Understanding the Relationship

* Frequency (f): How many wave cycles pass a point per second, measured in Hertz (Hz).

* Wavelength (λ): The distance between two consecutive crests (or troughs) of a wave, measured in meters (m).

* Speed of Light (c): The speed at which all electromagnetic radiation travels in a vacuum, approximately 3 x 10⁸ m/s.

The Formula

The relationship between these three is:

c = fλ

Solving for Wavelength

1. Rearrange the formula to solve for wavelength: λ = c / f

2. Plug in the values:

* c = 3 x 10⁸ m/s

* f = 3 x 10¹² Hz

3. Calculate: λ = (3 x 10⁸ m/s) / (3 x 10¹² Hz) = 1 x 10⁻⁴ m

Converting to Micrometers

Since infrared wavelengths are often expressed in micrometers (µm), convert the answer:

1 x 10⁻⁴ m = 100 µm

Answer

The wavelength of a 3 x 10¹² Hz infrared wave is 100 µm.