Question

The wavelength of a radio wave varies inversely as its frequency. A wave with a frequency of 720 kilohertz has a length of 500 meters. What is the length of a wave with a frequency of 450 kilohertz?

Answer 1

Answer:

648

Explanation:

720kHz/500m=X/450kHz

X=720*450/500=72*45/5=72*9=648 meters

Answer 2

The wavelength of a wave is inversely proportional to its frequency, which can be mathematically expressed as:

wavelength ∝ 1/frequency

We can write this relationship as an equation:

wavelength = k/frequency

where k is the proportionality constant.

To find the value of k, we can use the given information. When the frequency is 720 kilohertz, the wavelength is 500 meters. Substituting these values into the equation:

500 = k/720

To solve for k, we can multiply both sides of the equation by 720:

k = 720 * 500

k = 360,000

Now that we know the value of k, we can use it to find the wavelength when the frequency is 450 kilohertz:

wavelength = k/frequency = 360,000/450

wavelength ≈ 800 meters

Therefore, a wave with a frequency of 450 kilohertz has a length of approximately 800 meters.