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Standing Waves

  • Introduction
  • Video & Results
  • Materials
  • Procedure
  • Preparation & Notes
  • Download Files

Introduction

In these activities, students will:

  1. Swing a spring horizontally to observe the first, second and third harmonic standing waves.
  2. Make connections between how fast they swing the spring and frequency.
  3. Establish a connection between frequency and the number of waves that can be observed.

Modeling Standing Waves with a Spring

A wave traveling down a string with tension to a fixed point will reflect back towards the incoming wave. In this activity a 6 ft long spring will be used to demonstrate normal modes or harmonic frequencies. If the incoming wave and the reflected wave have a wavelength that is twice the length of the string, then half of a wave will be observed. This standing wave is termed the first harmonic. (L= lambda/2) The amplitude of the incident and reflected waves will add, so the standing wave will have twice the amplitude of each individual wave.

spring_half

If the frequency of the wave is doubled, the wavelength will be half the original wave. Now it will be possible to observe a full "S" of sine wave when the spring is swung back and forth. For this standing wave, the second harmonic, the length of the spring is equal to the length of the wave. (L = lambda)

spring_Second

As the frequency of the swinging at one end of the rope increases (the rope is swung back and forth faster and faster), the spring can demonstrate standing waves if the length of the spring (L) is an even multiple of the half wavelength (n * lambda/2). In standing waves, there are places where the rope experiences maximum movement. These locations in the spring are called antinodes. In addition there are places in the spring where the rope does not move if the system is working perfectly. These places are called nodes. The third harmonic is illustrated below. (L=3* lambda/2)

third spring

Video

First Harmonic (80 cpm) Second Harmonic (160 cpm)

Third Harmonic Fourth Harmonic

 

Materials

  • 6 ft Wave Modeling Spring from Education Innovations ($14.95 catalog spr-1)
  • Heavy Duty Umbrella stand
  • ~ 4ft PVC irrigation pipe that will fit into the umbrella stand
  • Eye hooks with bolts long enough to go through the PVC pipe
  • Goggles

Procedure

  1. Set up the umbrella stand with the PVC pipe secured.
  2. Loosen bolts on eye hooks and attach the spring.
  3. Set the metronome for 80 counts per minute.
  4. Have the student wear goggles, stand about 15 feet away from the post and swing the spring so that the spring swings back and forth at 80 counts per minute.
    Adjust speed until they get half of a sine wave, the first harmonic.
  5. Next set the metronome to double the counts per minute that gave the half sine wave. When the student swings the spring at this speed, they should be able to observe a full "S" curve of standing wave, the second harmonic.
  6. Next triple the original speed for the metronome, if it goes that high, about 240 counts per minute and see if the student can observe the third harmonic.

Preparation of the Spring Stand

    eye hook
  1. To prepare the base, drill holes in the PVC pipe at several heights. Insert the eye hooks through the PVC pipe and screw the nuts on the opposite side to attach.
  2. Place the PVC pipe in the umbrella stand.
  3. Insert spring into eye hook. These may need to be opened a bit to slide the spring.

umbrellastand

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