Question

Infrared waves from the sun are what make our skin feel warm on a sunny day. If an infrared wave has a frequency of 3.0 x 1012 Hz, what is its wavelength?

Answer 1

The wavelength of the infrared wave is 0.0001 m.

Step-by-step explanation:

Given:

Frequency of an infrared wave is,
`f=3.0* 10^(12)\ Hz`

We know that, infrared waves are electromagnetic waves. All electromagnetic waves travel with the same speed and their magnitude is equal to the speed of light in air.

So, speed of infrared waves coming from the Sun travels with the speed of light and thus its magnitude is given as:

`v=c=3.0* 10^8\ m/s`

Where, 'v' is the speed of infrared waves and 'c' is the speed of light.

Now, we have a formula for the speed of any wave and is given as:

`v=f\lambda`

Where,
`\lambda \to \textrm{Wavelength of infrared wave}`

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

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

Now, plug in
`3.0* 10^8` for 'v',
`3.0* 10^(12)` for 'f' and solve for
`\lambda`. This gives,

`\lambda=(3.0* 10^8)/(3.0* 10^(12))\\\\\lambda=0.0001\ m`

Therefore, the wavelength of the infrared wave is 0.0001 m.