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# Big Standing Wave - Small Effort!

Posted on March15,2012 by Arbor Scientific, authored by Dr. Joel Bryan There have been 1 comment(s)

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.

Image taken from http://www.watervalley.net/users/bolen/page5.html

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 SpringyProduct # 33-0130

\$13.00

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 SpringProduct # 33-0140

\$19.00

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)Product # 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 MachineProduct # 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 WaveProduct # P7-7220

\$22.00

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 SticksProduct # 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.

This post was posted in CoolStuff Newsletters, Sound & Waves

## 1 Response to Big Standing Wave - Small Effort!

• Irem says:

actually, it all depends on the wavetenglh of the IR.Near IR can go trough glass like the visible till around 1.5b5m.Glass absorbs at around 3b5m and up. Thermal imaging detects wavetenglhs around 10b5m, so you won't detect anything behind a glass.

Posted on September28,2012 at 1:24am