I have been using tuning forks in my classroom for 10 years, and in each of those years I have discovered several new tricks. I hope you can learn many of these from this publication. For a more complete treatment and my references, please see my article in “The Physics Teacher” March, 2013.
0. General Usage
When a tuning fork is struck it will vibrate wildly in unintended ways. Imagine putting your arms straight above your head and clapping. That is the proper motion of a tuning fork. The problem is that it is also wobbling at the “elbows.” You can get rid of the unwanted vibrations by touching gently near the joint after striking the fork. The vibrating tuning fork should be almost silent when used properly. Hold the tines near your ear and you will hear it clearly. It is best to hit the tuning fork on a knee or the ball of your hand, avoiding metal on metal. This is because when tuning forks become chipped they change their inertia and will vibrate at different frequencies. Spin the fork as you listen and notice that it is loudest right between the tines. (Constructive Interference.)
1. Water Dip
Putting a tuning fork in water is one of the best ways to get students accustomed to handling it. Give a tuning fork to each student or every other student. Set out several cups of water. It is always a surprise to see the splash, students will gasp. These introductory activities are important for laboratory management because the tuning fork is a fun toy and does require some getting used to; the sensation of hearing the tines vibrating is new and somewhat alarming. It is also a good idea to have boxes or desks or the whiteboard cleared off for students to place the base of the tuning fork against and cause the vibration to resonate.
2. Strobe Lights
A fun demonstration is to put the tuning fork in front of an adjustable strobe light (or a CRT computer monitor). The strobe light can be adjusted to make the vibration appear slower or even stop! This works better on a larger tuning fork. The flashing must match the frequency of the tines, or be very close. I found my 100 Hz tuning fork to be 99 Hz after investigation.
This effect comes from the strobe light “animating” the fork slowly through time by only making it visible after almost full cycle has passed. At that moment, the fork will look as though it has only moved slightly. The difference between the strobe rate and the tuning fork frequency determines the perceived rate of vibration. The CRT monitor can also act somewhat like a strobe light, but because of its trace across the screen, it causes a wobbly effects in the vibration.
Verifying the frequency of the tuning fork can easily be achieved by using an oscilloscope. This is done by hooking a speaker removed from its housing to the scope’s leads. You will need to have a proper connection (usually a BNC connector with probe) to achieve this. You can also use a microphone. Hold the tuning fork up to the speaker and adjust the settings. You can see that the fork’s tone is a pure sine curve. Compare this with the human voice or other instruments such as flutes and kazoos. Also, try comparing tuning forks of various frequencies and noting the different periods & wavelengths.
Two tuning forks that are the same frequency can be made to resonate audibly if the vibration is loud enough. For this purpose, I prefer using the large box-mounted versions. Most large glass or wooden objects will have so many resonance frequencies that any tuning fork will cause them to resonate. Tuning forks that are not the same frequency will not resonate. The important phrase to understand is “Forced vibration at natural frequency causes resonance.” Where “resonance” is high amplitude oscillation. We all experience resonance when singing in the shower; the longer notes resonate better and it makes our voice sound purer in tone. Also, when our wheels are not aligned in the car and we drive at the natural frequency of our shock springs the car will resonate up and down – but only at specific velocities.
5. Sound via Light
Shine a laser on a solar cell from across the room, hook that solar cell to a set of computer speakers and demonstrate the transmission of sound via electromagnetic waves. This is analogous to radio signals that we listen to because they are also modulated electromagnetic waves. The laser’s color doesn’t matter much. I sometimes add smoke to enhance the demo visually. You will get a less distorted sound if the fork is further into the beam rather than just barely touching it when vibrating. Clipping to the speakers may require some trial and error. The “male end” of a stereo cable has its tip going to the left speaker, the middle ring goes to right, and the inner metal goes to ground. Clip one end of the solar cell to either left or right, but you must clip the other to ground. A guitar amp will work fine, probably even better. Clip similarly to the plug of the guitar cord.
Demonstrating interference is important because it is a property of all waves. In this case I am using two close frequency waves to show the phenomena called “beats.” Beats are sometimes also used to tune musical instruments (see #10). The beating frequency is the difference between the interfering frequencies, the note you hear is the average of the two original frequencies.
This pattern can also be achieved by taking two identical tuning forks and heating one of them with a fire. (I demonstrate this in the introduction to the video.) Be sure to wear a hot glove! The heat reduces the Young’s modulus (similar to spring constant) of the aluminum and the vibrations no longer match. You can easily tell the difference even with a non-musical ear.
7. Measure the Speed of Sound
With a tube and some water in a bowl it is easy to measure the speed of sound by resonating it with a tuning fork. The wavelength of the sound must match the length of the tube, but the whole wave doesn’t have to fit inside for this to happen. Most commonly, the bottom is sealed and becomes a node (a place where the air can’t move) but the top is open and the air can vibrate liberally (anti-node). The smallest fraction of a standing wave that can fit in here is a ¼ wavelength. Multiplying wavelength and frequency gives the velocity of sound, usually within 1% error! If you don’t have a glass tube, this demonstration can also be done with a graduated cylinder that is being filled with water until resonance is achieved.
8. Smoke and Mirrors
Reflecting light from the end of a mirrored tuning fork can lead to exciting effects. It gives us a chance to view the motion of the fork by amplifying it as the reflected light is projected across the room. In the video, I add smoke to help you see the beam. Because the tuning fork’s motion is sinusoidal in time, it can be made to trace a nearly perfect sine curve in space when it is rotated smoothly at a point far away.
Lissajous Figures are an old method by which tuning forks were tuned. Excess fork was shaved off to bring the frequency down. These days, Lissajous Figures are mostly they are used to analyze electromagnetic oscillations in LRC circuits, but originally they were produced by tuning forks reflecting light that is pointed at two mirror loaded forks vibrating at 90 degree angles. When the frequencies are in ratio you get a Lissajous Figure. They come in the shape of donuts, pretzels, fish, and other edible items. It is best to have the forks close, but the wall far away because that will increase the size of the figures and reduces aiming difficulties.
9. Strike a Chord
Tuning forks come in various frequencies. You can use them to inform students that music is a branch of physics. With help you can create chords or even play songs with your students. Take time to notice that there are specific ratios between notes that are in harmony. For example, between G and C there is a 3/2 ratio – this is called a fifth. Between E and C is a 5/4 ratio – this ratio is used in the C major chord. And between C and A is a 6/5 ratio which is used in the A minor chord. All octaves (such as middle C and the next C above middle C) are separated by a doubling of the frequency. These ratios apply to both scientific and musical tuning fork frequencies and it is a fun game to try to discover them by reading your tuning fork labels.
Tuning an instrument with a tuning fork can be done in many ways. Typically, the tuning fork is merely listened to or held to the body of the instrument while it is tuned by ear. But the fork can also be used to resonate the strings into vibration (if they are already in tune). A completely different method is to strike the note and listen for beats as the sound from the instrument interferes with the sound from the tuning fork. As the two are brought into tune, they will beat less and less frequently until they are matched with no beating.
It is important to note that the scientific tuning forks do not match the musical frequencies. For example, A 440 Hz is a musical note, whereas A 426.7 Hz is the scientific note. In the figure, my guitar tuner thinks my scientific tuning fork is flat by a half step. The scientific scale is arranged around middle C being 256 Hz (C is 261.6 Hz on the musical scale). The setting of the musical scale was done somewhat arbitrarily done by German musicians in the early 20th century. The scientific scale is convenient where all C notes are a multiple of 2; for example, the first C above middle C is 29=512 Hz. Many of the other frequencies are also whole numbers, such as G 384 Hz and D 288 Hz.
Tarbut V’ Torah High School
Irvine, CA, USA
James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years. James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That” and the UCLA Physics Video Project.
Contact: [email protected]