Superposition, Standing Waves and Harmonics
Overlapping waves add displacement by displacement; two identical counter-propagating waves form a standing wave with fixed nodes and antinodes.
What is Superposition, Standing Waves and Harmonics?
Overlapping waves add displacement by displacement; two identical counter-propagating waves form a standing wave with fixed nodes and antinodes.
Key formula / rule: Node separation = λ/2.
Key points
- Derive the harmonic frequencies of strings and air columns.
- Analyse a resonance experiment to determine the speed of sound.
Common exam trap
Using the open-pipe series for a closed pipe.
Definitions
- Term
Superposition, Standing Waves and Harmonics
- Meaning
Overlapping waves add displacement by displacement; two identical counter-propagating waves form a standing wave with fixed nodes and antinodes.
- Term
Superposition, Standing Waves and Harmonics — explanation
- Meaning
Boundary conditions select which frequencies survive, giving the harmonic series of a string or an air column. This is why an open pipe supports all harmonics but a closed pipe supports only odd ones.
Learning objectives
Derive the harmonic frequencies of strings and air columns.
Analyse a resonance experiment to determine the speed of sound.
Formulae
- Key point
Node separation = λ/2.
- Key point
String and open pipe: fn = n v/2L; closed pipe: fn = (2n-1) v/4L.
- Key point
Standing waves transport no net energy.
Prerequisites
PHY-U4-WAV-T1-S1-C1
Common mistakes
Using the open-pipe series for a closed pipe.
Confusing node and antinode positions at boundaries.
Keywords
Superposition
Standing
Waves
Harmonics
Practice preview
What does the principle of superposition state regarding two or more waves simultaneously passing through the same region?…
easy
Two harmonic waves, y1 = A sin(kx - omega t) and y2 = A sin(kx - omega t + phi), superimpose. What is the amplitude of the resultant wave if phi = pi/2?…
medium
Which of the following statements is true for a standing wave?…
easy