The Mechanical Wave Value Pack is an important addition the laboratory of any teacher who is passionate about the physics of waves or the physics of sound. The applications for these materials are far reaching and they provide analogies for several topics in physics, chemistry, and other sciences. At the heart of the collection is the Mechanical Wave Driver. This device is very much like a speaker cone, but attaches effectively to every apparatus in the set. The driver is powered by the sine wave generator which is adjustable over a wide range of frequencies.

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Sound and Waves Demonstrations

*The Mechanical Wave Driver and Sine Wave Generator are used in all the experiments.*

A typical experiment which utilizes the driver is Standing Waves on a String. A string is threaded through one of the fitted plugs for the driver and the other end is tied to a weight. This is hung over a pulley or smooth surface and its weight provides a near-constant tension in the string.

*A variety of standing waves can be produced. The frequencies will be in simple ratios, in this case 3:2.*

The wave formulas can be checked against experiment, and usually generate good results. The wavelength is the distance between two nodes, which are the points that do not move. The places that move the most are called antinodes. A good lab would be to prove that the product of λ and f is a constant for a fixed length and tension. An advanced lab could be to prove that the second formula is valid in any situation.

The Tension is **Mg** where **M** is the mass hanging, and **L** is the length of the portion of string that is vibrating. However, only the part that is vibrating is to be considered as "m." Therefore, it is helpful to know the total mass of the string and the total length of the string. Then, measuring the un-stretched length of the portion vibrating, one can estimate its mass accurately as a fraction of the total string.

Attaching a spring to the apparatus will enable teachers and students to demonstrate longitudinal waves. Standing wave experiments (similar to the string ones) can be performed, including investigating the same wave formulas listed above. This device can serve as a useful analogy to sound, and students should be informed that all woodwind and brass instruments rely on standing longitudinal sound waves.

*Standing longitudinal waves on a spring is the first accessory that you may wish to try out from the value pack.*

Aside from it being interesting, the Resonance Wire Loop device provides an opportunity to show that standing wave propagation does not necessarily mean reflection is involved. In this case, the waves travel around the loop and cycle back upon themselves. There is a further application to the mathematics and visualization of electron waves which are also circular waves in the early Bohr / de Broglie model of the atom.

*The Resonance Wire Loop apparatus provides a new perspective on wave propagation.*

The standing electron waves model helps explain why electrons do not simply orbit any distance around the nucleus, but remain in specific resonant orbits. Like any standing wave, an electron wavelength that does not resonate would interfere destructively with itself and be quickly canceled.

Students will naturally be confused about how the Bohr atomic shell model is evidence for quantum wave behavior. But this device clarifies that the origin of the shells is a consequence of electrons behaving as standing waves. Only integral wavelengths will cycle around constructively.

*The Bohr model of the atom may be demonstrated*

Another device that serves both as a demo and as an analogy is the metal resonance strips. These strips will vibrate only at their specific frequencies (and higher harmonics). The application of this is that buildings can be destroyed when they resonate under the influence of earthquake waves. For this reason, buildings are sometimes fitted with seismic dampeners which reduce these resonant vibrations.

*Compare physical dimensions to harmonic frequencies*

Chladni Plates are a classic physics demonstrations that every teacher should have in his or her classroom. The plate is driven at various frequencies which produce unique wave patterns by moving sand grains away from places of large vibration toward nodal lines (where vibration is minimal). However, because the plate is flat (and not a string) there are many more paths for the transverse waves to vibrate through. These waves reflect freely off the edges and interfere constructively to create interesting standing wave patterns.

*The round Chladni plate displays waves that are radially symmetric.*

The plates can be vibrated with a violin bow, but this is not always available, takes practice, and must be driven in specific locations. One advantage of bowing is that you get resonances that have the center as a node. However, the mechanical wave driver offers the advantage of being able to resonate specific frequencies that work best. Having specific driving frequencies also emphasizes that it is not skill that causes the pattern, but rather the natural resonances of the plate.

*Julius Sumner Miller demonstrates that Chladni plates can be driven the old-fashioned way, with a violin bow.*

The square Chladni Plate can demonstrate a larger variety of patterns because of how the mass of the plate is not constant radially. As the waves travel out from the center, the amount of mass that vibrates is dependent upon the direction. This changes the speed at which the waves travel and thus the wavelength (and distance between nodes) thereby creating more intricate and surprising standing wave patterns. The mathematics of this phenomena is challenging and if you are interested in further study I recommend the following articles from the American Journal of Physics: Rossing, 50, (1982); Comer, et al, 72, (2004).

# About the Contributor: James Lincoln

James Lincoln is an experienced physics teacher with graduate degrees in education and applied physics. He has become known nationally as a physics education expert specializing in original demonstrations, the history of physics, and innovative hands-on instruction.The American Association of Physics Teachers and the Brown Foundation have funded his prior physics film series and SCAAPT's New Physics Teacher Workshops.Lincoln currently serves as the Chair of AAPT's Committee on Apparatus and has served as President of the Southern California Chapter of the AAPT, as a member of the California State Advisory for the Next Generation Science Standards, and as an AP Physics Exam Reader. He has also produced Videos Series for UCLA's Physics Demos Project, Arbor Scientific, eHow.com, About.com, and edX.org.