I saw some where frequncy means how fast a signal is changing and i am confused. Since frequncy means how much cycle a signal completes in unit of time and we may say how fast a signal is moving but the changing here i don't get. Can some body help? Thanks in advance.
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$\begingroup$ To complete a cycle, the signal has to change value. So the more cycles it completes in a given time, the "faster" it must be changing. $\endgroup$– The PhotonCommented Jul 19, 2020 at 5:49
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$\begingroup$ Like some source which produces of signal of constant cycle like 10 cycle per second. What is the change here?@The Photon $\endgroup$– bikashamitCommented Jul 19, 2020 at 5:57
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1$\begingroup$ Whatever the signal is. If it’s a voltage signal, the voltage changes. If it’s an air pressure signal the air pressure changes, etc. $\endgroup$– The PhotonCommented Jul 19, 2020 at 6:00
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$\begingroup$ Like source(voltage change, pressure change)which creats that signal. So to create a signal one have to change the voltage. Is it energy(cost) which get consumed for doing one cycle? So now it depends on source than measuring the cycle? $\endgroup$– bikashamitCommented Jul 19, 2020 at 6:08
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$\begingroup$ The signal itself is a measure of some physical quantity and how it varies with time, regardless of what the source is or how the signal is detected. If the signal has a higher frequency, then that physical quantity is changing between two values more often. If we speak colloquially rather than in the jargon of physics, we can say it changes "faster". $\endgroup$– The PhotonCommented Jul 19, 2020 at 13:50
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Let us start with a signal periodic in time with frequency $f$: $$u(t)=A\cos(2\pi f t).$$ This signal completes its cycle during time $1/f$, which means that at time $t + 1/f$ it has the same value as at time $t$. During its period the signal is changing, so in a way we can say that $f$ means how fast it is changing.
How fast is not a precise physics term. As a mathematically precise definition one could use, e.g., the instantaneous change rate, defined as $$\gamma(t) = \frac{\dot{u}(t)}{u(t)}.$$ This is clearly not the same as frequency, but more inspired by a linear change $u(t)=vt$ for which this rate would be constant.
Let us now take a signal changing in space: $$u(x) = A\cos(2\pi x/\lambda).$$ This signal is not changing in time at all, so speaking about how fast it changes doesn't make sense. Otherwise it is however very similar to the signal described earlier, where time is replaced by space: $t\rightarrow x, f\rightarrow 1/\lambda$.
In the context of wave phenomena one would often deal with signals that are dependent on both time and space coordinates: $$u(x,t) = A\cos(2\pi x/\lambda - 2\pi f t).$$ If we look at this signal at a particular space point, e.g. $x=0$, it is just changing in time, returning periodically to the same value. If we look at it at fixed time, it is changing periodically in space. It however always have the same value at the point where the time and space coordinates are related via $ x/\lambda = f t$, i.e. where $x = \lambda f t$ - these points are literally moving with speed $v=\lambda f$ and expression how fast is definitely applicable.
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$\begingroup$ What does singal changes means high and low? I don't get changes here the comment by the photon said that the change is the source which produces the signal. $\endgroup$ Commented Jul 19, 2020 at 7:12
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$\begingroup$ @bikashamit Perhaps, you could ask a more precise question or quote the relevant pages of your textbook. For now it all seems rather confused. $\endgroup$– Roger V.Commented Jul 19, 2020 at 8:24