What type of relationship is described by an inverse relationship in frequency and wavelength?

The correct answer describes the fundamental relationship between frequency and wavelength that is governed by the wave equation. In this context, frequency refers to the number of cycles a wave completes in a second, while wavelength is the distance between successive crests of a wave.

When frequency increases, the wave oscillates more rapidly, which means that the waves are packed closer together, leading to a shorter wavelength. This inverse relationship can be expressed mathematically by the equation:

[ c = f \cdot \lambda ]

where ( c ) is the speed of the wave (constant for a specific medium), ( f ) is the frequency, and ( \lambda ) (lambda) is the wavelength. If frequency ( f ) increases, to maintain the constant speed of sound ( c ), wavelength ( \lambda ) must decrease. Therefore, when frequency and wavelength are inversely related, an increase in one results in a decrease in the other.

In contrast, other options suggest incorrect relationships. For instance, if frequency were to increase alongside an increase in wavelength, this would contradict the established behavior of waves. Similarly, claiming that there is no relationship between frequency and wavelength overlooks the fundamental principles of wave mechanics. Therefore, acknowledging the inverse relationship is crucial