Standing wave with microwaves

In summary: L (sorry), So, the frequencies greater than 10 GHz that would create standing waves in the microwave cavity are 11.25 GHz, 12.19 GHz, 13.13 GHz, 14.06 GHz, 15.00 GHz, 15.94 GHz, 16.88 GHz, and 17.81 GHz.In summary, a microwave generator can produce microwaves at any frequency between 10 GHz and 20 GHz, which are then aimed into a "microwave cavity" consisting of a d = 8 cm-long cylinder with reflective ends. Using the equation f=c/4L, the possible frequencies that would create standing waves in the microwave cavity are 11
  • #1
holaholayo
2
0
A microwave generator can produce microwaves at any frequency between 10 GHz and 20 GHz. The microwaves are aimed, through a small hole, into a "microwave cavity" that consists of a d = 8 cm-long cylinder with reflective ends.

Select all frequencies from those tabulated below which will create standing waves in the microwave cavity.
14.06 GHz
12.19 GHz
13.13 GHz
15.00 GHz
15.94 GHz
16.88 GHz
11.25 GHz
17.81 GHz

I have a picture but its just a closed cylinder with microwaves aimed at it from a small hole on the side. Since this is a closed-closed container, the possible frequencies would be f=v/4L.
Because microwaves are used the velocity would be 3x10^8 m/s. I used the equation to calculate the fundamental frequency f=(3x10^8)/(4x0.08) then divided that by 10^9 to get them in GHz and I got f1=0.9375 GHz. I kept on adding 0.9375 to get all the other possible frequencies because they have to be in multiples of the fundamental frequency. The frequencies bigger than 10 GHz were 10.3125 11.25 12.1875 13.125 14.0625 15.00 15.9375 16.875 17.8125 18.75 19.6875 which if I rounded to 4 sig fis would include all the frequencies that were given. But if I selected all the options, it tells me that's not right. So, am I making a mistake in calculating the frequencies?
 
Physics news on Phys.org
  • #2
The wavelength of the nth harmonic in this case is 2L/n where L is the length of the cavity (Draw out diagrams of the first few cases and you should be able to see this for your self).

Therefore the frequency of the nth harmonic is c/(2L/n) = nc/2L.
 
  • #3
Thanks!
...I don't know why I used f=v/4L
 

What is a standing wave with microwaves?

A standing wave with microwaves is a special type of electromagnetic wave that is created when two identical waves traveling in opposite directions interfere with each other. This creates areas of constructive and destructive interference, resulting in a stationary pattern of energy known as a standing wave.

How is a standing wave with microwaves produced?

A standing wave with microwaves is produced when two identical waves with the same frequency and amplitude are traveling in opposite directions. This can be achieved by reflecting microwaves off of a metal surface or by using a waveguide to confine the microwaves.

What are the characteristics of a standing wave with microwaves?

The main characteristics of a standing wave with microwaves are its nodes and antinodes. Nodes are points on the wave where there is no displacement or energy, while antinodes are points of maximum displacement and energy. The distance between two nodes or antinodes is equal to half the wavelength of the microwaves.

What is the significance of standing waves with microwaves?

Standing waves with microwaves have a variety of practical applications, such as in microwave ovens, radar technology, and telecommunications. They also play a crucial role in understanding the behavior of electromagnetic waves and the principles of wave interference.

How are standing waves with microwaves different from traveling waves?

The main difference between standing waves with microwaves and traveling waves is that standing waves have stationary patterns of energy, while traveling waves move through space. Additionally, standing waves have nodes and antinodes, whereas traveling waves do not.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
4K
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
6K
  • Advanced Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
10K
  • Advanced Physics Homework Help
Replies
6
Views
14K
Back
Top