Skip to content
Login Register

#nodes and antinodes

2 public questions tagged with this topic.

Stationary Waves and Standing Waves in Strings

Why does the amplitude of a standing wave vary along its length?

**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. In a standing wave, interference of two opposite-traveling waves creates nodes (zero amplitude) and antinodes (maximum amplitude), causing spatial variation due to phase alignment. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Due to interference, illust

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

View Details
Stationary Waves and Standing Waves in Strings

Which condition must be satisfied for two waves to form a standing wave pattern?

**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. Standing waves form when two waves of the same frequency travel in opposite directions and interfere, typically due to reflection, creating nodes and antinodes. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Travel in opposite directions, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

View Details