When the frequency of a wave increases or decreases while the amplitude remains constant, the wavelength of the wave also changes. The relationship between wavelength, frequency, and wave speed is described by the equation:
wavelength = wave speed / frequency
In this equation, the wave speed represents how fast the wave propagates through a medium. The relationship indicates that as the frequency of a wave increases (i.e., more oscillations per unit time), the wavelength decreases, assuming the wave speed remains constant. Conversely, if the frequency decreases, the wavelength increases.
This relationship can be understood intuitively by considering that a higher frequency wave has more oscillations packed into a given time interval. Therefore, to maintain a constant wave speed, these oscillations must occur over a shorter distance, resulting in a shorter wavelength.
On the other hand, a lower frequency wave has fewer oscillations per unit time, so the wave takes longer to complete each oscillation. In order to maintain a constant wave speed, these oscillations must occur over a greater distance, resulting in a longer wavelength.
In summary, when the frequency of a wave changes while the amplitude remains constant, the wavelength of the wave will change in the opposite direction. An increase in frequency corresponds to a decrease in wavelength, while a decrease in frequency corresponds to an increase in wavelength.