Michigan Test for Teacher Certification (MTTC) Secondary Integrated Science Practice test

How are frequency and wavelength mathematically related?

1. Frequency plus wavelength equals speed of sound

2. Frequency multiplied by wavelength equals speed of light

3. Wavelength divided by frequency equals energy

4. Frequency is the inverse of wavelength

The correct answer is: Frequency multiplied by wavelength equals speed of light

The mathematical relationship between frequency and wavelength is expressed through the equation that relates these properties to wave speed. Specifically, the speed of a wave (such as light or sound) is equal to the product of its frequency and wavelength. This can be represented as: speed = frequency × wavelength In the context of light, this relationship shows that the speed of light in a vacuum is a constant approximately equal to 3.00 x 10^8 meters per second. Therefore, knowing either the frequency or the wavelength allows one to calculate the other when the speed is known. The choices reflect different misunderstandings or misapplications of wave principles. For instance, the notion that frequency plus wavelength equals speed of sound misunderstands the additive nature of these quantities, as they do not combine directly. Wavelength divided by frequency equating to energy is a misrepresentation, as energy in wave mechanics is typically calculated using the frequency in relation to Planck's constant, not through a division of those two. Lastly, while frequency and wavelength are indeed inversely related since one increases as the other decreases, the specific mathematical relationship is more accurately captured through the equation involving wave speed.