# Difference between temporal and spatial Wavelength?

I have recently learnt about the spatial frequency which is different from temporal one. Shouldn't the wavelength be different as well because one repeats in time and the other tells about repetition in space ?

But all the resources make no distinction between the two. Can anyone add to the void that is causing confusion ?

• Wavelength already describes the spatial periodicity of the wave. The inverse of the wavelength is the the spatial frequency or wave-number (up to a factor of $2\pi$ ). – nasu Sep 3 '16 at 15:56
• So would this mean that spatial and temporal wavelengths can be different at the same time for a wave travelling in space-time ? – vortex_sparrow Sep 3 '16 at 17:23
• physics.stackexchange.com/questions/265008/… – Frobenius Sep 3 '16 at 20:55
• There is no "temporal wavelength" in the usual description of waves. How would you define such a quantity? – nasu Sep 4 '16 at 0:32
• Wikipedia quotes ,"In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats, and the inverse of the spatial frequency." Then shouldn't the inverse of temporal frequency be something else ? – vortex_sparrow Sep 4 '16 at 5:52

The terms are each broad in their scope. For instance, the spatial frequency of a pattern of dots refers to number of instances of the pattern over the distance in which the pattern repeats. In general, the spatial frequency of some pattern, be it a wave or a pattern of dots, or lines on a beach, or pages in a book, refers to the number of occurrences per distance between occurrences of the pattern itself. In other words, $$f_\text{spatial} = \frac{\text{number of occurrences}}{\text{unit-distance}}.$$
Similarly, the temporal frequency of something refers to the separation in time of the event. In any song we hear, there is a temporal separation between the beats. There is a temporal frequency to the sound of waves crashing. The definition is analogous to that for spatial frequency: $$f_\text{temporal} = \frac{\text{number of occurrences}}{\text{unit-time}}.$$