# Standing wave with microwaves

1. Apr 26, 2009

### holaholayo

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?

2. Apr 26, 2009

### MalachiK

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. Apr 26, 2009

### holaholayo

Thanks!
...I don't know why I used f=v/4L