For a particular type of wave in a particular medium why must f and lambda be inversely proportional.
Frequency deals with the number of waves per second, while wavelength deals with the distance from peak to peak. It would be inversely proportional because lambda deals with horizontal displacement and f deals with just the number of waves per time
Why is it that wavelength and frequency are inversely proportional to one another. In the book they just show the rearrangement of the equation but give no reasoning.
Thank you
Velocity of the wave = frequency x wavelength. The velocity stays the same. So, if you increase the frequency, you must decrease the wavelength to keep v constant. And vice versa. That is what is meant by inversely proportional: as you increase one, you must decrease the other. I hope this helps!
To understand why frequency and wavelength are inversely proportional, let's consider the equation for the velocity of a wave, which is given by the product of frequency (f) and wavelength (λ). The equation is v = f * λ, where v is the velocity of the wave.
In a particular medium, such as air or water, the velocity of a wave remains constant. This means that if you increase the frequency of the wave, you must decrease the wavelength in order to maintain the same velocity. Similarly, if you decrease the frequency, you need to increase the wavelength to keep the velocity constant.
One way to visualize this is to imagine a wave traveling through a medium. If the frequency increases, it means that more wave crests pass through a specific point in a given time interval. As a result, the distance between each crest, the wavelength, must decrease to fit more wave crests within the same time interval. Conversely, when the frequency decreases, fewer wave crests pass through a specific point in a given time interval. As a result, the wavelength must increase to accommodate fewer wave crests within the same time interval.
So, the inverse relationship between frequency and wavelength arises from the need to maintain a constant velocity for a wave in a particular medium. As one increases, the other must decrease, and vice versa.