This is the second day of a lesson designed to provide students the opportunity to travel through a series of lab stations that connect to the following NGSS and Common Core Standards:
Longitudinal Waves Diagram. Longitudinal wave longitudinal waves are waves in which the displacement of the medium is in the same direction as or the opposite direction to the direction of propagation of the wave mechanical longitudinal waves are also called pressional or pression waves because they produce pression and rarefaction when traveling through a medium and pressure waves because. 2 GCE ‘O’ LEVEL Nov 1995 Transverse waves are waves that their direction of vibration is perpendicular to their direction of propagation. Longitudinal waves are waves that their direction of vibration is parallel to their direction of propagation. (continue on next slide) 38. 9.(b) The speed of sound in water is 1500m/s.
MS-PS4-1 Use mathematical representation to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.
MS-PS-4-2 Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials.
CCSS.ELA Reading: Science & Technical Subjects Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
CCSS.7.Ratios and Proportional Relationships 2 Recognize and represent proportional relationships between quantities.
CCSS.Mathematical Practice 2 Reason abstractly and quantitatively.
CCSS.ELA-LITERACY.WHST.6-8.2.A Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
At this point, students have had multiple experiences engaging with each of these standards in previous lessons. They have created models representing energy and amplitude and have explored the relationship between frequency, wavelength, and pitch using slinkies. Moreover, they have created models of transmission, absorption, and reflection. This series of lab stations is therefore an extremely independent activity for students providing them with more interactions with the standards. Therefore, it is a great lesson to focus on students that have not been demonstrating mastery on specific topics and help them make connections that they have not yet previously made.
In this lab rotation, students continue to create models that explain phenomena (SP2). In addition, students utilize the Crosscutting Concept of Patterns by using graphs to identify patterns and relationships between variables such as frequency and wavelength. However, one new aspect that we begin to discuss is the mathematical representation of what a wave looks like and how proportions and scale can effect the graph of a wave. Thus, this lesson also addresses the Crosscutting Concept of Scale, Proportion, and Quantity. This explains that 'in considering phenomena, it is critical to recognize how changes in scale, proportion, or quantity affect a system’s structure or performance.'
On Day 1 of the lesson, students are introduced to the idea of how a wave can be graphed in a coordinate plane on a Displacement vs. Time/Distance plot. In this lab, students have to create graphs that demonstrate general relationships of both transverse and longitudinal waves in order to develop their mathematical and conceptual thinking (SP5). On this second day of instruction, students are introduced to graphing a wave based on specific numbers instead of general relationships and begin manipulating the graphs of waves to demonstrate a proportional understanding of wave relationships.
Plane pressure pulse wave
Representation of the propagation of an omnidirectional pulse wave on a 2d grid (empirical shape)
Longitudinal waves are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure.
The other main type of wave is the transverse wave, in which the displacements of the medium are at right angles to the direction of propagation. Some transverse waves are mechanical, meaning that the wave needs an elastic medium to travel through. Transverse mechanical waves are also called 'shear waves'.
By acronym, 'longitudinal waves' and 'transverse waves' were occasionally abbreviated by some authors as 'L-waves' and 'T-waves' respectively for their own convenience.[1] While these two acronyms have specific meanings in seismology (L-wave for Love wave[2] or long wave[3]) and electrocardiography (see T wave), some authors chose to use 'l-waves' (lowercase 'L') and 't-waves' instead, although they are not commonly found in physics writings except for some popular science books.[4]
Longitudinal waves include sound waves (vibrations in pressure, particle of displacement, and particle velocity propagated in an elastic medium) and seismic P-waves (created by earthquakes and explosions).In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave, and waves can be either straight or round. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization.
Sound waves[edit]
In the case of longitudinal harmonic sound waves, the frequency and wavelength can be described by the formula
where:
y is the displacement of the point on the traveling sound wave;
x is the distance the point has traveled from the wave's source;
t is the time elapsed;
y0 is the amplitude of the oscillations,
c is the speed of the wave; and
ω is the angular frequency of the wave.
The quantity x/c is the time that the wave takes to travel the distance x.
The ordinary frequency (f) of the wave is given by
The wavelength can be calculated as the relation between a wave's speed and ordinary frequency.
For sound waves, the amplitude of the wave is the difference between the pressure of the undisturbed air and the maximum pressure caused by the wave.
Sound's propagation speed depends on the type, temperature, and composition of the medium through which it propagates.
Pressure waves[edit]
In an elastic medium with rigidity, a harmonic pressure wave oscillation has the form,
where:
y0 is the amplitude of displacement,
k is the angular wavenumber,
x is the distance along the axis of propagation,
ω is the angular frequency,
t is the time, and
φ is the phase difference.
The restoring force, which acts to return the medium to its original position, is provided by the medium's bulk modulus.[5]
Electromagnetic waves[edit]
Maxwell's equations lead to the prediction of electromagnetic waves in a vacuum, which are transverse (in that the electric fields and magnetic fields vary perpendicularly to the direction of propagation).[6] However, waves can exist in plasmas or confined spaces, called plasma waves, which can be longitudinal, transverse, or a mixture of both.[6][7] Plasma waves can also occur in force-free magnetic fields. [8]
In the early development of electromagnetism, there were some like Alexandru Proca (1897-1955) known for developing relativistic quantum field equations bearing his name (Proca's equations) for the massive, vector spin-1 mesons. In recent decades, some extended electromagnetic theorists, such as Jean-Pierre Vigier and Bo Lehnert of the Swedish Royal Society, have used the Proca equation in an attempt to demonstrate photon mass [9] as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum.
After Heaviside's attempts to generalize Maxwell's equations, Heaviside came to the conclusion that electromagnetic waves were not to be found as longitudinal waves in 'free space' or homogeneous media.[10] But Maxwell's equations do lead to the appearance of longitudinal waves under some circumstances, for example, in plasma waves or guided waves. Basically distinct from the 'free-space' waves, such as those studied by Hertz in his UHF experiments, are Zenneck waves.[11] The longitudinal modes of a resonant cavity are the particular standing wave patterns formed by waves confined in a cavity. The longitudinal modes correspond to those wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces. Recently, Haifeng Wang et al. proposed a method that can generate a longitudinal electromagnetic (light) wave in free space, and this wave can propagate without divergence for a few wavelengths.[12]
See also[edit]
References[edit]
^Erhard Winkler (1997), Stone in Architecture: Properties, Durability, p.55 and p.57, Springer Science & Business Media
^Michael Allaby (2008), A Dictionary of Earth Sciences (3 ed.), Oxford University Press
^Francine Milford (2016), The Tuning Fork, pp.43-4
^Weisstein, Eric W., 'P-Wave'. Eric Weisstein's World of Science.
^ abDavid J. Griffiths, Introduction to Electrodynamics, ISBN0-13-805326-X
^John D. Jackson, Classical Electrodynamics, ISBN0-471-30932-X.
^Gerald E. Marsh (1996), Force-free Magnetic Fields, World Scientific, ISBN981-02-2497-4
^Lakes, R. (1998). Experimental limits on the photon mass and cosmic magnetic vector potential. Physical review letters, 80(9), 1826-1829
^Heaviside, Oliver, 'Electromagnetic theory'. Appendices: D. On compressional electric or magnetic waves. Chelsea Pub Co; 3rd edition (1971) 082840237X
^Corum, K. L., and J. F. Corum, 'The Zenneck surface wave', Nikola Tesla, Lightning observations, and stationary waves, Appendix II. 1994.
^Haifeng Wang, Luping Shi, Boris Luk'yanchuk, Colin Sheppard and Chong Tow Chong, 'Creation of a needle of longitudinally polarized light in vacuum using binary optics,' Nature Photonics, Vol.2, pp 501-505, 2008, doi:10.1038/nphoton.2008.127
Further reading[edit]
Varadan, V. K., and Vasundara V. Varadan, 'Elastic wave scattering and propagation'. Attenuation due to scattering of ultrasonic compressional waves in granular media - A.J. Devaney, H. Levine, and T. Plona. Ann Arbor, Mich., Ann Arbor Science, 1982.
Schaaf, John van der, Jaap C. Schouten, and Cor M. van den Bleek, 'Experimental Observation of Pressure Waves in Gas-Solids Fluidized Beds'. American Institute of Chemical Engineers. New York, N.Y., 1997.
Krishan, S, and A A Selim, 'Generation of transverse waves by non-linear wave-wave interaction'. Department of Physics, University of Alberta, Edmonton, Canada.
Barrow, W. L., 'Transmission of electromagnetic waves in hollow tubes of metal', Proc. IRE, vol. 24, pp. 1298–1398, October 1936.
Russell, Dan, 'Longitudinal and Transverse Wave Motion'. Acoustics Animations, Pennsylvania State University, Graduate Program in Acoustics.
Longitudinal Waves, with animations 'The Physics Classroom'
External links[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Longitudinal_wave&oldid=918101525'