A light wave has a frequency of \(5 \times 10^{14}\) Hz. Using the speed of light \(c = 3 \times 10^8\) m/s, calculate its wavelength.

["Understanding Light Waves: How to Calculate Wavelength from Frequency", "Light is a form of electromagnetic radiation, and one of its key properties is its wavelength—the distance between consecutive peaks or troughs in a light wave. Understanding how to calculate wavelength is essential in physics, optics, and related fields.", "### The Relationship Between Frequency, Wavelength, and the Speed of Light", "Light waves travel at a constant speed in a vacuum, known as the speed of light, denoted by ( c ), which is approximately ( 3 \ imes 10^8 ) meters per second (( 3 \ imes 10^8 , \ ext{m/s} )). This speed is related to the frequency (( f )) and wavelength (( \lambda )) of a light wave by the fundamental equation:", "[\nc = \lambda \cdot f\n]", "Rearranging this formula allows us to calculate the wavelength:", "[\n\lambda = \frac{c}{f}\n]", "### Example: Calculating Wavelength for a Frequency of ( 5 \ imes 10^{14} ) Hz", "Let’s apply this formula to a specific case. A light wave with a frequency of ( f = 5 \ imes 10^{14} ) Hz travels at ( c = 3 \ imes 10^8 , \ ext{m/s} ). Plugging these values into the equation:", "[\n\lambda = \frac{3 \ imes 10^8 , \ ext{m/s}}{5 \ imes 10^{14} , \ ext{Hz}} = \frac{3}{5} \ imes \frac{10^8}{10^{14}} = 0.6 \ imes 10^{-6} , \ ext{m}\n]", "Expressing this in scientific notation:", "[\n\lambda = 6 \ imes 10^{-7} , \ ext{m}\n]", "Since ( 1 , \mu\ ext{m} = 10^{-6} , \ ext{m} ), we can also write:", "[\n\lambda = 600 , \ ext{nm}\n]", "This corresponds to visible light in the violet-blue region of the spectrum.", "### Why This Matters", "Knowing the wavelength helps scientists identify the color, energy, and behavior of light in applications ranging from telecommunications to laser technology. The precise calculation of ( \lambda = \frac{c}{f} ) is foundational in optics and spectroscopy.", "In summary: For a light wave with a frequency of ( 5 \ imes 10^{14} ) Hz and the speed of light ( c = 3 \ imes 10^8 , \ ext{m/s} ), the wavelength is ( 6 \ imes 10^{-7} ) meters or 600 nanometers—key to unlocking insights about visible light."]