Fun with Less Kilowatts —What is Frequency?

By Vernon Trollinger, October 25, 2017, Family

Welcome to Fun with Less Kilowatts! We believe that science experiments at home can be a creative way to engage kids in learning while having fun. They can be educational AND great activities to keep your kids busy and away from the television. Each month, we’ll feature a new science experiment that can be a great resource for parents and teachers.

What’s ‘Frequency’?

One common project for little kids is the classic shoe box guitar. That’s where they stretch rubber bands over a shoebox and discover it makes a musical-ish sound. But if you’ve ever looked at a real guitar, violin, banjo, or even inside a piano, you’ll see that the length of the string is what determines how high the note is. The longer the string, the lower the note; the shorter the string length, the higher the note.

Stringed instruments make sound when their strings vibrate, which is called “oscillation”. Long strings have lots of room to oscillate, so they vibrate slowly. Shorter strings have less room, so they vibrate faster.

The rate or speed at which things vibrate or oscillate is called the frequency. The really neat thing is that frequencies and vibrations have a basic mathematical relationship that is really easy to show with a stringed instrument.

But because not everyone happens to have a guitar lying around, we’re going to use something just a little more basic.

Create a DIY Music Box


Fun with Less Kilowatts —What is Frequency? | Bounce Energy Blog

  1. A long cardboard box or shoe box. Ideally, it should be around 12” long.
  2. A thick-ish rubber band
  3. Ruler
  4. A marker


Fun with Less Kilowatts —What is Frequency? | Bounce Energy Blog

  1. Stretch the rubber band over the box.
  2. Measure the distance at which the rubber band can openly vibrate without touching anything.
  3. Take that measurement and divide by 2. Mark that point accurately on the rubber band. This is the center. Decide which side of that mark will be the side that you will pluck the rubber band. The other will be the pinch side.
  4. From this center mark, measure the length of the rubber band again and divide by 2. Measure and mark these points accurately on the rubber band. These are the quarter-length points.
  5. From one of the quarter points, measure the length of the rubber band and divide by 2. Measure and mark this point on the rubber band on the pinch side. This is a one-eighth length point.

    Fun with Less Kilowatts —What is Frequency? | Bounce Energy Blog

Now, pinch the rubber band at the marked measurement. Pluck the rubber band on the “pluck side” with the other hand.

The Result

Where you pinch the rubber band determines the pitch or frequency of the sound according to a uniform set of ratios.

Fun with Less Kilowatts —What is Frequency? | Bounce Energy Blog

  1. Pluck the rubber band. Notice the pitch of this “open” note.
  2. Pinch the rubber band at the center and pluck. It should be one octave higher in pitch. The center is also known as the second harmonic.
  3. Pinch the rubber band at the quarter mark closer to where you pluck. The pitch should be one octave higher than the one at the center.
  4. Pinch the rubber band at the quarter mark furthest from where you pluck. That pitch will be four notes above the open note and is known as a perfect fourth. Both these quarter places are located at the 4th harmonic.
  5. Pinch the rubber band at the last mark you made and pluck. That note will be one full step above the open note.

The Science

The vibration of strings —and rubber bands — are mostly governed by their length. Tension also affects the speed of a string’s vibration but the amount of tension depends on how long the string is, the size of the string (mass), and how high the string is “tuned”. That’s why stringed instruments use so many different kinds of strings.

But how do you find where the notes are?

Length determines the location of harmonic nodes. These was first described by Marin Mersenne in 1637. Harmonic nodes are places on the string that hardly vibrate at all. You can actually see this happen if you vibrate a string under a strobe light at certain frequencies. Harmonic nodes also let you locate specific notes on ANY stringed instrument without the benefit of frets or any kind of markings. That’s because the location of the nodes is determined by ratios of the total length of the string. Common harmonic nodes are:

  • at one half the string length
  • every third of the string length
  • every fourth of the string length
  • every  fifth of the string length
  • every sixth of the string length

I compared my rubber band box to my digitally-tuned bass guitar and discovered it is tuned to a low B flat.

Pinching one half of the rubber band length produced the first octave, a B flat.
The next line, one fourth the string length, produced two notes:
•  The first nearest the pluck side produced a second octave B flat.
•  The second furthest away from the pluck side produced an E flat, known musically as a perfect fourth.
The last mark, one-eighth the entire string length, produced a C, which was one full step up from the low B flat.

What’s the Frequency?

Sound and electromagnet energy (light, electricity, etc) are different types of energy. However, their wave forms are both measured by their oscillations per second. Because Heinrich Rudolf Hertz proved the existence of the electromagnetic waves, sound and electromagnetic frequencies are measured in hertz (Hz).

Consequently, musical notes have known frequency ranges:

Low B flat=58.27 Hz
The first octave =roughly 116.5 Hz. (58.27 Hz x 2)
The second octave = 233 Hz. ( 116.5 Hz x 2)
The E flat, perfect fourth = approximately 72.7 Hz (58.27 Hz + 25%)

Humans can hear sound frequencies ranging from 20 Hz to 20,000 Hz.

One more thing—
Household alternating current (AC) changes polarity 60 times a second. That’s 60 Hz. Because refrigerator motors (and household fan motors) run at 60 Hz, they emit a 60 Hz hum. This hum is just a few “cents” flat of being correct for a B natural —which is 61.74 Hz. On a guitar, a low B is one octave above, about 123.4 Hz.

If you ever need to tune your guitar but don’t have a good tuner handy, listen to a refrigerator. It’s not dead-on but if just tune your axe a little sharper than the octave above your fridge’s 60 Hz hum, you’ll be in the ball park and good to go!

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A native of Wyomissing Hills, PA, Vernon Trollinger studied writing and film at the University of Iowa, later earning his MA in writing there as well. Following a decade of digging in CRM archaeology, he now writes about green energy technology, home energy efficiency, DIY projects, the natural gas industry, and the electrical grid.

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