest without oscillation, overdamping slows return, underdamping shows decaying oscillations, classification based on b relative to 2mω₀, important for practical systems. Total energy: E = (1/2) k A² . 1 = (1/2) × 200 × A² ⇒ 1 = 100 A² ⇒ A² = 0.01 ⇒ A = 0.1 m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.1 m follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

Which feature of SHM explains why two particles with identical amplitude and frequency may not reach their extreme posit

**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. Different phase constants ( Φ ) shift the oscillation cycles, causing particles to reach extremes at different times despite equal amplitude and frequency. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result Difference in phase constants follows, reflecting SHM

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations