the relation of frequency and wavelength

Question

By v=f入
we can know that frequency is inversely proportional to wavelength.
If frequency is y-axis and wavelength is x-axis
the slope should be negative
但係我想問點解條線係曲,係curve,唔係直線?

Answer 1

well, first of all, you have to understand what frequency is. frequency is simply 1/time.

so you have 1/time on your y-axis, the relationship is of course to the wavelength, following a reciprocal graph order.

v = f入 is just like a time-distance-speed formula we usually use. for the analogy, here the distance is equivalent to wavelength; speed is still v (or c, speed of light); and frequency is inversely proportional to time, 1/t. therefore, your graph, with 1/t or frequency as the y-axis, wavelength as your x-axis, you're presenting the inverse proportionality between the wavelength and time. for electromagnetic waves, all waves travel with the same speed ( = speed of light ) and the negative gradient indicates that the higher the frequency (the short time it is), the shorter the wavelength. it's important to remember that the gradient of the frequency-wavelength graph is NOT the speed of the wave.

note that if you plot your graph with time against wavelength instead, surely you'll get a straight line then and of course the gradient will be the speed of the wave; but for eletromagnetic waves, talking about time in terms of frequency is more convenient.

i hope this helps.