The frequency of an electromagnetic wave varies inversely with the wavelength. If a wavelength of 200 meters has a frequency of 800 kilocycles per second, what frequency will be associated with wave length of 400 meters?

you know they vary inversely ... when one goes up , the other goes down

so if you double the wavelength , what happens to the frequency?

To find the frequency associated with a wavelength of 400 meters, we can use the inverse relationship between frequency and wavelength.

Let's call the frequency of the first wave f1 and the wavelength of the first wave λ1. Similarly, let's call the frequency of the second wave f2 and the wavelength of the second wave λ2.

According to the given information, we have:

λ1 = 200 meters and f1 = 800 kilocycles per second

We need to find f2 when λ2 = 400 meters.

Using the inverse relationship, we can write the equation:

f1 * λ1 = f2 * λ2

Substituting the given values:

800 kilocycles per second * 200 meters = f2 * 400 meters

(800,000 cycles/second) * (200 meters) = f2 * (400 meters)

160,000,000 cycles = f2 * 400 meters

To find f2, divide both sides of the equation by 400 meters:

f2 = 160,000,000 cycles / 400 meters

Simplifying, we get:

f2 = 400,000 cycles per meter

Therefore, a wavelength of 400 meters will have a frequency of 400,000 cycles per meter.

To solve this problem, we need to understand the relationship between frequency and wavelength. The frequency of an electromagnetic wave is inversely proportional to its wavelength. This means that as the wavelength increases, the frequency decreases, and vice versa.

In this case, we are given the wavelength of 200 meters and the corresponding frequency of 800 kilocycles per second. To find the frequency associated with a wavelength of 400 meters, we can use the inverse relationship between frequency and wavelength.

Let's set up a proportion to find the unknown frequency:

200 meters / 400 meters = 800 kilocycles per second / x

To solve for x, we can cross-multiply:

200 * x = 400 * 800

x = (400 * 800) / 200

x = 1600 kilocycles per second

Therefore, a wavelength of 400 meters will be associated with a frequency of 1600 kilocycles per second.