What is the relationship between wave frequency and wavelength?

The correct answer highlights an important aspect of wave behavior in physics. Frequency and wavelength are inversely related, which means that as the frequency of a wave increases, its wavelength decreases. This relationship is derived from the wave equation, which states that the speed of a wave is equal to the product of its frequency and wavelength.

Mathematically, this can be expressed as:

[ \text{Speed} = \text{Frequency} \times \text{Wavelength} ]

In many scenarios, especially when discussing electromagnetic waves in a vacuum, the speed is a constant (approximately (3.00 \times 10^8) m/s). If the frequency increases, since the speed remains constant, the wavelength must decrease to maintain equality in the equation.

Thus, when a wave has a higher frequency, it oscillates more times per second, resulting in shorter distances between wave peaks, which is indicative of shorter wavelengths. This fundamental concept applies across various types of waves, including sound and light waves. Understanding this relationship is crucial in fields such as optics, acoustics, and telecommunications, where managing wave properties is essential for technology and science.