Editing Wave (section)

=== Wave forms ===
{{main|Waveform}}
[[File:Waveforms.svg|class=skin-invert-image|thumb|right|280 px|[[Sine wave|Sine]], [[Square wave (waveform)|square]], [[Triangle wave|triangle]] and [[Sawtooth wave|sawtooth]] waveforms]]

The form or shape of ''F'' in [[d'Alembert's formula]] involves the argument ''x'' − ''vt''. Constant values of this argument correspond to constant values of ''F'', and these constant values occur if ''x'' increases at the same rate that ''vt'' increases. That is, the wave shaped like the function ''F'' will move in the positive ''x''-direction at velocity ''v'' (and ''G'' will propagate at the same speed in the negative ''x''-direction).<ref name=Lyons>{{cite book |url = https://books.google.com/books?id=WdPGzHG3DN0C&pg=PA128 |pages = 128 ''ff'' |title = All you wanted to know about mathematics but were afraid to ask |author = Louis Lyons |isbn = 978-0-521-43601-4 |publisher = Cambridge University Press |year = 1998 }}</ref>

In the case of a periodic function ''F'' with period ''λ'', that is, ''F''(''x'' + ''λ'' − ''vt'') = ''F''(''x'' − ''vt''), the periodicity of ''F'' in space means that a snapshot of the wave at a given time ''t'' finds the wave varying periodically in space with period ''λ'' (the [[wavelength]] of the wave). In a similar fashion, this periodicity of ''F'' implies a periodicity in time as well: ''F''(''x'' − ''v''(''t'' + ''T'')) = ''F''(''x'' − ''vt'') provided ''vT'' = ''λ'', so an observation of the wave at a fixed location ''x'' finds the wave undulating periodically in time with period ''T'' = ''λ''/''v''.<ref name="McPherson0">{{cite book |title = Introduction to Macromolecular Crystallography |last = McPherson |first= Alexander |chapter-url = https://books.google.com/books?id=o7sXm2GSr9IC&pg=PA77 |page = 77 |chapter = Waves and their properties |isbn = 978-0-470-18590-2 |year = 2009 |edition = 2 |publisher = Wiley }}</ref>