weirdfacts
Year 11 / Waves

Where waves meet.

When waves overlap, their displacements add. Equal in-phase waves reinforce; equal opposite displacements cancel momentarily. Reflections can create standing waves with fixed nodes and antinodes. Adjacent nodes are half a wavelength apart.

For a string fixed at both ends, allowed wavelengths satisfy L = nλ/2. Resonance produces a large response when a driving frequency approaches a natural frequency; damping limits the amplitude. Real measurements need uncertainty estimates and repeated trials before a model can be evaluated.

INTERACTIVE MODEL

A string fixed at both ends

READ THE GRAPH

Explore the relationship

A 1 m string. The graph is one maximum-displacement snapshot; nodes stay fixed as the string oscillates.

Displacement envelope / m-1-0.48750.0250.53751.0500.250.50.751Position / m
Displacement envelope / m

Tap or focus a plotted point to read its values.

View plotted data as a table
Explore the relationship
SeriesPosition / mDisplacement envelope / m
Displacement envelope / m00
Displacement envelope / m0.01666670.104528
Displacement envelope / m0.03333330.207912
Displacement envelope / m0.050.309017
Displacement envelope / m0.06666670.406737
Displacement envelope / m0.08333330.5
Displacement envelope / m0.10.587785
Displacement envelope / m0.1166670.669131
Displacement envelope / m0.1333330.743145
Displacement envelope / m0.150.809017
Displacement envelope / m0.1666670.866025
Displacement envelope / m0.1833330.913545
Displacement envelope / m0.20.951057
Displacement envelope / m0.2166670.978148
Displacement envelope / m0.2333330.994522
Displacement envelope / m0.251
Displacement envelope / m0.2666670.994522
Displacement envelope / m0.2833330.978148
Displacement envelope / m0.30.951057
Displacement envelope / m0.3166670.913545
Displacement envelope / m0.3333330.866025
Displacement envelope / m0.350.809017
Displacement envelope / m0.3666670.743145
Displacement envelope / m0.3833330.669131
Displacement envelope / m0.40.587785
Displacement envelope / m0.4166670.5
Displacement envelope / m0.4333330.406737
Displacement envelope / m0.450.309017
Displacement envelope / m0.4666670.207912
Displacement envelope / m0.4833330.104528
Displacement envelope / m0.51.22465e-16
Displacement envelope / m0.516667-0.104528
Displacement envelope / m0.533333-0.207912
Displacement envelope / m0.55-0.309017
Displacement envelope / m0.566667-0.406737
Displacement envelope / m0.583333-0.5
Displacement envelope / m0.6-0.587785
Displacement envelope / m0.616667-0.669131
Displacement envelope / m0.633333-0.743145
Displacement envelope / m0.65-0.809017
Displacement envelope / m0.666667-0.866025
Displacement envelope / m0.683333-0.913545
Displacement envelope / m0.7-0.951057
Displacement envelope / m0.716667-0.978148
Displacement envelope / m0.733333-0.994522
Displacement envelope / m0.75-1
Displacement envelope / m0.766667-0.994522
Displacement envelope / m0.783333-0.978148
Displacement envelope / m0.8-0.951057
Displacement envelope / m0.816667-0.913545
Displacement envelope / m0.833333-0.866025
Displacement envelope / m0.85-0.809017
Displacement envelope / m0.866667-0.743145
Displacement envelope / m0.883333-0.669131
Displacement envelope / m0.9-0.587785
Displacement envelope / m0.916667-0.5
Displacement envelope / m0.933333-0.406737
Displacement envelope / m0.95-0.309017
Displacement envelope / m0.966667-0.207912
Displacement envelope / m0.983333-0.104528
Displacement envelope / m1-2.44929e-16
Displacement envelope / m: 0

Explore: Change the harmonic number and count nodes and antinodes.

L=nλ2fn=nv2LL=\frac{n\lambda}{2}\qquad f_n=\frac{nv}{2L}
WORKED EXAMPLE

A 0.60 m string has wave speed 120 ms1\mathrm{m}\,\mathrm{s}^{-1}.

  1. Fundamental wavelength = 2L = 1.20 m.
  2. Fundamental frequency = 1201.20\frac{120}{1.20} = 100 Hz.
Assumed knowledge

Wave speed and frequency.

Learning checkpoints & sourceYOUR LEARNING CHECKPOINT
  • Apply superposition and identify standing waves.
  • Explain resonance and experimental uncertainty.
QCAA Physics · Unit 2 · Waves
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