(ADVANCED PHYSICS TOPIC)

If a stretched string is plucked or struck, stationary waves may be produced.

Since the velocity of the waves along the string remains constant, a change in frequency causes the wavelength to change and different modes of vibration arise.

As the ends are fixed in position, there must be a node at each end of the string.

In general we can see that the frequency for the n^th harmonic is given by:

 

 

All stringed instruments such as guitar, piano, violin are musical instruments that behave like a wave on a string.

Example

A wire is fixed at each end under tension. A transverse wave of speed 300 m s⁻¹ is propagated along the wire and forms a standing wave pattern. In a certain mode of vibration, it is found that the nodes are 0.40 m apart. What is the frequency of this standing wave? Distance between consecutive nodes = λ / 2                                                           λ = 0.40 × 2                                                              = 0.80 m v = f λ f  = v / λ    = 300 / 0.80    = 380 Hz (2 sf) Show Answer

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Links
Demo of Standing Waves Part 1: https://www.youtube.com/watch?v=-gr7KmTOrx0
Demo of Standing Waves Part 2: https://www.youtube.com/watch?v=QcoQvzNQp6Q
“A Better Description of Resonance” Steve Mould – Rubens Tube https://www.youtube.com/watch?v=dihQuwrf9yQ
https://en.wikipedia.org/wiki/Harmonic
https://www.youtube.com/watch?v=wYoxOJDrZzw