Waves On Strings - Frequency - Propagates - Linear Mass - Science Assignment Help

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Waves On Strings - Frequency - Propagates - Linear Mass -  Science Assignment Help 

Background
We use a mechanical vibrator to vibrate a string that is stretched to a given tension. Using a signal generator, we control the frequency and the amplitude of the system’s vibration. When the frequency is tuned to just the right value, a standing wave pattern appears along the string.

Standing Waves
By applying Newton’s Laws of Motion to the system, we derive that a vertical displacement of a horizontally stretched string propagates with speed:

where T is the string’s tension and μ is the string’s linear density (mass per unit length).
Once displaced and released, the string vibrates due to its innate elasticity. As it does, it produces a train of vertical displacements that propagates horizontally across the string. These displacements constitute a wave that travels along the string with speed v. The travelling waves reflect and reverse direction at the string’s boundaries (end-points). Trains of outgoing reflected waves superimpose upon incoming incident waves and produce a chaotic pattern of vibration. Generally, the superposition tends to dampen the string’s vibration. If the wavelength is just the right value, however, the travelling reflected and incident waves match and reinforce each other. The results then are not chaotic but stable – they are the patterns we observe as standing wave patterns.

 

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