Is there a physical quantity which is the reciprocal/multiplicative inverse of time?
If time =distance/speed what is speed/distance. Please forgive my ignorance if there is a really simple explanation.
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2$\begingroup$ In a certain sense, frequency is opposite (or conjugate) to time via the Fourier transform. $\endgroup$– Alfred CentauriCommented Feb 1, 2014 at 23:02
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In a mathematical sense ${ speed \over distance }$ would give you a unit of ${time^{-1}}$. For example. Say we are in a car driving $5 {m \over s}$ and in a certain time we move $10m$. If we take this information and divide distance by speed we have: $$ { 5 { m \over s} \over 10m } = 0.5s^{-1}$$ This leaves us with a ratio that (in this case) says that half of the distance was traveled per second. This unit, $s^{-1}$ is considered the inverse of the unit seconds. Physically, the inverse of time represents "something" per second (or minute or hour or whichever time unit you are working in). In the example I presented it represents a portion of distance traveled per second.
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3$\begingroup$ $s^{-1}$ is the unit of frequency also caled $Hz$ hertz $\endgroup$ Commented Feb 1, 2014 at 23:24
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2$\begingroup$ That depends on the context. A $bq$ (Becquerel) is also $s^{-1}$. $\endgroup$– pfnueselCommented Feb 1, 2014 at 23:52
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2$\begingroup$ Correct, it can be denoted as hertz, but the argument still stands. Frequency is simply a measure of "something" per second, whether that something be radians, cycles, oscillations, etc. $\endgroup$– wgrenardCommented Feb 1, 2014 at 23:59