# Monthly Archives - March 2012

## “It’s Spring… Time for the “Spring Wave!”

A really great addition to the Standing Wave lab that I did with my students this year is using the new plastic “Spring Wave” along with the metal Helical “Snakee spring” that we all use for demonstrating a Standing Wave. I have added them as an unknown to the lab. The students will have to use the “Spring Wave” at a set distance to determine its speed.  I used to use telephone cords but they are becoming much more scarce and besides, the “Spring Wave” works so much better and it introduces a new medium for the wave to pass through.  I have the students stand apart the EXACTLY same distance as the Helical spring.  The velocity in the two springs WILL be different because the two springs are made of a different material (steel vs. plastic). If you keep the same distance between the spring, you introduce the variant of the wave medium while keeping the distance constant.  I can tell you that the students had a good time doing the lab and it really hammers home the concept that the two oppositely-traveling waves MUST have the same frequency.  The students cannot produce the different standing wave modes unless they achieve JUST the right frequency, otherwise the resulting wave is just a chaotic mess. Finally using an unknown in the lab that the wave will be produced in is a real plus in driving home the point that waves travel different speeds in different media. The best part is that you don’t need any cutting pliers… No tangles!

## 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.

## Go Nuts with Neodymium Magnets!

This week I began Magnetism in class and wanted to “wow” my students with Magnetism. Take a Neodymium magnet to show the concepts of Ferromagnetism and Diamagnetism. I used an American “crisp” \$5 bill and taped a thread to it. Hanging it from a crossbar and using the Neodymium magnet, you can attract the bill. Then… I took a WHOLE flake of “Total” cereal and taped it to a thread, hanging it from the crossbar. The Neodymium attracts the flake to about 30 degrees from the vertical! If you REALLY want to astound your students, take two FRESH grapes and stick them on each end of a tiny dowel rod (like a “grape barbell”) and hang the arrangement from the crossbar. I held the Neodymium near one of the grapes and the grape rotated AWAY from the magnet. When the students see that food is repelled from a magnet, they are amazed! The Diamagnetism of water is demonstrated in a cool way!