Wave Frequency and Wavelength Relationship

The relationship between the speed, frequency, and wavelength of a wave is fundamental in physics. It is defined by the wave equation:

$ v = f \lambda $

• Here, $v$ represents the wave speed (the speed at which the wave propagates through a medium).
• $f$ represents the frequency of the wave (the number of wave cycles passing a point per second).
• $\lambda$ represents the wavelength (the spatial distance between consecutive corresponding points of the same phase on the wave, like crests or troughs).

Analyzing the Inverse Relationship

For a wave traveling in a specific medium, its speed ($v$) is generally constant. From the equation $v = f \lambda$, we can see that if the speed $v$ is constant, then frequency $f$ and wavelength $\lambda$ must be inversely proportional. This means:

• If the frequency ($f$) increases, the wavelength ($\lambda$) must decrease to maintain the constant product $v$.
• Conversely, if the frequency ($f$) decreases, the wavelength ($\lambda$) must increase.

Therefore, as the frequency of a wave increases, its wavelength decreases.

Conclusion

Based on the inverse relationship derived from the wave equation, an increase in frequency corresponds to a decrease in wavelength.

The correct option is that the wavelength decreases.