# Tag Info

### Can we quantify the pitch of a sound that is a mixture of many frequencies?

Pitch can be described as a subjective perception of an auditory stimulus which cannot be objectively, unambiguously quantified. It is strongly related to the objective physical property of frequency ...
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### How to predict the time domain of pulse from an amplitude mask in frequency domain?

First of all, I think the OP has some misconceptions, so I will start by addressing them "These pulses often contain multiple frequencies (i.e. polychromatic pulse) that are generated by pulse ...
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### Derivation of Fourier Transform in Quantum Mechanics

Hint: start with basic Fourier transform $$F(x)=\frac{1}{\sqrt{2\pi}}\int dk f(k)e^{ikx}dk$$ and perform a change of integration variable: $$p=\hbar k.$$
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### Can we quantify the pitch of a sound that is a mixture of many frequencies?

In physics, high pitch is translated to high frequencies and low pitch is lower frequencies in sound frequency spectrum. for example in the spectrum chart below: the signal has most of its power ...
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### Can we quantify the pitch of a sound that is a mixture of many frequencies?

The description of pitch consisting of multiple frequencies that are harmonics of the fundamental frequency is called timbre. It is the timbre of a note that gives the difference in tone between a ...
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### Propagators in Frequency Space and Dyson's Expansion

It seems to me that there is a typo in Holstein's book. The operator $V$ is not supposed to be time-dependent (except, of course, in the interaction picture). So e.g. in Eq. (4.18), it is supposed to ...
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### Propagators in Frequency Space and Dyson's Expansion

Just factorize all t1 values, and integrate over the integrand. You then replace the substituent value from the delta function and you will get your formal equation
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I think I have some answers to your questions. To begin with, note that, according to the text you have to take the spatial average of the equation you are referring to. Namely, for some volume $V$ $$\... • 844 1 vote Accepted ### Fourier Component And Resonance It means that the driving force is decomposed into sines and cosines and if one of this sinusoidal functions oscillates with frequency equal or close to the natural frequency, then the system ... • 16.4k 1 vote Accepted ### What is the form of the wave packet in terms of momentum? In your equation 2 you implicitly make the following definition of \phi(p) $$A\left(\frac{p}{\hbar}\right) = \phi(p)$$ Let's think a bit more about how \phi(p) should ... • 34.4k 1 vote Accepted ### D'Alembert operator interaction term in QFT Lagrangian I think he has a typo in (2.21). In the first line the m^2 at the numerator of the second integral should actually be a p^2. You can see that in the second line a p^2 appears out of nowhere. ... • 1,944 1 vote Accepted ### Interpreting a normalized Power Spectral Density (PSD) You can interpret the PSD in units of dB the same way as you interpret it in more common units of dBm/Hz. The time integral squared amplitude of the voltage signal in the time domain can be thought of ... • 482 1 vote Accepted ### Explicit formulas for eigenstates of field operators Yes, \phi(x) is an arbitrary function of x (maybe with some regularity and boundary conditions if we want to be completely precise) This second point is a generalization of the formula expressing ... • 3,946 1 vote Accepted ### Complex \Phi to prove the group velocity of a wavepacket Suppose that we have waves with dispersion equation \omega =\omega(k). A right-going wave-packet of finite extent, and with initial profile \varphi(x), can be Fourier analyzed to give$$ \varphi(x)...
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