Java Physics


standing wave

Generating Standing Waves in String (Resonance)

The length of the string can be varied by dragging the stand to the left/right.
The tension in the string can hence be changed.



Internal Links :

Mechanical Resonance (Applet)

Electrical Resonance I (Applet)

Electrical Resonance II (Applet)

Solving the wave equation (Pdf)

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  • A stationary wave is produced when the wavelength of the wave in the string, which are fixed at its two ends, satisfies λn = 2L/n, where L is the length of the string and n = 1, 2, 3,…
  • When a stationary wave of wavelength λn is formed, there are n loops formed in the string.
    n = 5 stationary wave
  • Each stationary wave is a normal mode of the system.
  • Besides the normal modes, the string has infinite modes of oscillations, e.g., plucking the string at any point on it. However, any mode can be represented by a series sum of the normal modes of different amplitudes. An analogy in mathematics is that any 3D vector can be expressed like P = a i + b j+ c k, where ij and k are the unit vectors.
  • The system is forced to oscillate when a periodic force is applied to it. When the frequency of the periodic force matches with one of the frequencies fn = wave speed / λn, resonance will occur. Then, stationary wave of that normal mode appears on the string.
  • When the system is forced to oscillate at off-resonance, the oscillation is a combination of the neighboring modes. The resultant amplitude is usually small becuase none of the normal modes is dominant.




Author and Copyright:

Chiu-king Ng

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