Suppose that the inside length of a microwave oven is 30 cm. If the length of a microwave oven is one half of the wavelength of microwaves used by the oven, find the frequency of the microwaves used in the oven.

What is the equation that relates the three of these???

Microwaves travel at the speed of light.

You must have seen this equation before for electromagnetic radiation:
(wavelength) * (frequency) = (speed of light)

Rewrite that as

2*(Microwave length)*(frequency) = 3*10^10 cm/s

Solve for the frequency

f = 5.00^10^8 Hz = 0.5 GHz

Actually, microwave ovens use a higher frequency than that.

To solve this problem, we need to determine the equation that relates the inside length of a microwave oven, the length of the microwave, and the frequency of the microwaves used.

The equation that relates these three quantities is the speed of light equation, which is given by:

Speed of light (c) = Frequency (f) x Wavelength (λ)

In this equation, the speed of light is a constant value, approximately equal to 3 x 10^8 meters per second (m/s). The frequency (f) represents the number of complete waves passing a given point in one second, and the wavelength (λ) is the distance between successive wave crests.

We are given that the inside length of the microwave oven is 30 cm. We also know that the length of the microwave is one half of the wavelength. Let's represent the wavelength as 2x, where x is the length of the microwave. Therefore, the equation becomes:

c = f * 2x

Rearranging the equation to solve for frequency (f), we get:

f = c / (2x)

where c is the speed of light and x represents the length of the microwave.

Now, we can substitute the given values into the equation:

c = 3 x 10^8 m/s
x = 30 cm = 0.3 m

Plugging these values into the equation gives us:

f = (3 x 10^8 m/s) / (2 * 0.3 m)

Simplifying:

f = 5 x 10^8 Hz

Therefore, the frequency of the microwaves used in the oven is 5 x 10^8 Hz.