Mechanical Waves - Revision history

Zhaoxian Zhang at 19:17, 24 July 2022

2022-07-24T19:17:02Z

← Older revision		Revision as of 15:17, 24 July 2022
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	Find the speed of the wave described above		Find the speed of the wave described above:

Smathur62: /* Connectedness */

2022-04-26T02:12:58Z

Connectedness

← Older revision		Revision as of 22:12, 25 April 2022
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	==Connectedness==		==Connectedness==

	* This topic is connected to the way sound ~~move~~. They're created by an object vibrating and generating pulses of pressure waves that travel through the air and carry energy over distances.		* This topic is connected to the way sound moves. They're created by an object vibrating and generating pulses of pressure waves that travel through the air and carry energy over distances.

	==History==		==History==

Smathur62 at 01:02, 26 April 2022

2022-04-26T01:02:52Z

← Older revision		Revision as of 21:02, 25 April 2022
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	== See also ==		== See also ==

	Connected topics include Electromagnetic Waves and Spring Motion,		Connected topics include Electromagnetic Waves and Spring Motion.

	===Further reading===		===Further reading===

Smathur62: Completed first push of full page

2022-04-26T01:01:56Z

Completed first push of full page

← Older revision		Revision as of 21:01, 25 April 2022
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	Q1) What kind of wave is a stadium wave?		Q1) What kind of wave is a stadium wave?


	A1) Transverse Wave		A1) Transverse Wave
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	To find the wavelength <math>\lambda</math>, we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:		To find the wavelength <math>\lambda</math>, we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:

	<math>v = (210^9)(1010^9) = \textbf{2*10^{19}}</math>		<math>v = (210^9)(1010^9) = \textbf{2*10^19}</math>

	===Difficult===		===Difficult===

			Q3) A transverse wave moves across a string. The wave can be represented with the equation <math>y(x,t)=0.5*sin(7x-3t)</math> with respect to it's position <math>x</math> in meters and time <math>t</math> in seconds. Find the amplitude, wavelength, period, and speed of the wave.


			A3) For this question, we can use a lot of the wave functions we've learned from the past in order to convert the constants in this equation to the characteristics needed. First, we can write this equation as a form of its parent function:

			<math>y(x,t)=Asin(kx-\omega t)</math>

			Where <math>A</math> is the amplitude, <math>k</math> is the wave number, and <math>\omega</math> is the angular frequency. From reading the given equation, we can find:

			<math>\textbf{Amplitude = 0.5 m}</math>

			<math>k = 7</math>

			<math>\omega =3</math>

			We can use the wave number <math>k</math> to find the wavelength:

			<math>k=\frac{2\pi}{\lambda}</math>

			<math>\textbf{Wavelength = λ}=\frac{2\pi}{k}≈\textbf{0.898 m}</math>

			To find the period <math>T</math>, we convert from the angular frequency with this equation:

			<math>\omega =\frac{2\pi}{T}</math>

			<math>\textbf{Period = T = }=\frac{2\pi}{\omega}≈\textbf{2.094 s}</math>

			Finally, to find the speed, we can an altered version of the wave equation to substitute in <math>k</math> in order to make it easier:

			<math>v=\frac{\omega}{k}</math>

			<math>=\frac{3}{7}≈0.429</math>

			<math>\textbf{Speed = v ≈ 0.429}</math>

	==Connectedness==		==Connectedness==
	~~#How is this~~ topic ~~connected to something that you are interested in?~~
	~~#How~~ is it connected to ~~your major?~~		* This topic is connected to the way sound move. They're created by an object vibrating and generating pulses of pressure waves that travel through the air and carry energy over distances.
	~~#Is there~~ an ~~interesting industrial application?~~

	==History==		==History==

	~~Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.~~		*Wasn't able to find directly related information to mechanical waves

	== See also ==		== See also ==

	~~Are there related~~ topics ~~or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?~~		Connected topics include Electromagnetic Waves and Spring Motion,

	===Further reading===		===Further reading===

	~~Books, Articles or other print media on this topic~~		From cK-12.org: [https://www.ck12.org/physics/mechanical-wave/lesson/Mechanical-Wave-MS-PS/?referrer=concept_details]

			From Texas A&M University: [http://people.tamu.edu/~mahapatra/teaching/ch15.pdf]

	===External links===		===External links===

Smathur62 at 23:52, 25 April 2022

2022-04-25T23:52:56Z

← Older revision		Revision as of 19:52, 25 April 2022
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	(The units of both of axis of this graph are in nm)		(The units of both of axis of this graph are in nm)


	Find the speed of the wave described above		Find the speed of the wave described above



	A2)		A2)

Smathur62: Completed simple and middle example problems

2022-04-25T23:51:59Z

Completed simple and middle example problems

← Older revision		Revision as of 19:51, 25 April 2022
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	===Simple===		===Simple===

	Q1)~~https://calendar.google.com/calendar/u/0/r~~		Q1) What kind of wave is a stadium wave?

			A1) Transverse Wave

			===Middling===

			Q2)
	A wave travels with a period of 5 ns. The wave can be seen in the image below:		A wave travels with a period of 5 ns. The wave can be seen in the image below:
	[[File:SimpleWave.png]]		[[File:SimpleWave.png]]
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	Find the speed of the wave described above		Find the speed of the wave described above

	A1)		A2)
	The wave equation to find the speed of this function is: <math>v = \lambda f</math>. To find the frequency, we apply the conversion from period to frequency: <math>f=1/T</math>		The wave equation to find the speed of this function is: <math>v = \lambda f</math>. To find the frequency, we apply the conversion from period to frequency: <math>f=1/T</math>

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	To find the wavelength <math>\lambda</math>, we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:		To find the wavelength <math>\lambda</math>, we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:

	<math>v = (210^9)(1010^9) = ~~</math>~~		<math>v = (210^9)(1010^9) = \textbf{2*10^{19}}</math>
	~~<bold><math>~~2*10^19</math~~></bold~~>


	~~===Middling===~~
	===Difficult===		===Difficult===

Smathur62 at 23:34, 25 April 2022

2022-04-25T23:34:15Z

← Older revision		Revision as of 19:34, 25 April 2022
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	===Simple===		===Simple===

	Q1)		Q1)https://calendar.google.com/calendar/u/0/r
	A wave travels with a period of 5 ns. The wave can be seen in the image below:		A wave travels with a period of 5 ns. The wave can be seen in the image below:
	[[File:SimpleWave.png]]		[[File:SimpleWave.png]]

	(The units of both of axis of this graph are in nm)		(The units of both of axis of this graph are in nm)

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	A1)		A1)
	The wave equation to find the speed of this function is: <math>v = \lambda f</math>. To find the frequency, we apply the conversion from period to frequency: <math>f=1/T</math>		The wave equation to find the speed of this function is: <math>v = \lambda f</math>. To find the frequency, we apply the conversion from period to frequency: <math>f=1/T</math>
	<math>f=\frac{1}{510^{-9}} = \~~boldmath$~~210^8$</math>
			<math>f=\frac{1}{510^{-9}} = 210^8</math>

			To find the wavelength <math>\lambda</math>, we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:

			<math>v = (210^9)(1010^9) = </math>
			<bold><math>2*10^19</math></bold>

Smathur62 at 23:13, 25 April 2022

2022-04-25T23:13:55Z

← Older revision		Revision as of 19:13, 25 April 2022
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	==Examples==		==Examples==

	~~Be sure to show all steps in your solution and include diagrams whenever possible~~

	===Simple===		===Simple===

			Q1)
			A wave travels with a period of 5 ns. The wave can be seen in the image below:
			[[File:SimpleWave.png]]
			(The units of both of axis of this graph are in nm)

			Find the speed of the wave described above

			A1)
			The wave equation to find the speed of this function is: <math>v = \lambda f</math>. To find the frequency, we apply the conversion from period to frequency: <math>f=1/T</math>
			<math>f=\frac{1}{510^{-9}} = \boldmath$210^8$</math>


	===Middling===		===Middling===
	===Difficult===		===Difficult===
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	===External links===		===External links===
	[https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/16.4/primary/lesson/surface-wave-ms-ps/]		[https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/16.4/primary/lesson/surface-wave-ms-ps/]

	[https://webhome.phy.duke.edu/~lee/P142/Ref_Waves.pdf]		[https://webhome.phy.duke.edu/~lee/P142/Ref_Waves.pdf]

Smathur62: Completed the mathematical model section

2022-04-25T20:13:11Z

Completed the mathematical model section

← Older revision		Revision as of 16:13, 25 April 2022
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	===A Mathematical Model===		===A Mathematical Model===

	~~What are the mathematical~~ equations that ~~allow us~~ to ~~model this topic~~. ~~For example~~ <math>{\~~frac{d~~\~~vec~~{~~p}}{dt}}_{system~~} = \~~vec~~{~~F}_{net~~}</math> where ~~'''p'''~~ is the ~~momentum~~ of the ~~system~~ and ~~'''F''' is the net force from~~ the ~~surroundings~~.		Mechanical waves implement a variety of equations that can be used to solve for different characteristics of a wave.
			The wave equation is used to find the speed of propagation of a transverse wave:

			<math>v = \lambda f</math>

			Where <math>v</math> is the velocity, <math>\lambda</math> is the wavelength, and <math>v</math> is the frequency. Another form of this equation specific to mechanical waves is the formula:

			<math>v = \sqrt{Stiffness/Inertia}</math>

			Another common form of this equation is the wave speed for a stretched string, <math>v = \sqrt{T/\mu}</math>, where <math>T</math> is the string tension and <math>\mu</math> is the mass per unit length of string. This equation allows for the calculation of the speed of a wave in different forms of matter. To find the equation of a wave that falls under two different mediums, we can apply superposition to find the new wave equation by adding the functions the two different functions that describe possible waves in the medium:

			<math>y(x,t)=y_{1}+y_{2}</math>

			Where <math>y_{1}</math> and <math>y_{2}</math> are the two possible wave functions for different mediums.

	===A Computational Model===		===A Computational Model===
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	===External links===		===External links===
	[https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/16.4/primary/lesson/surface-wave-ms-ps/]		[https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/16.4/primary/lesson/surface-wave-ms-ps/]
			[https://webhome.phy.duke.edu/~lee/P142/Ref_Waves.pdf]

Smathur62: Completed Main Idea with examples for all three types of mechanical waves

2022-04-25T18:39:52Z

Completed Main Idea with examples for all three types of mechanical waves

← Older revision		Revision as of 14:39, 25 April 2022
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	'''Transverse Waves:'''		'''Transverse Waves:'''

	Waves in which the particles oscillate back and forth in the direction perpendicular to the motion of the wave. The particle travels the length of the amplitude of the and completes its oscillation corresponding to when the wave moves over one wavelength. Some examples of transverse waves are ripples in the water and a ~~rope being~~		Waves in which the particles oscillate back and forth in the direction perpendicular to the motion of the wave. The particle travels the length of the amplitude of the and completes its oscillation corresponding to when the wave moves over one wavelength. Some examples of transverse waves are ripples in the water and a vibrating string.

			[[File:Twave.gif]]
			[https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html]


	'''Longitudinal Waves:'''		'''Longitudinal Waves:'''

	Waves in which the particles move in the same direction as the wave motion. While still in an oscillating motion, they move "~~side~~-to-~~side~~" with respect to the direction the wave is ~~moving~~ in		Waves in which the particles move in the same direction as the wave motion. While still in an oscillating motion, they move "back-and-forth" with respect to the direction the wave is propagating in. Some examples of longitudinal waves include sound waves and the motion of compressing and stretching a spring.

			[[File:Lwave.gif]]
			[https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html]


	'''Surface Waves:'''		'''Surface Waves:'''

			Waves in which the particles within the medium move both parallel and perpendicular to the propagation direction of the wave. They're called surface waves due to their nature of travelling along the surface of a medium. This gives the particles on the wave a circular-like motion. The surface of a wave in the water is the most direct example of a surface wave; other examples include seismic waves and gravity waves along the surface of liquids.

			[[File:Swave.gif]]
			[https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html]

	===A Mathematical Model===		===A Mathematical Model===
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	===External links===		===External links===
	[~~http~~://~~www~~.~~scientificamerican~~.~~com~~/~~article~~/~~bring~~-science-~~home~~-~~reaction~~-~~time~~/]		[https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/16.4/primary/lesson/surface-wave-ms-ps/]