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#wave relationship

3 public questions tagged with this topic.

Energy, Intensity and Momentum of EM Waves

An electromagnetic wave in vacuum has an electric field amplitude of \( 90 \, \text{V/m} \). What is the magnetic field

**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 B₀ = (E₀/c) , we have B₀ = (90/3 × 10⁸) = 3 × 10⁻⁷ T . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 3 × 10⁻⁷ T, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

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Stationary Waves and Standing Waves in Strings

What is the effect on a standing wave’s frequency if the length of the vibrating medium is halved?

**Standing wave in fixed string** has nodes at ends, quantizing modes. Fundamental n=1 has λ₁ = 2L, higher harmonics multiples of fundamental f₁. Third harmonic n=3 has three half-wavelengths in length L, f₃ = 3v/(2L), illustrating standing wave condition and boundary enforcement. For a standing wave, v_n = (n v/2L) . Halving the length L to L/2 gives v_n' = (n v/2 · (L/2)) = (n v/L) = 2 · (n v/2L) , doubling the frequency. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Doubles, illustrating frequency-length-speed interdependence and quantiza

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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Stationary Waves and Standing Waves in Strings

In a standing wave, what is the relationship between the wavelength and the distance between consecutive antinodes?

**Quantization due to boundaries** leads to discrete harmonic series. Frequency difference between harmonics is f₁, so f₃ - f₁ = 2f₁ = v/L. Understanding node-antinode pattern explains resonance and overtones in strings. In a standing wave, antinodes are points of maximum displacement, occurring every half wavelength. Thus, the distance between consecutive antinodes is λ/2 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Half the wavelength, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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