Standing Wave Question: Wavelength of Resultant Wave with Two Opposing Waves

In summary, the wavelength of the resultant standing wave produced by two identical waves traveling in opposite directions is the same as the wavelength of the original wave. This is because a standing wave requires that the nodes and antinodes remain in the same place, and the equation for a standing wave (ysin(kx)cos(wt)) shows that the wavelength remains constant. Drawing diagrams can help visualize this concept.
  • #1
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Homework Statement



If a standing wave is produced by two identical waves traveling in opposite directions, is the wavelength of the resultant wave simply the wavelength of the original wave?


Homework Equations



ysin(kx)cos (wt)

The Attempt at a Solution



I'm pretty sure it produces a wavelength of the original wave because A standing wave requires that the nodes and antinodes remain in the same place, but I want to make sure. Please help!
 
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  • #2
sinA + sinB == 2sin((A+B)/2)cos((A-B)/2)

so a sin(kx - wt) + a sin(kx + wt) = 2a sin(kx)cos(wt)

k is 2pi/wavelength.

Any help?
 
  • #3
davieddy said:
sinA + sinB == 2sin((A+B)/2)cos((A-B)/2)

so a sin(kx - wt) + a sin(kx + wt) = 2a sin(kx)cos(wt)

k is 2pi/wavelength.

Any help?

Does that mean that the standing wave has the same wavelength as the original?
 
  • #4
vivekfan said:
Does that mean that the standing wave has the same wavelength as the original?

I think so.
Try drawing some pictures.
 

What is a standing wave?

A standing wave is a type of wave that appears to be stationary and does not move in space. This is because it is formed by the interference of two waves with the same frequency and amplitude traveling in opposite directions.

What causes standing waves to form?

Standing waves are formed when two waves with the same frequency and amplitude are traveling in opposite directions and interfere with each other. The points where the two waves meet and interfere constructively are called nodes, while the points where they interfere destructively are called antinodes.

What are the properties of standing waves?

Standing waves have a fixed pattern of nodes and antinodes, with the nodes being points of zero amplitude and the antinodes being points of maximum amplitude. They also have a fixed wavelength and frequency, which are determined by the distance between the nodes and the speed of the wave.

What are some real-life examples of standing waves?

Standing waves can be found in musical instruments, such as a guitar string or a flute. They are also present in microwave ovens, where they are used to heat food. Other examples include earthquake waves, electromagnetic waves, and water waves in a bathtub.

How are standing waves used in scientific research?

Standing waves are used in various fields of science, including physics, engineering, and acoustics. They can be used to study the properties of materials, such as their elasticity and density. They are also used in medical imaging techniques, such as ultrasound, to create detailed images of internal body structures.

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