Description:

Features of standing waves such as nodes and anti-nodes can be seen in a spring that is fixed at one end and vibrated at the other end.

 


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Possible Incorporated Topics:

  • Standing Waves
  • Springs
  • Longitudinal Waves

 


Theory:

A longitudinal wave sent down the length of a spring can be seen as a zone of compression followed by a zone of rarefaction. The wave will eventually reflect off of the other end of the spring and travel back.

If a second wave is traveling out as the first wave is traveling back, the two waves will interfere with one another. If one end of the spring is oscillated at certain frequencies, a standing wave (or resonance) appears in the spring. One then sees points on the spring which are standing still (nodes) and other points which are oscillating vigorously (anti-nodes).

Increasing the frequency of oscillation of the spring will make the spring oscillate chaotically. As the frequency of oscillation approaches another resonant frequency, standing waves again appear on the spring. This new oscillation mode (or standing wave pattern) has one more node than the previous one.

Figure 1: Three visible nodes

Figure 2: Increasing frequency

Figure 3: Six visible nodes

 


Apparatus:
  • Mechanical vibrator
  • Frequency counter
  • Frequency oscillator
  • Spring
  • Clamps
  • Metal stand



Figure 4: Set-up


Procedure:

  • Set up the apparatus as shown in the picture to the right.
  • Hang the spring from a clamp, then attach the spring to the mechanical vibrator.
  • Turn on the frequency counter along with the low frequency oscillator. It will take a few moments for the equipment to warm up.
  • Adjust the frequency until you see nodes and anti-nodes within the spring.
  • Slowly increase the frequency to the next resonance level, where you will again witness nodes and anti-nodes.