#wave amplitude

Electromagnetic Spectrum - Radio Waves and Microwaves

The amplitude of the electric field in an electromagnetic wave is \( E_0 = 120 \, \text{V/m} \). What is the amplitude o

**Hertz experiment** produced radio waves using spark gap LC oscillator, detected with loop antenna, confirming Maxwell's prediction, frequency ≈10⁸ Hz, wavelength ≈3 m, demonstrating EM waves travel at c, transverse, can be reflected, refracted, polarized. Using B₀ = (E₀/c) , we have B₀ = (120/3 × 10⁸) = 4 × 10⁻⁷ T . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 4 × 10⁻⁷ T, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Electromagnetic Spectrum - Radio Waves and Microwaves

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Superposition and Interference of Waves

A wave on a string has an amplitude of 0.015 m and a frequency of 40 Hz. What is the maximum transverse speed of a parti

**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. ω = 2π v = 2π × 40 = 80π rad/s . Max speed: vₘₐₓ = a ω = 0.015 × 80π ≈ 3.77 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3.8 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Wave Equation and Displacement Relation

A wave on a string has an amplitude of 0.02 m and a period of 0.01 s. What is the maximum transverse speed of a particle

**Wave equation** y(x,t) = A sin(kx - ωt + φ) describes displacement of progressive harmonic wave, where k = 2π/λ wave number (rad/m), ω = 2πf angular frequency (rad/s), v = ω/k wave speed (m/s). Sign of ωt indicates direction, amplitude A is maximum displacement. ω = (2π/T) = (2π/0.01) = 200π rad/s . Max speed: vₘₐₓ = a ω = 0.02 × 200π ≈ 12.57 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 12.6 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Transverse and Longitudinal Waves

A wave has an amplitude of 0.05 m and frequency of 15 Hz. What is the maximum transverse acceleration of a particle?

**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. ω = 2π v = 2π × 15 = 30π rad/s . Max acceleration: aₘₐₓ = a ω² = 0.05 × (30π)² . aₘₐₓ = 0.05 × 900π² ≈ 4441 m/s² . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 4440 m/s², illustrating frequency-length-speed interdependen

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

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Transverse and Longitudinal Waves

A wave on a string has an amplitude of 0.03 m and a frequency of 25 Hz. What is the maximum transverse speed of a partic

**Nature of wave** determines energy transfer mechanism. Longitudinal nature of sound explains propagation through fluids with density variations carrying energy, unlike transverse waves needing rigidity for restoring force. ω = 2π v = 2π × 25 = 50π rad/s . Max speed: vₘₐₓ = a ω = 0.03 × 50π ≈ 4.71 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 4.7 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Superposition and Interference of Waves

What happens to the amplitude of two identical waves undergoing destructive interference when their phase difference is

**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. For two identical waves with phase difference Φ = π , the resultant amplitude is A = 2a cos(Φ/2) = 2a cos(π/2) = 0 , leading to complete cancellation. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Becomes zero, illustrating frequency-length-sp

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

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