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Well, first of all, a complex series RLC circuit can be analyzed using the following method. The total impedance of the circuit is given by: $$\underline{\text{Z}}_{\space\text{in}}=\text{R}+\text{j}\omega\text{L}+\frac{1}{\text{j}\omega\text{C}}\tag1$$ The input voltage can be written as: $$\underline{\text{V}}_{\space\text{in}}=\hat{\text{u}}\exp\left(\...


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The forces on elements of the string that are responsible for the oscillations of the string are not due to changes in tension. Provided that amplitude << $\lambda$, the tension is almost constant, as the fractional change in the string's length due to the wave is very small. So Hooke's law isn't involved (except in determining the constant tension). ...


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The spring constant hasn't been neglected. If f is proportional to $\sqrt{kx}$ then they differ only by a constant multiple. Since the spring constant is a constant, f is also a constant multiple of $\sqrt{x}$, so f is proportional to $\sqrt{x}$.


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Everything shown in the plot is in normalized units. That is, the frequency, $\omega$, is normalized to the plasma frequency, $\omega_{p}$, and the wave number, $k$, is normalized to the inertial length or skin depth, $c/\omega_{p}$. So you need only redefine the dispersion relation to: $$ \frac{ \omega }{ \omega_{p} } = \sqrt{ 1 + \left( \frac{ k \ c }{ \...


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Since this has the tag of acoustics I believe it is meant to be for sound waves, so I'll just cite what I know about those. As far as I am aware there can be no change in the frequency of a "monochromatic" sound wave. Instead, the non-linearities associated with its propagation can indeed change the waveform of a travelling wave. Due to the difference in ...


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I’m not really sure what you are trying to ask but if you look at where k=0, your frequency becomes the plasma frequency I.e. the y-intercept of your graph.


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The wave speed can be related to the tension and the mass per unit length of the string by the following equation: $$ v = \sqrt{\frac{T}{\mu}}$$ Here, $T$ is the tension, $\mu$ the mass per unit length and $v$ the speed of waves on the string. For a derivation of this equation refer to this or to any first year Physics textbook (e.g. Halliday & Resnick)...


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Let's first fix to some number. I'll choose $\omega=2\pi f$ with $f=1Hz$, but you can choose any other number". Now let's plot the three functions After the time $t = T_0 = \frac{2\pi}{\omega} = \frac{1}{f} = 1s$ the blue function $\sin{(\omega t)}$ has done a full oscillation. Thus, it has also done full oscillations after $t=\{2, 3, 4, \ldots\}$. ...


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Frequency and wavelength change with interactions with a material, for example a red crystal will change white light to red, but a lot of the energy of the beam of different wavelengths will be absorbed or reflected so the verb "convert" cannot be used. For example I have a source that emits X-Rays, is it possible to turning them into visible light ...


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Yes, you can, I.e. doubling the frequency by shining the light through a specific cristal. This is used e.g. in a green laser pointer, that uses a red light laser diode and the cristal turns it into green. https://en.m.wikipedia.org/wiki/Second-harmonic_generation But I don‘t think that there exist a general mechanism to convert light frequencies which, I ...


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This is an image that I like to show my students. It shows that the electric field of the wave in OP's question is everywhere: I have tried to make an animation of how the electric field moves, but that is not very pleasant to look at. Sine waves look better and can represent the phase of the wave, but the color wheel provides visualizations of phase that ...


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Yes, it is possible for a wave to have a frequency change along its propagation direction; famously, this was demonstrated by an experiment with gravity causing a frequency change in gamma rays, by Robert Pound and Glen Rebka. The change isn't large, but the effect is real. In non-relativistic theory, this would not happen; it relies on the nature of time ...


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Will $f_{1}$ tend to $\infty$? Kind of, but not in the way I think you are implying. The acoustic wave generated by the moving source can steepen into a discontinuity known as a shock wave. In Fourier space, a time discontinuity turns into an infinite number of frequencies. If something moved at the local speed of sound and emitted a monotonic tone, an ...


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Your professor is correct. Your argument doesn't make much sense at all (it is not really an argument at all, to be honest), so it's hard to pinpoint exactly where it is that you're going wrong, but it definitely does not apply here. The minimal time to reliably determine the source of the wave in this situation is $$ t_\mathrm{min} \approx \frac{1}{\Delta \...


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This is a complex question. The pure vibration of a string at a single frequency takes on a sine wave pattern. The plucking of a string deforms the string in a non-sine shape, so the disturbance is a linear combination of sine and cosine (a $\pi/2$ phase shift of sine) of multiple frequencies which are determined by properties of the string. The string acts ...


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The velocity of propagation of a wave in a string ( v ) is proportional to the square root of the force of tension of the string ( T ) and inversely proportional to the square root of the linear density ( $\mu$ ) of the string: $$ v=(T/\mu)^{1/2} $$ Once the velocity of propagation is known the fundamental harmonic frequency is given by: $$ f=(v/(2L))=(1/...


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There are several questions here. First, the factors that determine the resonance frequency of a piece of pipe are 1) the speed of sound waves in the pipe, 2) the length of the pipe, and 3) the nature of the termination of the undriven end of the pipe. 1) and 2) tell you how long it takes a sound wave to travel from one end of the pipe to the other and 3) ...


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