Question

An FM radio station generates radio waves that have a frequency of 101.3 MHz. The frequency of the waves from a competing station have a frequency of 107.1 MHz. What is the difference in wavelength between the waves emitted from the two stations

Answer 1

Given Information:

`f_(1) = 101.3`
`Mhz`

`f_(2) = 107.1`
`Mhz\\`

Required Information:

λ₁ - λ₂ = ?

Answer:

λ₁ - λ₂ = 0.16 m

Step-by-step explanation:

To find out the difference between two wavelengths , first we have to find the individual wavelength of two radio waves.

As we know Radio waves are electromagnetic waves and they travel at the speed of light. The relation between frequency, wavelength and speed of radio waves is given by

λ = c / f

Where c is the speed of light and is equal to 299792458 m/s

λ₁ = c / f₁

λ₁ = 299792458 / 101.3x10⁶

λ₁ = 2.959

λ₂ = c / f₂

λ₂ = 299792458 / 107.1x10⁶

λ₂ = 2.799 m

Therefore, the difference between the wavelengths is

λ₁ - λ₂ = 2.959 - 2.799

λ₁ - λ₂ = 0.16 m

Answer 2

0.161m

Step-by-step explanation:

Wavelength is given by:

Wavelength = speed/frequency

Where speed = speed of light (radio waves move at the speed of light)

Wavelength = c/f

For the first radio station:

Wavelength = (3 * 10^8)/(101.3 * 10^6)

Wavelength = 2.962m

For the second station:

Wavelength = (3 * 10^8)/(107.1 * 10^6)

Wavelength = 2.801m

Difference in wavelengths = 2.962 - 2.801 = 0.161m