Question

What is the wavelength of a light wave if the frequency of the wave is 7.1 x 10^14 s^-1 (Hz)?

Answer 1

Wavelength =
`4.225* 10^(-7)\ m`.

Step-by-step explanation:

Given:

The wave is a light wave. So, speed of light wave is,
`c=3* 10^8\ m/s`

The frequency of the light wave is,
`f=7.1* 10^(14)\ s^(-1)`

Let the wavelength of the light wave be
`\lambda`.

Now, velocity of a wave is related to its frequency and wavelength as:

`c=f\lambda`

Now, rewriting the above formula in terms of wavelength
`\lambda`, we have

`\lambda=(c)/(f)`

Plug in
`c=3* 10^8\ m/s` and
`f=7.1* 10^(14)\ s^(-1)`. Solve for
`\lambda`. This gives,

`\lambda=(3* 10^8\ ms^(-1))/(7.1* 10^(14)\ s^(-1))\\\\\lambda=4.225* 10^(-7)\ m`

Therefore, the wavelength of the light wave is
`4.225* 10^(-7)\ m`.