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12

The "intuition" here is that the wave equation is the equation for a general "disturbance" that has a left- and a right-travelling component, i.e. spreads without any preferred direction given by the equation of motion. Observe that $$ \left(v^2 \frac{\partial^2}{\partial x^2} - \frac{\partial^2}{\partial t^2}\right) y = 0$$ can be factored as (which is ...


5

It is tempting to think that if something is moving there must be a force that keeps it moving. However ever since Newton formulated his first law of motion we know this isn't the case. An object, whether it's a massive object or a light ray, will carry on moving at a constant velocity unless some force acts on it. So nothing is needed to keep the light ray ...


4

we all know waves are of two types transverse and longitudinal, and we do have studied about de broglie wave as well,so which ond of them is it?. or we have other means to classify them.. For a wave to be either transverse of longitudinal it must be a vector field quantity (e.g., the electric field). This is because "transverse" means that the ...


4

There are two primary factors that allow the cochlea to isolate frequencies. These are generally referred to as passive and active properties: tl;dr version: The passive properties are due to the mechnical properties of one of the membranes in the cochlea, the basilar membrane, primarily the width and stiffness at a given point. The active properties are ...


3

To the point of Is it hard to measure the resonant frequencies directly: it's tricky and careful discussion of the measuring procedures is needed. Some of the main problems: Destruction of the open-end behavior: If you place the speaker and microphone in front of the vocal tract to measure the response, you may have just switched open end behavior of your ...


3

First of all, $\frac{\partial^2 y}{\partial x^2}$ and $\frac{\partial^2 y}{\partial t^2}$ are second partial derivatives of $y(x,t)$ with respect to $x$ and $t$. So you can't obtain the wave equation from the first order equation $$v \frac{\partial y}{\partial x} = \frac{\partial y}{\partial t}$$ by squaring it in an algebraic sense. Also the square of ...


3

I don't think it's very likely, but one other thing I can think of: when the sign before the $\omega$ is a minus then the wave represents a wave travelling to the "right" - positive x direction - and maybe your TA wants only waves travelling to the right. ^^ In case you don't know why the minus sign represents a wave travelling in the positive x direction: ...


3

The resonances are quite broad: each cavity will amplify a broad range of frequencies, spanning most of or more than an octave. Driving those resonances isn't as simple as choosing a pitch. You have to do some work to efficiently couple the different cavities to your vocal apparatus, and to maintain the resonance while you're singing. The people who are ...


3

D'Alembert equation reads, for the considered case, $$\mu\frac{\partial^2 y}{\partial t^2} = T_0 \frac{\partial^2 y}{\partial x^2}\:.\tag{1}$$ It is nothing but $F=ma$ along the vertical direction ($y$). Here $y$ denotes the small deformation of the string along the vertical direction from the stationary (horizontal) configuration. We disregard horizontal ...


2

In light propagation, oscillation does not mean any movement in space. It is the value of the electromagnetic field, at one given point in space, that oscillates. The picture that you quote does not represent the movement in space, but the electromagnetic field value as a function of time. Compare to waves in water: if you put a little boat on the water, ...


2

Planck's law of black-body radiation can be stated in many different ways, depending on whether one is interested in the spectral energy density per volume or per area. It can also be expressed in terms of radiation wavelength or frequency. The energy of a photon is $$ \epsilon = h\nu = \frac{hc}{\lambda}$$ I will not derive Planck's law here. It can be ...


2

UPDATE - With a reference to: http://www.researchgate.net/publication/48323925_Applying_physics_makes_auditory_sense__a_new_paradigm_in_hearing OP, user263399, COMMENT: Can you explain the phase wave and its cause? On reading the linked paper I'm confused on how ther explanation involving the change in liquid volume velocity would create a ...


2

Due to the Structure of Glass, No Interference. To determine the thickness required to cause thin-film interference, both in light and in oil or soap bubbles, you rely on the following equations: $$2n_{film}d_{film} \cos{\theta} = m\lambda$$ $$2n_{film}d_{film} \cos{\theta} = (m-\frac{1}{2})\lambda$$ These being the equations for constructive and ...


2

You may have lost marks for leaving out the imaginary unit $i$. If not, then understand that either $e^{\pm i\,\omega\,t}$ can be used to represent the real signal with positive frequency $\omega$ - it's wholly a question of convention. But once you have made the choice you must stick with it and the choice has implications throughout all the equations of ...


2

I think The Physics of Musical Instruments (Springer Science & Business Media, 1998) by Fletcher and Rossing would be a good starting point for you. The general physical description of sound rests on the investigation of the impedance changes on the boundaries. For example: the reflection at the end of the string is caused by the discontinuity between ...


2

The slinky approximation is essentially the assumption that the extensions we are dealing with (including the equilibrium length) are much greater than the natural length of the spring. For example, this is true in a slinky, which stretches to much greater lengths when you pull it than its natural length. Thus, while we would normally have, for a length $x$ ...


2

According to maxwell's electromagnetism, a changing magnetic field gives rise to electric field, and a changing electric field gives rise to magnetic field lines.. So simply put, when a changing field of either type(electric or magnetic) is produced it gives rise to its counter parts (magnetic and electric).. So once a changing field comes to existance ...


2

In this case the wave is a sound wave i.e. a compression wave moving through air. The velocity of the wave is determined by the elastic properties of the air. Specifically it is given by: $$ v = \sqrt{\gamma\frac{P}{\rho}} $$ where $P$ is the air pressure, $\rho$ is the air density and $\gamma$ is a constant called the adiabatic index. So for any given ...


2

Using a process called interference, we can find wavelength, because the way that waves interfere is reliant of wavelength. Interference is based off of two key principles of waves: they are made up of peaks and troughs. When troughs overlap, they go lower. When peaks overlap, thy go higher. When a peak meets a trough, they cancel. Of course, the positions ...


2

The point of restricting the string to length $L$ is that we can then construct a periodic function (with wavelength $L$) by imagining repeated copies of the string connected to each other. In this case we can construct the function as a Fourier series with the lowest frequency sine/cosine having the same wavelength $L$. If we have an infinite string then ...


2

This diagram would help. You need to approximate the two longer sides of the trangle to be parallel to obtain $\varDelta l = d \sin \theta$. Source: http://www.wikipremed.com/01physicscards.php?card=876


1

It is commonly believed that the speed of sound at high densities is bounded from above by $c/\sqrt{3}$, where $c$ is the speed of light. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent ...


1

One of the most useful ways of describing SHM is obtained by associating it with the projection of uniform circular motion. Imagine that a disk of radius $\mathit{A}$ rotates about a vertical axis at the rate of $\omega~\text{rad/s}$. Also imagine that a peg $\mathtt{P}$ has been attached to the edge of the disk and that a horizontal beam of parallel light ...


1

You could consider omega to be a pure indicator of periodicity in the cycle. Larger omega gives you more rads per second. Larger omega gives you shorter wavelength, and therefore more energy required to keep the cycle going. You can look at omega in the equation and get an idea of the amount of energy you are dealing with.


1

It's not volts per millisecond, it's volts at particular milliseconds. Think of the wave as displayed on an oscilloscope. Waves can actually be anything as a function of anything. It's just that voltage as a function of time is a really nice example. Of course, when you're talking about Fourier transforms, you get into complex numbers. For example, you can ...


1

When you first start moving the end of the rope, there will be points along the rope that are not yet moving, and have not experienced the greater tension that results from your motion. It stands to reason that as these points first "feel" the wave, they will move towards the source of the wave (where the tension is greater) as well as transversely. If that ...


1

Look at the original, Heinrich Hertz, 1889! If E=B=0 on a plane, S=0 => no energy Transport through that plane. I agree with Annix: "The pictures may be depicting a static wave, but certainly, not a propagating wave."


1

A solution to the Schrodinger equation for a free particle is a plane wave, and because any combination of solutions is also a solution we can construct solutions by summing up plane waves. The equation you quote is constructing a solution by Fourier synthesis. Since the plane wave function $e^{i(kx-\omega t)}$ is a solution we can use Fourier synthesis to ...


1

Hint: Use light cone coordinates. What is the full solution to $$ \frac{\partial^2 f(x^{+},x^{-})}{\partial x^{+}\partial x^{-}}~=~0~?$$


1

You can show this by noting that $k_1^2=k_2^2$ and $X(x)T(t)= F(k_1x\pm k_2vt)$. You can see that by: $$ { \partial^2 f \over \partial t^2 } = v^2 { \partial^2 f \over \partial x^2 } $$ Is more common take $k_1=k$ and $k_2v=-\omega$. Then you may note that the equation imposes the choices of $k_1$ and $k_2$, or $k$ and $\omega$. The imposes is ...



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