Mechanical Waves: Difference between revisions
(Completed Main Idea with examples for all three types of mechanical waves) |
(Completed the mathematical model section) |
||
| Line 37: | Line 37: | ||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
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=== | ||
| Line 70: | Line 83: | ||
===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] | |||
Revision as of 16:13, 25 April 2022
Claimed by Snehil Mathur (Spring 2022)
Mechanical Waves are waves that propagate through a medium, one that is either solid, liquid, or gas. The speed at which a wave travels depends on the mediums' properties, both elastic and inertial.
The Main Idea
Waves can be described as disturbances that travel through space and can transport energy from its source to another location. These are often represented in an oscillating manner.
Mechanical waves are waves that propagate through matter (gas, liquid, or solid) and require a medium in order to transport energy. Inherently, these waves cannot travel through a vacuum.
There are three main types of mechanical 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 vibrating string.
Longitudinal Waves:
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.
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.
A Mathematical Model
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]\displaystyle{ v = \lambda f }[/math]
Where [math]\displaystyle{ v }[/math] is the velocity, [math]\displaystyle{ \lambda }[/math] is the wavelength, and [math]\displaystyle{ v }[/math] is the frequency. Another form of this equation specific to mechanical waves is the formula:
[math]\displaystyle{ v = \sqrt{Stiffness/Inertia} }[/math]
Another common form of this equation is the wave speed for a stretched string, [math]\displaystyle{ v = \sqrt{T/\mu} }[/math], where [math]\displaystyle{ T }[/math] is the string tension and [math]\displaystyle{ \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]\displaystyle{ y(x,t)=y_{1}+y_{2} }[/math]
Where [math]\displaystyle{ y_{1} }[/math] and [math]\displaystyle{ y_{2} }[/math] are the two possible wave functions for different mediums.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
Middling
Difficult
Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
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?
Further reading
Books, Articles or other print media on this topic
External links
References
This section contains the the references you used while writing this page