Standing Waves: Strings and Pipes

Physics
Class 11
3D model
English · Hindi

Standing Waves: Strings and Pipes: a 3D model for Class 11 Physics, covering A pulse reflected from a fixed end comes back inverted; two pulses crossing add point by point (superposition)., Two identical waves travelling opposite ways make a standing wave: nodes never move, antinodes swing most., On a string fixed at both ends L = nλ/2, so the frequencies are v/2L, 2v/2L, 3v/2L …: all the harmonics., The fundamental has one loop between the two end nodes; the nth harmonic has n loops and n times the frequency., A pipe closed at one end has a displacement node at the closed end and an antinode at the open end: L = (2n − 1)λ/4..

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Also called

standing waves · stationary waves · nodes and antinodes · harmonics · overtones · fundamental frequency · string fixed at both ends · closed organ pipe · open organ pipe · odd harmonics · resonance tube · speed of sound · superposition of waves · reflection of a pulse · sonometer · Melde's experiment · end correction · अप्रगामी तरंग · निस्पंद · प्रस्पंद · अनुनाद नली

Topics

A pulse reflected from a fixed end comes back inverted; two pulses crossing add point by point (superposition).
Two identical waves travelling opposite ways make a standing wave: nodes never move, antinodes swing most.
On a string fixed at both ends L = nλ/2, so the frequencies are v/2L, 2v/2L, 3v/2L …: all the harmonics.
The fundamental has one loop between the two end nodes; the nth harmonic has n loops and n times the frequency.
A pipe closed at one end has a displacement node at the closed end and an antinode at the open end: L = (2n − 1)λ/4.
So a closed pipe sounds only the odd harmonics f, 3f, 5f …; an open pipe has antinodes at both ends and all harmonics.
In the resonance tube the air column rings loudly when its length is λ/4, and again at 3λ/4.
From the two lengths λ = 2(l₂ − l₁), and the speed of sound is v = fλ with f the frequency of the fork.
Neighbouring nodes are λ/2 apart; the antinode lies a little beyond the open end (the end correction).

About this model

A GLB file of about 704 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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