The speed of a wave is determined by the product of its wavelength and frequency. In the given scenario where the frequency and amplitude remain constant but the wavelength increases, the speed of the wave will also increase.
The equation that relates the speed of a wave (v), its wavelength (λ), and its frequency (f) is:
v = λ * f
Since the frequency and amplitude remain constant, we can focus on the relationship between wavelength and speed. If the wavelength increases while the frequency stays the same, the speed of the wave must increase to maintain the equality.
To understand this, consider that wavelength represents the distance between successive points in a wave that are in phase (e.g., two adjacent crests or troughs). When the wavelength increases, it means that each complete cycle of the wave occupies a larger spatial extent.
Since the frequency is the number of complete cycles per unit time, if the distance between cycles (wavelength) increases while the frequency remains constant, it implies that the wave is covering a larger distance in the same amount of time. Thus, the wave must be traveling at a higher speed to maintain the same frequency and accommodate the increased wavelength.
In summary, if the wavelength of a wave increases while the frequency and amplitude remain constant, the speed of the wave will increase as well.