#wave frequency

Wave Properties, Frequency and Energy Conservation

What is the effect on the energy of a light wave when its speed decreases in a denser medium?

**Intensity not depend on speed** when enters denser medium because intensity I ∝ n E₀²? Actually Poynting vector S = E×H, energy density u =½ ε E², for same amplitude E₀ intensity proportional to n, but amplitude changes at interface due to reflection, total energy conserved incident = reflected + transmitted, interference does not destroy energy, it redistributes. Energy of a light wave depends on its amplitude, not its speed, so it remains unchanged when speed decreases. 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

Ref: NCERT > Physics Book > Wave Optics > Wave Properties, Frequency and Energy Conservation

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Ultraviolet, X-rays, Gamma Rays and Their Properties

An electromagnetic wave travels in vacuum with frequency \( 10 \, \text{MHz} \). What is its wavelength? (Given \( c = 3

**X-rays in medicine** treat certain cancers because high-energy photons ionize and damage DNA of malignant cells, also imaging because bones absorb more than tissue, contrast. Gamma rays from Co-60 used for radiotherapy, energy ≈1.17 and 1.33 MeV, highly penetrating. Using v λ = c , we have λ = (c/v) = (3 × 10⁸/10 × 10⁶) = 30 m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 30 m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Ultraviolet, X-rays, Gamma Rays and Their Properties

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Wave Equation and Displacement Relation

A wave is described by \( y(x, t) = 0.01 \sin (40x - 80t) \), where \( x \) and \( y \) are in meters and \( t \) in sec

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. Compare with y = a sin (kx - ω t) , ω = 80 rad/s . Frequency: v = (ω/2π) = (80/2π) ≈ 12.73 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 13 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Beats Phenomenon

Two strings produce beats of 3 Hz. One has a frequency of 288 Hz. When the tension in the second string is increased, th

**Beat formation** is interference in time with time-varying amplitude. Frequencies close together generate slow modulation, count in given duration obtained by multiplying beat frequency by duration, e.g., 6 Hz × 5 s = 30 beats. Let v₂ be the original frequency. |288 - v₂| = 3 ⇒ v₂ = 285 Hz or 291 Hz . Increasing tension increases frequency. If v₂ = 285 , new v₂’ > 285 , beat = 288 - v₂’ < 3 , becomes 1 Hz ( v₂’ = 287 ), consistent. If v₂ = 291 , beat increases, contradicts. So, v₂ = 285 Hz . Using v = fλ and

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Wave Equation and Displacement Relation

A wave is described by \( y(x, t) = 0.03 \sin (50x - 200t) \), where \( x \) and \( y \) are in meters and \( t \) in se

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. Compare with y = a sin (kx - ω t) . ω = 200 rad/s . Frequency: v = (ω/2π) = (200/2π) ≈ 31.8 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 32 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Wave Equation and Displacement Relation

A wave is described by \( y(x, t) = 0.06 \sin (15x - 45t) \), where \( x \) and \( y \) are in meters and \( t \) in sec

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. Compare with y = a sin (kx - ω t) , ω = 45 rad/s . Frequency: v = (ω/2π) = (45/2π) ≈ 7.16 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 7.2 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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