# Sound & Waves

## Reflection, Refraction, Diffraction & Interference…… That’s COOL!

The Mini Ripple Tank is a great way to address the wave-energy standards and to teach about the properties of waves by showing how water waves behave.  This is in keeping with the history of physics and the modern experimental approaches to science instruction.

The Mini Ripple Tank eliminates the clumsiness of the larger ripple tanks of old and gives the opportunity for students and teachers to interact with the wave properties quickly and engagingly.  Because of the competitive price, and variety of available experiments.  It is even reasonable to buy a class set.

Fig 1.  Plane waves are being produced and are readily visible on the built-in screen.

Getting Familiar

The Mini Ripple Tank contains a small pan for water and a vibrating source.  The strobe light below projects waves of various frequencies on a fold-down screen.  Both the strobe and the wave frequencies can be varied, generating many interesting effects.  There is also a synchronizing mode which links the two (this is very helpful when measuring wavelength).

Fig 2. Water is filled up to half of the height.  The adjustable strobe projects from underneath.

The device comes with three distinct wave generating mechanisms: single source, double source, and plane waves.  The single source is the most fundamental and is helpful in instructing on wave basics and Huy gen’s Principle (plane waves are a sum of circular waves).  The double source can be used best at teaching interference experiments (more below) as well as testing out the diffraction formula.  The plane wave source is the one I tend to use the most often because it sets up a standard wave that can readily land upon the other implements which are used to redirect the waves.

Fig 3. The nine components.  Left to right: the two lenses and the prism, the two barriers and the parabolic mirror, and the double and single sources, as well as the plane wave source.

As for general tips, it is helpful to use a document camera for larger classes, also adding blue dye can sometimes improve visibility, and try to not overload the tank with water – either fill halfway or just enough to barely cover the lenses and prism.  Experiment a lot with wave and strobe speeds to improve the visibility of the desired effects.

Refraction by the Lenses and the Prism

The bending of light waves by glass is well-known, but is this a property of all waves?  Yes! Demonstrate this dramatically by bending water waves with lenses and prisms.  The shallower the water, the slower the waves.  This is analogous to the denser the medium, the slower the light waves (with few exceptions).

Fig 4. The prism can bend the waves by slowing their propagation.

Again, remember to keep the water shallow.  Some experiments can include measuring the focal lengths of the two lenses (positive for convex, negative for concave), measuring the index of refraction for the prism (by wavelength change, speed change, or Snell’s Law), and measuring how water depth affects refractive index.

Fig 5. The refraction formulas that can be used for quantitative experiments.  The first formula might be the least familiar – wavelength changes with index of refraction.  The second formula compares a standard speed c with the new slower one v to define the index n.  The third is the famous Snell’s Law.

Somehow it is very satisfying to see the focusing of water waves when using lenses.  The ray approach to drawing images known as geometric optics does not provide a hypothesis as to the wave nature of light, but this experiment convincingly demonstrates that refraction and focusing is something that waves do!  Refraction and lens effects are a powerful piece of evidence that demonstrates the wave nature of light.

Fig 6. The convex and concave lenses demonstrate convergence and divergence of waves respectively.

Reflection by Barriers and the Parabolic Mirror

The law of reflection can be readily demonstrated by the Mini Ripple Tanks (by stacking the barrier pieces) however, the best demonstration is the focusing of waves by the parabolic mirror.

When a plane wave enters parallel to the axis of a parabolic mirror, it will be reflected to the focus of that mirror.  This is the basis for Newtonian Reflector telescopes that remain the standard style in modern times.  A reversal can also be achieved by placing the single source at the focal point and reflecting out plane waves.

Fig 7.  Reflection of plane waves off a parabolic mirror will focus them to a point.

Diffraction by Barriers

le-slit diffraction of waves is easily demonstrated with this simple device.  Just place the barriers in the path of the plane wave source and the effect is immediately present.  Manipulating the opening and wavelength can help illustrate the variables: more diffraction occurs the smaller the opening is allowed to be.

Fig 8.  Single slit diffraction shows the bending of a plane wave source as it passes through an opening, illustrating Huygen’s Principle that plane waves are a sum of circular waves.

The diffraction formula for quantitative experiments is best applied to the two-source case, however, and while this is only a case of interference and not diffraction, it does provide an opportunity to apply the formula experimentally.    Here, we see both versions of the formula, the angular version, and the small angle approximation.  I prefer the second one because lengths are usually easier to measure than angles.

Fig 9. The diffraction formulas:  The symbol d represents the distance between the sources, and lambda as always is wavelength (which is the dependent variable in this experiment).  Theta is the angular distance to an interference fringe as measured from the spot half-way between the sources.  X is the linear distance between the interference fringes, these are the locations of constructive interference.  L is the linear distance from the point between the sources to the point of interest, and because there is more than one location of constructive interference, m is the index number which labels these points as m=1,0,-1,2, etc, (any integer).

Fig 10. An interference pattern is easily generated with these two sources.  The diffraction formulas above will apply to this double source interference pattern, even though no diffraction is occurring.  This demonstration can be converted into a quantitative experiment.

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## Fun and engaging activities using the Energy Stick [W/Video]

Welcome to our March 2015 Issue of our CoolStuff Newsletter. This month, we are featuring a simple, safe and Cool device called an Energy Stick. Physics teacher James Lincoln demonstrates several experiments that help students understand the principles of electric current and light. James has authored many of our past CoolStuff Newsletters, and teachers have really enjoyed his insight, passion and creativity. We encourage you to let us know what you think, and please feel free to contribute to the conversation by submitting a comment. Thank you for being a CoolStuff subscriber – enjoy!

Arbor Scientific
We find the CoolStuff

The Energy Stick is a fun and easy way to demonstrate many of the principles of electric current and light. These topics are important for both the physics and the chemistry teacher. In this article I will outline several of these such experiments including new ones not seen anywhere else.

1) GETTING STARTED
To operate the Energy Stick, make bodily contact with both ends of it. This sends a microcurrent through your body which is amplified by the circuit inside and sent to the LEDs and speakers inside. This is how you can know whether a measurable electric current is able to flow from one side of the stick to the other.

2) CONDUCTIVITY OF VAROUS OBJECTS
One of the first experiments you will want to do with the Energy Stick is check what other objects conduct electricity. This is a good lesson in the properties of metals for chemistry, physics, or middle school science. You will find that mostly metals conduct electricity. I have also found that even distilled water conducts electricity well enough to have an effect. This should not be a surprise since the human body is mostly water and the human body works well.

Miscellaneous household items are good candidates for conductivity tests.

The open circuit fails to light

Closing hands completes the loop and current can flow

3)THE IDEA OF A COMPLETE CIRCUIT
An important lesson is that for current to flow the circuit must complete a closed loop. Thus, if there is a break anywhere in the circuit electricity cannot move through any part. This can be dramatically demonstrated by having several members of the class join hands in a ring and complete a very large circuit.

The Energy Stick’s Voltage is only about 30 milliVolts. The current output depends on the circuit it is connected through but is always only a few milliamps at most.

4) INVESTIGATIONS OF THE CURRENT
Connecting the two ends of the Energy Stick with a wire activates the circuitry inside. You can connect that wire to other electric devices such as a ammeter and voltmeter. In both cases the measurements will be quite small so it helps to have sensitive meters. The Energy Stick is a safe way to familiarize students with these probes.

5) THE PLASMA GLOBE and the Frequency of Light
A plasma globe can also be used to turn on the circuitry of the Energy Stick. Since the circuit inside amplifies very small currents, the electric field near the plasma is enough to get an effect. Inside the Energy Stick the red, green, and blue diodes turn on at different distances. This is a lesson in modern physics and chemistry. That is the meaning of the formula E=hf.

The Red Diode is the first to turn on.

As the Energy Stick is brought nearer the plasma globe, the other colors turn on. Next green, then blue last.

Red light having a lower frequency (longer wavelength) than blue and green light will can be produced at a lower voltage (energy/electric charge). Therefore, the blue diode is the last one turn on. This recalls the idea of the photoelectric effect that it is not the brightness of the light but its frequency that determines how energetic it is.

James Lincoln

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]

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## Liquid Crystal Sheet Demos [W/Video]

Safely demonstrating the principles and properties of heat can sometimes be a risky proposition. But it needn’t be. Watch as Physics Teacher James Lincoln uses the safe, simple, and inexpensive Liquid Crystal Sheet to visually display some very cool things about heat we usually only TELL our students about.

Introduction
These Liquid Crystal Sheets are heat sensitive and offer a wide-range of possibility for experiments. Because they change color based on temperature, they can be read visually and quickly, at a distance, allowing the whole class to enjoy your demonstrations. The sheets easily warm to the touch and as they do, will display the visible spectrum ROYGBIV – with blues and purple signifying the warmest temperatures. If they get too hot, they will become dark again. The color change is caused by tiny crystal layers – on the micron scale – twisting as they warm.

The thin layer responds rapidly to the touch. These sheets offer a wide range of possibilities.

Fun and Easy Explorations
After warming a sheet with your hand, try putting some cold water or ice on it. Then, you can put some hot water on it and demonstrate evaporative cooling (blow air on the hot water and it cools rapidly). The thin design of the sheet allows for rapid color changes. Another cool thing to try is to compare the hands of male students to female students. Male hands are usually warmer because of higher blood pressure and surface area-to-volume ratios. This is plain to see using the Liquid Crystal Sheet.

A streak of warm water beautifully demonstrates the color changes. Notice the far end is already demonstrating evaporative cooling.

Efficiency of Light Sources
One experiment you should conduct is to compare the heat output of various light sources. Of course the candle puts out an enormous amount of heat. This is easily tested by holding the Liquid Crystal Sheet above the light source, since heated air rises by convection. The classic incandescent light bulb is next and it puts out a medium amount of heat, because it has to heat up to glow. But the fluorescent bulbs barely put out any heat at all compared to these other sources – they are much more efficient. This topic is appropriate for Physics and Environmental Science. The more modern light sources are light-emitting diodes (LEDs), and they are the most efficient of all, putting out almost no heat. You can get one of the new, futuristic diode bulbs at your local hardware store.

Insulation and Conduction
You can demonstrate insulation using a piece of Styrofoam. Place the Styrofoam below the sheet to delay the transfer of heat to the tabletop and hold the thermal images longer. Once you have your image, use a piece of metal to demonstrate thermal conductivity. The metal takes the heat away faster. You can also demonstrate that friction generates heat when the metal is applied to the surface.

Placing the sheet on Styrofoam will lengthen the duration of the thermal image.

Thermocline
As an example of how well the sheets can display ‘what’s hot & what’s not”, I offer the thermocline. Cold water and warm water will sort themselves based on temperature due to density differences, called a thermocline. Thermoclines occur in swimming pools, lakes, and the ocean. Generally, the warm water rises and the cold water sinks. However, in the ocean there are also haloclines, which are density differences caused by salt content. This is a good chance to probe the water line and determine which color corresponds to which temperature.

Measuring the Microwave’s Wavelength
In this experiment, we are going to measure the wavelength of a microwave with a ruler, a piece of Styrofoam, and the Liquid Crystal Sheets. Insert two sheets on a plate into the microwave; make sure that they do not rotate by using a tube or rack to hold the plate up, then let it cook for only a few seconds. When you take the sheets out the pattern you will see patterns in the shape of the microwaves. You can measure the wavelength of the microwave by measuring the distance between these hot spots. You will probably notice two different distances between spots. Between two close spots measure only half the wavelength (antinode to antinode distance) but when spots are far apart, it is a full wavelength (think cosine). The full wavelength is about 12 cm. Using the microwave oven’s frequency (usually stamped on the back or the inside), you can calculate the speed of light. My microwave oven is 2450 MHz. Multiplying this by .12 meters, and using v = λ f gives us the speed of light: 3 x 108 m/s.

Lasers
I have found that these sheets absorb heat well from red, and sometimes blue, lasers. Though I haven’t thoroughly tested the effect of different colored lasers, my belief is that the red is absorbed more readily than the green, for example, and so it can be used to write messages. Awesome!

With a red laser you can write not-so-secret messages. Light waves transfer energy.

James Lincoln

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]

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## Doing the Wave: Connecting Physics to Baseball [W/Video]

Ever heard the crack of a bat when a hitter launches a homerun? Well there’s a wave that’s responsible for that sound. Watch the video to learn how waves are an integral part of baseball. Who knew!

Dr. David Kagan has been at CSU Chico for over thirty years. During this time, Dr. Kagan has served in numerous roles including: Chair of the Department of Physics; founding Chair of the Department of Science Education; and Assistant Dean in the College of Natural Sciences to name a few. He is a regular contributor to The Physics Teacher having had over thirty papers published in the journal. Kagan continues his deep devotion to quality teaching by avidly engaging his students with methodologies adapted from the findings of Physics Education Research. In addition, he has remained true to his lifelong obsession with baseball by using the national pastime to enhance the teaching and learning of physics.

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## Top 10 Demonstrations with Tuning Forks [W/Video]

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.

3.      Oscilloscope

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.

4.       Resonance

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.

6.     Interference

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.

10. Tuning

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.

James Lincoln

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]

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## Download Joel’s student lab activity as a word document:Standing Waves Vertical Spring Lab

A standing wave is formed when two identical traveling waves continually pass through the same medium in opposite directions. Not only can standing waves be produced on springs by sending continuous traveling waves down a horizontal spring that is held firmly at the far end, they can also be produced using a spring that is held vertically such that its lower end is free. This results in a node at the upper end of the spring and an antinode at the lower end of the spring, and yields standing waves having 0.5 loops, 1.5 loops, 2.5 loops, 3.5 loops, etc…, as depicted in Figure 1.

In the video clip, you will see Arbor Scientific’s new Spring Wave (Product #P7-7220) held above the floor.  By adjusting the frequency of the waves, the wavelength may be manipulated so that different numbers of loops can be formed. As with all standing waves, the length of one loop is one-half wavelength.

You can determine the frequency of each standing wave by timing the motion for 10 complete cycles.  The frequency in Hertz will be 10 cycles divided by the time in seconds taken to produce the 10 cycles.  Since the tension in the vertically held spring remains constant for all trials, the speed of the standing waves will be the same, regardless of the number of loops formed.  This allows us to determine the ratio of frequencies needed to produce different standing wave patterns.

Assume we use a spring of length L when suspended vertically.  The standing wave form in Figure 1 having 0.5 loops will have a wave speed v = f0.5λ0.5, where λ0.5 = 4L and f0.5 is the timed frequency.  Therefore, f0.5 = v/4L = ¼ v/L.  Because the tension in the vertical spring has not changed, the standing wave in Figure 2 will have the same speed as the standing wave in Figure 1.  In this case, the wave speed v = f1.5λ1.5, where λ1.5 = 4/3 L = 4L/3.  Therefore, f1.5 = v/4L/3 = 3v/4L = 3(¼ v/L) = 3f0.5.  We should therefore expect that the frequency to produce 1.5 loops will be three times the frequency needed to produce 0.5 loops.  Similarly, the standing wave in Figure 3 will have a wave speed v = f2.5λ2.5, where λ2.5 = 4/5 L = 4L/5.  Therefore, f2.5 = v/4L/5 = 5v/4L = 5(¼ v/L) = 5f0.5.  Comparing f2.5 and f1.5:  f2.5/f1.5 = 5f0.5/3f0.5 = 5/3.  We would therefore expect that the frequency needed to produce 2.5 loops would be 5 times the frequency need to produce 0.5 loops, and 1.67 times the frequency needed to produce 1.5 loops.

In the video, the total time needed to produce 10 cycles when 0.5 loops were formed in the Spring wave was approximately 18.21 sec.  This results in a frequency f of 10 cycles/18.21 sec = 0.549 Hz.  Similarly, the frequency when 1.5 loops were formed = 10 cycles/6.06 s = 1.650 Hz.  The ratio of the frequency to produce 1.5 loops to the frequency to produce 0.5 loops = 1.650/0.549 = 3.01, which is quite close to the expected ratio of 3.00.

For 2.5 loops, the frequency is found to be 2.882 Hz (10 cycles in 3.47 seconds).  This frequency is approximately 5.25 times as great as the frequency to produce 0.5 loops, which is close to the expected value of 5.00, and 1.75 times as great as the frequency to produce 1.5 loops.

Slight discrepancies in the calculated ratios can likely be attributed to errors in measuring time and quite likely in not producing the most “perfect” standing wave form.  The actual ratios your students measure when they perform this investigation for themselves will depend on the types and lengths of springs used.

The video clip concludes with vertical standing waves produced using another plastic toy spring.  Although the measured frequencies will differ using springs with different lengths, diameters, and elastic constants, the ratios of frequencies needed to produce the standing waves should be the same.

## Download Joel’s student lab activity as a word document:Standing Waves Vertical Spring Lab

See Joel’s other wave demo: Big Standing Wave – Small Effort!

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## Big Standing Wave – Small Effort!

A standing wave is formed when two identical traveling waves continually pass through the same medium in opposite directions. One convenient way to produce standing transverse waves is to allow a traveling transverse wave sent continuously down the Super Springy to interfere with its own reflection.  To do this, the spring should be stretched out a specified distance and held firmly in place at the far end.  The spring is moved rapidly in a back and forth motion in order to produce continuous transverse pulse down the spring. The reflected pulses are inverted (i.e., “shifted” one-half wavelength). This causes a node (result of total destructive interference) to form at the far end of the spring, and allows for anti-nodes, or loops, to be formed along the length of the spring.

In the video clip, you see the Super Springy stretched out a distance of 24 feet. By adjusting the frequency of the waves, the wavelength may be manipulated so that different numbers of loops can be formed.  As with all standing waves, the length of one loop is one-half wavelength. You can find the wavelength (λ) of the standing wave by dividing its total length by the number of loops to get the length of one loop, and then doubling it. Since the Super Springy is stretched out 24 feet, the wavelength when two loops are formed will be 24 feet, the wavelength when 3 loops are formed will be 16 feet, and when four lops are formed will be 12 feet, and for 5 loops, the wavelength will be 2/5 of 24 feet = 9.6 feet.

You can determine the frequency of the waves by timing my motion for 10 complete cycles. The frequency in Hertz will be 10 cycles divided by the time in seconds taken to produce the 10 cycles.  You can then multiply the frequency of the standing wave by its wavelength to determine the speed of the wave in the Super Springy. Since the tension in the Springy remained constant for all trials, you should expect to calculate the same speed for the wave, regardless of the number of loops formed.

In the video clips, the total time needed to produce 10 cycles when 2 loops were formed was approximately 9.75 sec.  This results in a frequency f of 10 cycles / 9.75 sec = 1.026 Hz.  Since the wavelength λ is 24 feet, the speed v of the wave in the Super Springy is calculated as v = f λ = 1.026 Hz x 24 feet = 24.62 ft/s.

Similarly, the frequency when 3 loops were formed = 10 cycles / 6.21 s = 1.610 Hz.  The speed of the wave when 3 loops were formed is v = f λ = 1.610 Hz x 16 feet = 25.76 ft/s.

For 4 loops, the frequency is found to be 2.16 Hz (10 cycles in 4.64 seconds), yielding a speed v of v = f λ = 2.16 Hz x 12 feet = 25.92 ft/s.  The frequency for 5 loops was 2.75 Hz (10 cycles in 3.64 sec), resulting in a wave speed of v = f λ = 2.75 Hz x 9.6 feet = 26.40 ft/s.

*Slight variations in the calculated speeds can likely be attributed to errors in measuring time and quite likely in not producing the most perfect standing wave form.

It should be no surprise that the speed calculations for standing wave are approximately equal (average speed = 25.68 ft/s), since the speed of a wave is determined by the properties of the medium, and is not affected by changes in the frequency or amplitude of the generated wave. In this case, since all standing waves were formed in same large spring that was maintained at the same constant tension, all waves should have the same speed. The actual speeds your students measure when they perform this investigation for themselves will depend on the type of spring used and how tightly it is stretched out. Students can check their wave speed by timing a single pulse as it travels down the length of the spring and back and dividing the total distance traveled by the total time.

The free computer simulation at http://phet.colorado.edu/en/simulation/wave-on-a-string allows you to further investigate wave motion, including standing waves, on a “virtual” spring.  You can read more about the production of standing waves at the free web site http://www.physicsclassroom.com/Class/waves/u10l4a.cfm.

## Super Springy

In Stock SKU: 33-0130
\$12.95
This extra-long version of the familiar and always popular spring toy provides an excellent demonstration of wave theory. Measuring 75mm in diameter, with a length of 150mm, the Super Springy stretches to 10 meters.

## Helical Spring

In Stock SKU: 33-0140
\$19.50
2cm diameter, 180cm long (collapsed) helical spring. “Snaky” is ideal for demonstrating fundamentals of wave theory, including transverse and longitudinal waves and wave behavior at the interface of two media.

## Standing Wave Kit (10pk)

In Stock SKU: P6-7700
\$55.00
Perfect for middle school and high school students, this kit includes all the materials you need to make 10 standing wave demonstrations. Instructions include qualitative and quantitative experiment ideas.

## 3D Standing Wave Machine

In Stock SKU: P6-7800
\$39.00
Turn out the lights for this mesmerizing, interactive show. A plain white string is connected to two motors to create beautiful 3D standing waves. AA batteries not included.

## Spring Wave

In Stock SKU: P7-7220
\$19.00
Use this highly-visible Spring Wave to observe phase reversal at the fixed end of wave pulses and to test fundamental and multiple vibrations. Experiment with determining the speed of propagation of transverse and longitudinal waves. expands 20in to 12ft.

## Wave Sticks

In Stock SKU: P7-7310
\$79.50
With this true torsional wave, you can easily demonstrate nearly all the fundamental aspects of mechanical waves, including: frequency, wavelength, amplitude, propagation, superposition, amplitude decay, standing waves, resonance, and reflection.

## Vortex Rings in nature and your physics classroom!

You’ve probably seen a smoker blow smoke rings or you’ve created whirlpools in your tub or pool when you were little. These phenomena are known as Vortices, formed when a fluid swirls around a central point because of a complex combination of friction and pressure. These Vortex Rings are more common and widespread in nature than most people had probably thought; in fact, they are studied in great detail by aeronautical engineers and combustion scientists. But we just think they are cool! Take a look at the video and then read below as Physics Teacher Buzz Putnam of Whitesboro High School provides more commentary on these amazing natural occurrences:

The video illustrates Vortex Rings being formed by various sources including dolphins and volcanoes. You’ll notice in the video that the Vortex Rings are quite stable until they slow down and then at some critical speed, the core enlarges very suddenly causing the vortex to breakdown. Dolphins make, watch and chase them, even using their flippers to stop them rising in what appear to be games similar to those we humans play with soap bubbles. Watch Mt. Etna emit gigantic ring-shaped clouds of steam and gas up to 200 m in diameter that can fly up to 1000 m high, lasting more than 10 minutes. Your students will realize that humans aren’t the only ones who love to make and watch Vortex Rings, one of the coolest phenomena in nature!

### Physics Teacher Magazine thinks it cool too!

The November 2011 cover for Physics Magazine shows the steam ring expelled by Etna’s summit crater.
View Physics Teacher Article>>

If you want to bring the vortex ring right into your classroom, you can do so with an Airzooka Air cannon and a fog machine (or fog in a can). Here is our Airzooka Air cannon in action:

## Resources:

Do more with vortex rings right in your classroom, check out these great links:

BBC News article: Etna hoops it up

The Physics Teacher – Smoke Ring Physics vol. 49, November 2011.

Acknowledgements: Thank you to Dwight “Buzz” Putnam for his assistance in writing this Cool Stuff. Buzz is a 25-year veteran physics teacher at Whitesboro High School, New York Science Teacher of the Year and host of the Regents Physics Answers television show on PBS. You can also find him refereeing high school basketball games as well as presenting at the NSTA national conferences.

## Products:

### Airzooka Air Cannon

This amazing new vortex launcher sends a strong blast of air all the way across the room!

### Super Fog Machine

A lab full of safe, non-toxic water-based fog in 2 minutes!

### Fog in a Can

Makes chemical fog quick and easy. Non-flammable and non-toxic. 8 oz. spray can.

## Resonance Bowl: The Original Standing Wave Demo!

The Resonance Bowl can be traced back to ancient Tao tradition in China during the Han Dynasty (202 BC – AD 9) making this an ancient, but still highly effective, way to discuss and demonstrate behavior of waves and their interactions. Fill the bowl with water, rub the handles just the right way, and water will shoot up like tiny fountain jets. Some resonance bowl masters claim to even get water leaping as high as 2 feet!

The Concepts Behind the Resonance Bowl

The vibration of the handles, in turn, increases the vibrations of the bowl, causing the bowl to vibrate. In Physics, we call this Resonance, where one vibrational frequency causes the natural vibrational frequency of another object to increase. The vibration causes two phenomenons to occur:

a. The bowl will create a sound, depending on its size (~196 Hz for a “big” bowl and ~330Hz for a “medium-sized” bowl).

b. In addition, standing waves are created in the water illustrating an interference pattern called a Chladni pattern. Standing waves are produced by the addition of two identical waves traveling simultaneously in opposite directions through any elastic medium. These waves will constructively and destructively interfere with each other as they pass one another. The resulting composite wave from the addition of these two waves will form a standing wave in the metal rim. The standing wave that is produced sets up FOUR areas of maximum vibration called antinodes, these are areas in the water that “spout” and cause the water droplets to jump off the surface. There are also FOUR areas where minimum vibration occurs and these are known as nodes. These nodes show very little water rippling while the antinodes show maximum water rippling. With practice, you should be able to create four antinodes along the entire rim of the bowl that are so strong that the water will spray out of the bowl. This occurs where the artist intentionally engraved the four fish mouths.

Other Experiments

1. If the bowl is touched firmly at any of the antinodal positions, the finger will absorb the vibrational energy, and the waves will be reduced or totally stopped. This effect is called dampening. However, if the bowl rim is touched at any nodal area, there will be little energy lost since the node has minimal vibrational energy and the spouting should continue as before.

2. By varying the amount of water in the bowl, you can investigate with your student what might be the optimal water level for maximum effect and have them explain why. Is it easier or more difficult to create the standing waves with different water levels?

3. By rubbing harder and faster, you can cause the bowl to produce a high-pitched squeak. When it does, you can sometimes create additional nodal and antinodal points in the water.

4. Try floating a cork in the water while playing with the Resonance Bowl. Observe its movements.

5. You can also place a small amount of sand in the bottom of the bowl (…instead of water) and observe how the vibrations move the sand.

Thank you to Buzz Putnam of Whitesboro High School in Marcy, NY for his contributions to this article.

## Sound and Wave Products

### Resonance Bowl

See water dance to the vibrations from your hands with the Resonance Bowl. An ancient, but highly effective way to discuss and demonstrate the behavior of waves and their interactions.

### Spring Wave

No kinks in this wave! No more kinks in your wave experiments with this versatile but light, non-tangling plastic spring. Experiment with determining the speed of propagation of transverse and longitudinal waves.

### Singing Rods

No one sleeps through this demo! Singing Rods provide an unforgettable introduction to longitudinal waves, pitch and wavelength, standing waves, nodes and anti-nodes.

### Mini Ripple Tank

A Ripple Tank that sets up in moments! The completely self contained device, requiring no setup apart from the addition of water that allows for detailed observation of all aspects of actual moving waves.

Engage, Explain, Explore, Expand and Evaluate…

## Making Ripples in Your Lecture Just Got Easier

Every once in a while we come across something that has the chance to make a real difference in the classroom in both engaging the students and making your life as a professor a little easier. We think this may be one of those times. Ripple tanks are such a wonderful way to teach your students about the concepts behind waves, but they can be time consuming to set up and take down. The new Mini Ripple Tank (PA-8638) addresses these issues by providing a completely self contained device, requiring no setup apart from the addition of water. The tank has settings that allow you to adjust the frequency of the wave and light and show everything from perfectly static to rapid wave patterns. It can be used for a small group demonstration, such as a lab, or in combination with the Physics Flex Cam for larger lecture hall settings.Waves are generated in a small, rectangular tank which is placed on a raised, transparent shelf over the internal illumination source. The wave generator is built onto the body of the unit and has an electronic drive circuit to vary the frequency which can also be synchronized to the light source. Dippers can be plugged into the generator by simply pushing them into the stem. A hinged, semi-opaque screen is situated above the tank and images of the wave are projected onto this for study. When access to the tank is required the screen lifts up out of the way. The sides of the tank are designed to absorb waves thus avoiding multiple reflections which cause confused patterns.

### INVESTIGATIONS:

The various accessories allow different wave effects to be studied. Strobe illumination gives the best results at all frequencies. Higher frequencies give shorter wavelengths with the waves closer together. Since the patterns are stationary a sheet of tracing paper or OHP film can be placed on the viewing screen and drawings made for subsequent analysis.

### REFLECTION

Observe the incident and reflected wave directions from plane waves. Vary the plate angle to see the effect. Circular waves and the reflection of these can also be studied.

### DIFFRACTION

Plane wave diffract around and behind the plate. If two plates are used with a narrow gap between them, circular waves can be seen.

### INTERFERENCE

Use the twin point dipper with nothing else in the tank. Constructive and destructive interference will be seen where the two sets of circular waves meet.

### REFRACTION

Refraction relies on the different speeds of water waves in different depths of water. As the waves slow down in the shallow water they bend round slightly towards the normal. With a single point dipper, the distortion of the circular wave pattern is very obvious. With a convex lens shape the plane waves create a focusing effect. With a concave shape and plane waves there is a divergence of the waves as they pass over the shape.

## Check Out These Cool Tools!

### Mini Ripple Tank

The Mini Ripple Tank creates Reflected, Diffracted, Refracted, and Interference waves with no fuss! It is compact and easy to use; don’t be afraid to let students experiment in groups and see for themselves.

### Physics Flex Cam

The Physics Flex Cam can easily show waves
or whatever you want to a Lecture Hall or large Classroom. You can also capture to upload or stream to the web.
1280 x 960 SXGA resolution.

### The Original Ripple Tank

The Ripple Tank is the original way to demonstrate wave phenomena in the classroom without an an overhead projector.