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#antinode

3 public questions tagged with this topic.

Beats Phenomenon

A stationary wave is given by \( y = 0.05 \sin (\frac{\pi x}{2}) \cos (100\pi t) \), where \( x \) and \( y \) are in me

**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. Form: y = A sin (kx) cos (ω t) , k = (π/2) rad/m . Wavelength: λ = (2π/k) = (2π/(π/2)) = 4 m . Distance between node and antinode: (λ/4) = (4/4) = 1 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Stationary Waves and Standing Waves in Strings

A stationary wave is given by \( y = 0.08 \sin (\frac{\pi x}{3}) \cos (60\pi t) \), where \( x \) and \( y \) are in met

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. Form: y = A sin (kx) cos (ω t) , k = (π/3) rad/m . Wavelength: λ = (2π/k) = (2π/(π/3)) = 6 m . Distance between node and antinode: (λ/4) = (6/4) = 1.5 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1.5 m, illustrating frequency-length-speed interdepen

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 transverse wave, what is the relationship between particle velocity and wave velocity at an antinode of a standing

**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. At an antinode, particle displacement is maximum, oscillating perpendicular to wave propagation. Particle velocity (rate of displacement change) is perpendicular to wave velocity (along the string). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields They are perpendicular, illustrating frequency-length-speed interdependence and q

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

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