Understanding the Relationship
* Wavelength (λ): The distance between two consecutive crests or troughs of a wave. You're given this: 400 nanometers (nm).
* Frequency (f): The number of wave cycles passing a fixed point per second. This is what we want to find.
* Speed of Light (c): The constant speed at which light travels in a vacuum, approximately 3 x 10⁸ meters per second (m/s).
The Formula
The relationship between wavelength, frequency, and the speed of light is:
* c = λf
Calculations
1. Convert wavelength to meters:
* 400 nm = 400 x 10⁻⁹ meters
2. Rearrange the formula to solve for frequency:
* f = c / λ
3. Plug in the values:
* f = (3 x 10⁸ m/s) / (400 x 10⁻⁹ m)
4. Calculate:
* f = 7.5 x 10¹⁴ Hz (Hertz)
Answer
The wave frequency for 400 nanometers is 7.5 x 10¹⁴ Hz.
