35

Summary Yes they can. False positives arising from the acoustic sources you name are ruled out by seismological analysis and the examination of correlation between the separate gravitational wave detection stations. Pretty obviously, the LIGO detectors are probably the most sensitive microphones ever built. So how do we know they are detecting gravitational ...


20

Usually a guitar does not produce a pure tone/frequency. If so, its sound would be very close to a diapason. The difference between noise and a musical tone is not that a tone is made by a unique frequency, but there is a continuum between a pure tone (one frequency) and noise (all frequencies, not only multiple of a fundamental, without any regular pattern ...


16

Is it that the wooden block vibrates with lesser frequency than the metal block? If so, why is that? 'Yes', to the first question. Metal is stiffer than wood and produces higher frequencies (higher pitch). This follows from the wave equation (here in one dimension): $$u_{tt}=\frac{E}{\rho}u_{xx}$$ $E$ is Young's Modulus and $\rho$ the material's ...


15

Human perception is involved here because when you humans talk about noise this generally means a sound that is aperiodic. However the tone produced by a guitar will be something like: $$ A(t,x) = \sum_{i=0}^\infty A_i \sin(n\omega_i t - k_i x) $$ i.e. a superposition of the frequencies $f$, $2f$, $3f$, etc. The function $A(t,x)$ is periodic in time with ...


13

The metal block has a relatively low level of internal damping, however the wooden block has a high level of internal damping: Much of the energy imparted to the wooden block is dissipated internally as heat and deformation, also the higher frequencies are damped more than the lower frequencies (it acts like a low pass filter). So the wooden block will ...


13

The first image shows a string oscillating at its fundamental frequency $f$. The second image shows a string oscillating at $2f$. The third image shows a string (or the wooden soundbox of a guitar or the air in and around a guitar) oscillating at both frequencies at the same time. Finally, here is a graph showing the height of a point a short way along ...


9

For an ideal string, the key point is that all the harmonics are "harmonic" : their frequency is a integer multiple of the frequency of the fundamental. So the movement of the string is periodic and has a well definite frequency. For an ideal string, the harmonics have frequency ${{f}_{1}}$ , $2{{f}_{1}}$, $3{{f}_{1}}$.....and ${{A}_{1}}\cos (2\pi {{f}_{1}}...


9

This exceprt doesn't quite get what a black hole is. Once you're inside the Schwarzschild radius, it's not that "you can't go fast enough too get out", it's that the idea of "going outside of the black hole" is a concept that doesn't make sense. Once you are inside, all timelike paths (which are the allowable physical paths of objects that move from the ...


5

The body of the guitar will vibrate at both frequencies at the same time. This is because the body of the guitar is approximately a linear system so the vibration at each frequency is independent of each other. This is also the case for air, which is why we can hear multiple things at the same time.


5

Has any scientist practically confirmed that H2O molecules vibrate... Yes, molecular vibration and rotation can be measured using Raman Spectroscopy. when heat energy is provided to them? And yes, the population in rotationally/vibrationally excited states depends on the temperature of the molecules. You can see some nice spectra of this here. Side ...


4

This question, from a(n inanimate) physics viewpoint, seems closely related to asking whether increasing the speed of an object necessarily increases its temperature (under the reasoning that high temperatures generally involve faster molecular motion). It does not. Thermal energy is characterized by random motion. In contrast, the vibrational motion you'...


4

So resonance requires three things: An oscillator—a system which has some inertia and some restoring force, usually able to contain energy with some sort of characteristic frequency of stable oscillations. A driving force—an oscillation at a fixed frequency that is adding energy into the system. Dissipation—a drag force like friction that is removing energy ...


4

in the ringing sound, the structure is vibrating as if it were a solid, seamless metal bar like in a xylophone or a wind chime, which indicates that all the individual bricks in it are tightly and firmly cemented together into a single mass, which is a good thing. if the sound instead is dull and "drummy", it means there are gaps and breaks or "debonds" ...


3

In my opinion, your instructor has no in-depth understanding of resonance, as he mentioned in his statement about merely memorizing a statement from the author that he was using. Kinetic energy increases quadratically and potential energy increases linearly, but both energy forms increase monotonically, meaning that there is nothing cyclic about them. For ...


3

If the equations of motion of the vibrating system are equivalent to real and symmetric mass and stiffness terms, the normal modes will be real vectors, which means that all parts of the system move in the same phase. That excludes travelling waves, where there is a phase difference between points in the direction of travel of the wave. There is a special ...


3

In a vibrating string, the inertance arises from the mass per unit length of the string. The compliance arises from the string's elasticity, or "stretchiness". The energy storage in the inertance (because of its velocity) goes to zero at the moment of peak displacement of the string, at which point the energy storage in the stretch of the string goes through ...


3

In trying to answer this question I came across a lot of interesting phenomena related to primes. This is not a very detailed answer but will hopefully I can share the intuition and feel of the concepts involved. The phenomena we are dealing with is resonance. In any machine, there are several parts. Each part has some resonant frequency(a natural ...


3

Prime numbers are generally used to reduce the magnitude of resonances. These occur in a non-linear multi-frequency system when two of the frequencies $\omega_1:\omega_2$ match at a ratio $p:q$, where $p,q$ are comprime integers. For simplicity, you can think of a minimal example of such a system as two (non-linear) oscillators that are coupled with a ...


3

Anything happening on a guitar string can be always written as a superposition of standing waves of different harmonic frequencies. Even the initial motion, which is clearly bouncing back and forth, can be written in this way. (This should not be surprising. After all, standing waves themselves are written by combining solutions that only propagate in one ...


3

Yes. Sound is a direct product of motion or vibration. When something moves, it compresses the air in front of it (literally pushes the air), which creates a pressure wave that we interpret as air. Now its true that most things "vibrate" even while at rest, and as such can make noise if the oscillations are large enough, but for the most part, these ...


2

Yes they can, and the designers of the LIGO system took extraordinary pains to get the very best isolation numbers they could so as to minimize the influence of external noise on their data. It's worth reading about.


2

Unfortunately your question does not specify all of the conditions under which you are observing the effect, so it is not possible to give a definitive answer; however, you might find the following useful. The elapsed time for the vibration to fade to zero depends on several factors. You might get a better conceptual grasp by considering a comparison with ...


2

The Ritz paper is pretty in depth but the simple take away is this formula for integers m and n plotted where it implicitly equals 0.


2

Certainly, using one pendulum you can do the experiment to find the $g$ value. But the time period $T$ you measured should have some error any way. While finding $g$ you have to square the time period in single pendulum case. Using two pendulum you don't have to do that. Just multiply the two time period. The error caused in the former case is more than the ...


2

The first system that you mentioned is the LC circuit, which I will take to be the series circuit. Let us review this, as we will compare it to the string equation later. The governing differential equation is $$ L\ddot{I} + \frac{1}{C}I = 0 \ . $$ $$ \ddot{I} = - \frac{1}{LC}I \ . $$ I have used the compact notation for time derivatives, but the equation ...


2

You're right: the reflected wave, being shifted by $\pi$, interferes destructively with the incoming wave and gives a zero total disturbance at the end of the string. If you think about it, the $\pi$ phase shift actually derives from the fact that you want a zero disturbance at the boundary: you indeed derive it by applying the boundary condition to the ...


2

I think your logic is correct, you probably just overlooked something in the algebra. Right traveling wave: $y_R=\mathrm{e}^{i(kx-\omega t)}$ Left traveling wave: $y_L=\mathrm{e}^{i(-kx-\omega t +\Delta)}$ The sum $y=y_R+y_L$ must be constant in time at position $x=0$: \begin{align} y(x=0) &= \mathrm{e}^{-i\omega t} + \mathrm{e}^{-i\omega t +i\Delta}\\...


2

If two strings touch at a point, they can interact by recombining: That is, if the midpoints of your two strings come into contact, the four "half-strings" can pair up differently, and then go their separate ways as two new strings. (In the upper right picture, the green string is not broken, it's just "behind" the blue string.)


2

Yes, travelling wave systems have normal modes. In fact, the physics and mathematics of two coupled oscillators is strikingly similar to that of coupled waveguides. I'm most familiar with electrical oscillators, but everything written below applies to any coupled harmonic oscillators. Coupled oscillators Consider two electrical oscillators "$a$" and "$b$". ...


2

It's very important to learn about the phase variation of the response through the resonance - I feel that is not usually appreciated when encountering harmonic oscillators for the first time. Here is the equation of motion for the displacement of a driven harmonic oscillator: $ m\ddot{x} + 2\gamma \dot{x} + kx = F(t)$ where the three terms on the left-...


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