Why are we using RMS value over average value for a periodic wave?
124042
$$P = I_{\text{eff}}^2 \times R$$ where \$I_{\text{eff}}\$ is the effective current. For power to be average \$I\$ must be average current, so I am surmising that the effective current is the average current.  In that case, why is \$I_{\text{eff}}\$ not simply $$I_{\text{eff}} = \frac{1}{t}\int_{0}^{t} |i|dt$$  Instead it is defined like so:  $$I_{\text{eff}} = \sqrt{\frac{1}{t}\int_{0}^{t} i^2dt}$$  Thus, using these two expressions to calculate \$P\$ results in different answers.  Why is this so? It makes no sense to me. I can only guess that I am misinterpreting the effective current is the average current. If this is not the case, however, I do not see how \$P\$ can be the average power when \$I_{\text{eff}}\$ is not the average current.
46939
I have  (link to multisim) and i am asked to find the transfer function, the max and min value, the cutoff frequency, angle and the type of the filter.   [the actual problem][2]][2]   I have done the calculations and found that the circuit is a low pass filter, and its cutoff frequency is  26842 Hz which is awfully high and therefore i am very worried that i have gotten something wrong. I also found that when w=0 the value for the transfer function = 0.6803 and when w approaches infinity the value for the transfer function =0 and hence i concluded that it was a low pass filter. here is my calculate for the transfer function:   $$H_w=\frac{1}{(((R1+R3)*(j*w*C))+(((R3*R1)/(R2))*(j*w*C))+(R1/R2)+1)}$$  here is how it looks after i plug in the values for the resistors:  $$H_w= \frac{1}{(1.47 + j*w*0.000054562299999999998836925505310975)}$$  j represents the imaginary number. Basically you can see that if w=0 i get 1/1.47= 0.6803  Anyone can varify this is correct for me? and if so any chance that that "anyone" knows how verify that with multisim as i cant read the graph it produce. Please help.  [2]:
103576
It makes intuitive sense to me for the apparent frequency of a sound as modified by the Doppler effect to be based entirely on the speed at which the observer and the source get closer or farther apart, regardless of whether the source or the observer is moving, based on the principle of relativity. However, the general equation I receive from every source $$f'=f((v±v_o)/(v∓v_s))$$ does not have this property. For example, if the speed of sound in the medium is 2 units and the observer and source are coming closer at a rate of 1 unit, then if we take the observer to be moving then we get $$f'=f(3/2)$$ but if we take the source to be moving then we get $$f'=f(2/1)$$ What is the difference between these two cases?
57771
We know that in a wave equation $y = A \sin (\omega t + kx + \phi)$, $y$ = Displacement of particle on y-axis (assuming transverse wave) $A$ = Amplitude $\omega$ = Angular velocity $k$ = wave number and $\phi$ = phase difference  I understand that the everything within the bracket in the equation is an angle. But I dont understand what is the difference between those terms. When do we use $\omega t$ and $kx$ and $\phi$?  As much as I understand $\phi$ is taken into account when we need to find the angle difference between two waves. But I am really confused between the other two. Is there even any difference between both of them?  NOTE: I read  and  Phys.SE questions but they don't take into account the $kx$ term in their phase.
91851
What is the maximum/minimum possible sampling rate for the signal to be full recovered for a passband signal?
51555
I'm working on a 2nd order passive low pass filter, consisting of two passive low pass filters chained together.         &ndash; Schematic created using   Let \$ H(s) = H_1(s)H_2(s) \$ where \$ H_1(s) \$ and \$ H_2(s) \$ are the transfer functions for each separate filter stage.  Then \$ |H(s)| = |H_1(s)||H_2(s)| \$  Knowing the magnitude of a passive low pass filter,   $$|H(s)| = \dfrac1{\sqrt{ (\omega R_1C_1)^2 + 1} } \times \dfrac1{\sqrt{ (\omega R_2C_2)^2 + 1} } = \dfrac1{\sqrt{((\omega R_1C_1)^2 + 1)((\omega R_2C_2)^2 + 1)}} $$  Then trying to find the cutoff frequency:  $$ \left(\dfrac1{\sqrt{2}}\right)^2  = \dfrac1{\sqrt{((\omega R_1C_1)^2 + 1)((\omega R_2C_2)^2 + 1)}} $$ $$ 2  = \sqrt{((\omega R_1C_1)^2 + 1)((\omega R_2C_2)^2 + 1)} $$ $$ 4  = ((\omega R_1C_1)^2 + 1)((\omega R_2C_2)^2 + 1) $$ $$ 4  = (\omega R_1C_1)^2(\omega R_2C_2)^2 + (\omega R_1C_1)^2 + (\omega R_2C_2)^2 + 1 $$  And I'm stuck. Research on the web tells me \$ \omega_c = \dfrac1{\sqrt{R_1C_1R_2C_2}} \$, but I can't find why? Can anybody show my the derivation to find this?
2082
$\sin\sqrt x$ is not a periodic function. How can one prove this?
19779
Show that if $u$ is harmonic in $\mathbb R^n$ and $u=o(|x|)$, then $u$ is a constant.(Hint: use the solid version of the mean value property $u(x)=\frac{1}{\omega R^n} \int _{B_{R(x)}} u(y)dy$, and estimate $|u(x)-u(x')|$.)  Can anyone tell me how to use this hint?
50431
Why the log? Is it there to make the growth of the function slower?  As this is a common experimental observable, it doesn't seem reasonable to take the range from $[0,\infty)$ to $(-\infty,\infty)$ (For a particle emitted along the beam axis after collision $\theta = 0$ wouldn't be better to have a number that says how close it is to zero rather than one that says how large a number it is. I hope that makes the question clear.)
23265
Suppose I have two counter-propagating travelling waves of the same frequency but of different amplitude, like the transverse waves produced in a string by partial reflection off an endpoint.  I read that we will get a mixture of standing and traveling waves, and I can see the theoretical part, but what does this mean, exactly? What are the nodes now? Also, can I now say that energy between loops will be non-transmitting? Because now we have both a traveling and a standing wave.  If possible please provide a picture for better visualization.
7219
It is well known that a  can "split light" by separating different frequencies of light:    Many sources state that the reason this happens is that the  is different for different frequencies.  This is known as .  My question is about why dispersion exists.  Is frequency dependence for refraction a property fundamental to all waves?  Is the effect the result of some sort of non-linearity in response by the refracting material to electromagnetic fields?  Are there (theoretically) any materials that have an essentially constant, non-unity index of refraction (at least for the visible spectrum)?
51952
I have a problem with energy conservation in case of interfering waves.  Imagine two harmonic waves with amplitudes $A$. They both carry energy that is proportional to $A^2$, so the total energy is proportional to $2A^2$. When they interfere, the amplitude raises to $2A$, so energy is now proportional to $4A^2$ and bigger than before.  The equivalent question is what happens to the energy with the superposition of two waves that interfere destructively.  Also, if someone could comment on the statement about this problem in my physics book (Bykow, Butikow, Kondratiew):      The sources of the waves work with increased power during the interference because they feel the wave from the other source.
36117
Why use Root Mean Squared Error (RMSE) instead of Mean Absolute Error (MAE)??    Hi  I've been investigating the error generated in a calculation - I initially calculated the error as a Root Mean Normalised Squared Error.  Looking a little closer, I see the effects of squaring the error gives more weight to larger errors than smaller ones, skewing the error estimate towards the odd outlier. This is quite obvious in retrospect.   So my question - in what instance would the Root Mean Squared Error be a more appropriate measure of error than the Mean Absolute Error? The latter seems more appropriate to me or am I missing something?  To illustrate this I have attached an example below:                    The scatter plot shows two variables with a good correlation,  the two histograms to the right chart the error between Y(observed ) and Y(predicted) using normalised RMSE (top) and MAE (bottom).     There are no significant outliers in this data and MAE gives a lower error than RMSE. Is there any rational, other than MAE being preferable, for using one measure of error over the other?
101515
For a better detection of the modulated signal with the diode detector below, one requirement is that the time constant of the RC filter conforms to:  $$ \frac{1}{\omega_{c}} \leq RC \leq \frac{ \sqrt{1-\mu^{2}}}{\omega_{m}\mu}  $$  where:   \$\omega_c\$ is the angular frequency of the carrier \$\omega_m\$ is the angular frequency of the information, and \$\mu\$ is the modulation index.   How exactly can we prove that?
61910
I understand the equation explaining angles of refraction related to wavelengths. But I'm looking for a more intuitive approach/visual explanation? Perhaps related to QM?
47210
A  posted on Youtube.  How does this phenomenon work? I know he is using frequency to propagate water in a sine/cosine wave, but how does it exactly work this way? Why do we see it as if its paused, or in slow motion, or even in reverse?  Can someone please explain this? I am intrigued by the video and want to know it's physics.
42585
While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:-  Now, the author writes      As the amount of damping increases, the peak shifts to lower frequencies.   Why does this happen? And does this imply that at higher damping levels one cannot achieve a higher amplitude by setting the period of the forced oscillation to be equal to the natural frequency? This seems strange because, the highest amplitude is achieved when the natural frequency is equal to the driving frequency. But, I guess that the rules are somehow different for the damping case.