2
votes
1answer
21 views

Understanding the displacement of a particle in a wave

I have a question regarding waves and the equation we use to describe their motion. My understanding feels shaky, so i'd like to see if I can get a good explanation/way of thinking about it. The ...
1
vote
0answers
35 views

How do I get around the fact that boundary conditions don't apply in the equation's region of validity?

A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by $y(x, t)$. It is attached to a boundary at $x = 0$. The condition at the boundary is ...
1
vote
1answer
33 views

Properties of 3D waves [on hold]

I have a few questions about 3D waves: Are all 3D waves types of electromagnetic radiation? Are all 2D waves mechanical?
1
vote
0answers
35 views

Stationary wave on a string

The problem says: A string lies on the x-axis, and is fixed at $ x=-a $ and $ x=a $. At $ t=0 $ we impose a transversal velocity given by $ a^2-x^2 $. Assuming that the velocity of the wave is $ c ...
-1
votes
0answers
41 views

General wave equation derived from Maxwell's equation

I need to derive the general wave equation from Maxwell's equation without using the divergence therom (because I haven't read multivariable calc yet!). My physics book gives one but I don't fully ...
3
votes
2answers
69 views

Locations of destructive interference for two spherical waves

I have looked at this, but it did not help with locations. Really this just comes down to mathematical manipulation, which for some reason I fail to see. Here is my paraphrased setup: Consider two ...
0
votes
0answers
29 views

Number of wave modes in a cavity

I'm trying to calculate the number of acoustic modes that can exist in a room in a certain range of frequencies. I thought of using the Rayleigh-Jeans formula for the electromagnetic standing wave ...
-1
votes
1answer
43 views

What are the the characteristics of a standing wave? [closed]

May someone explain #24 from this picture? B is apparently the correct answer. Can any of the other answers be correct here? Isn't D also correct?
0
votes
2answers
54 views

Deriving group velocity formula

A formula for the group velocity of waves is: $u=k*dv/dk + v$ But then, since $k=2π/λ$, this equation can be rewritten as: $u=v-dv/dλ*λ$ But how? My attempt: $k*dv/dk$ = $((2π/λ)*dv/d(2π/λ)$ ...
0
votes
1answer
23 views

Differentiate wave speed, don't understand

The speed $v$ of some wave is $ω/k$ and I want to differentiate this with respect to $k$. Apparently this equals: $dv/dk = d(ω/k)/dk-ω/k^2$ But I don't understand why. Isn't this just saying "the ...
0
votes
1answer
69 views

Help deriving the general linear wave equation $d^2y/dx^2=(1/v^2)d^2y/dt^2$ [closed]

How do I derive the General Linear Wave Equation $$d^2y/dx^2=(1/v^2)d^2y/dt^2?$$ My teacher differentiated the general wave function $f(x + vt)+g(x - vt)$ twice with respect to both variables to get ...
0
votes
2answers
395 views

What is the fringe separation in Young's double slit experiment?

In the double slit experiment, a pattern of dark and bright bands appears on the screen. Is the fringe separation the distance between two bright bands? Question: In a double slit experiment ...
3
votes
1answer
143 views

If the k of a wave is negative, is the wavelength negative too?

My friend went to an interview for a reputed scholarship program and was asked this question. A wave has an equation $a\sin(\omega t-kx)$. Sometimes k surely can become -ve. We know that ...
0
votes
1answer
212 views

Simple Harmonic Motion Question - Block on Platform [closed]

A platform is executing SHM in a vertical direction with an amplitude of $5$ cm and a frequency of $\frac{10}{\pi}$ vibrations per second. A block is placed on the platform at the lowest point of its ...
0
votes
0answers
76 views

Inverse of the D’Alembert wave operator

Let $f(x)$ a solution of the wave equation $\square f(x) = 0$. I don't understand why the following operator $$ \mathcal{D} \equiv \frac{1}{2}(\nabla^2)^{-1} (x_0\partial_0 - C) $$ for arbitrary ...
1
vote
1answer
142 views

Electron and photon collision

So electron moving left ($v_{initial}=0.8c$) collides into photon going right. After the collision electron is moving to right ($v_{after}=0.6c$) and the photon is moving to left. What is the ...
2
votes
3answers
162 views

How to calculate Standing Waves in Electrical Cables?

I have a 20 metre Coaxial Cable. I send digital signals down the cable ranging from 5 KHz to 50 KHz. I have noticed a pattern in the noise ratio, an oscillating wave. I predict this is to do with ...
0
votes
1answer
63 views

Fourier Transform of E-Field with Decay Constant

Given an atomic transition with associated E-field $E(t) = E_{0}\cos(\omega_{0}t)e^{-t/\tau}$ where $\omega_{0}$ is the natural line frequency and $\tau$ is the decay constant of the simple harmonic ...
2
votes
2answers
281 views

Doppler effect problem with moving mirror

This was the given question: A light beam of intensity $I$ and frequency $f$, directed along the positive $z$-axis, is reflected perpendicularly from a perfect mirror which itself is moving ...
1
vote
2answers
173 views

A foundational question about harmonic motion : 2 pipes with different length and frequencies [closed]

How to solve the following question? A pipe open only at one end has a fundamental frequency of 256Hz. A second pipe, initially identical to the first pipe, is shortened by cutting off a portion ...
2
votes
1answer
537 views

Harmonics in an open organ pipe

How to solve the following question? An open organ pipe has two adjacent natural frequencies of 500 and 600 Hz. Assume the speed of sound in the air 340m/s. The length of the organ pipe is? What ...
1
vote
1answer
168 views

How to determine the positions of two points in a radial line by an intensity level dB?

The following is the question from my school. A source emits sound uniformly in all directions. A radial line is drawn from this source. On this line, determine the positions of two points, 1.00m ...
5
votes
1answer
178 views

Work Done by Vibrating String - Without Small-Amplitude Assumption

I'm trying to derive the equation for work done by a vibrating string, but I'm running into problems. The easiest way - the method used by the other question by this name - makes the approximation ...
1
vote
2answers
375 views

How do you calculate the position of the antinodes on a wave?

if for example i have a waveform with the formula $y=\sin(1.2x)+\sin(1.8x)$. The first 6 antinodes on my graph come up at around: $$ x=\begin{cases} 1.01\\ 2.97\\ 4.65\\ 5.80\\ 7.48\\ 9.46\\ ...
-1
votes
1answer
328 views

Equation of progressive wave [closed]

A progressive wave traveling in positive x-direction given by $y=a\cos(kx-\omega t)$ meets a denser surface at $x=0,t=0$. The reflected wave is then given by: I know that since the wave changes its ...
2
votes
1answer
164 views

Is there a way to increase photon energy by decreasing its wavelength?

Can I decrease a photon's wavelength by a medium or a vacuum? Are there other ways of decreasing the wavelength?
0
votes
2answers
173 views

What type of electromagnetic radiation strikes the Earth's surface the most?

If you can could you lists the types of light from the greatest amount to the least amount (Ex: Visible, Infrared, Violet).
0
votes
1answer
86 views

Uncertainty and wave-trains

My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an ...
2
votes
2answers
150 views

Relative velocity of sound

Relative velocity of sound. As I know that speed of sound in medium is property of medium. And independent of source motion but depend on motion of audience or observer and motion of medium. But it ...
4
votes
2answers
333 views

FFT distortion, harmonics (singing wine glass)

I'm doing a school assignment on Singing Wine glasses (you rub the rim of the wine glass with a wet finger and it produces a pure tone). I have recorded $30\,\text{ms}$ of the "singing" at a sampling ...
2
votes
1answer
175 views

Is sound relative?

Is sound relative? For example, if I and my friend are having a ride at 1000 mph and I shout towards him (speed of sound 700 mph). What would happen? Will the speed of the sound relative to the ...
2
votes
0answers
51 views

Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly ...
3
votes
1answer
1k views

A Doppler Effect problem with a moving medium

I tried solving the following question and started having multiple doubts: Two cars A and B are moving towards each other with some speed $25$ m/s. Wind is blowing with speed $5$ m/s in the ...
1
vote
1answer
75 views

How large of a solar sail would be needed to travel to mars in under a year?

I'm attempting to approach this using the identity $$F/A = I/c$$ I can solve for Area easily enough $$A = F(c/I)$$ and I know the distance $d$ is $$d=1/2(at^2)$$ But I'm having difficulty trying to ...
0
votes
1answer
137 views

The second resonance of string?

What is the relationship between "the second resonance " and string and the wavelength. Like in this question: if the length of the string is 2cm with second resonance, then what is wavelength?
0
votes
0answers
69 views

Minimum thickness of bubble ensuring max reflectance

A soap bubble has index of refraction of 1.33. What minimum thickness of this bubble will ensure max reflectance of normally incident 530 nm light? Ans is 99.6, but how do I get that? I am ...
2
votes
3answers
337 views

How to determine the direction of medium's displacement vectors of a standing wave?

Consider the following problem taken from a problem booklet. My questions are: What is displacement vector? And how to determine the direction of displacement vector at a certain point? Where is the ...
1
vote
3answers
171 views

Waveguides (in the ocean?)

The speed of sound in the ocean is given by $$c_s(\theta,z) = 1450 + 4.6\theta - 0.055\theta^2 + 0.016z$$ $\theta$ is the temperature in degrees celcius, and $z$ is the depth. In a simplified model, ...
-1
votes
1answer
620 views

Standing Waves: finding the number of antinodes [closed]

A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
0
votes
2answers
1k views

Calculating phase difference of sound waves

An observer stands 3 m from speaker A and 5 m from speaker B. Both speakers, oscillating in phase, produce waves with a frequency of 250 Hz. The speed of sound in air is 340 m/s. What is the phase ...
-3
votes
1answer
272 views

How to reconstruct information from a graph of an oscillation? [closed]

We are given a graph of the position of a wave (amplitude). How can we calculate the wavelength, frequency and the maximum speed of a particle attached to that wave? We have Speed = wave length ...
0
votes
1answer
240 views

Transmission of Gaussian Beam Through Graded-Index Slab

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=\cos(\alpha d)$, $B=\frac{1}{\alpha}\sin(\alpha d)$, $C=-\alpha ...
2
votes
0answers
145 views

Help With Difficult Deductive Proof [closed]

Suppose we have a Gaussian beam with a complex envelope expressed by the following equation 1: $$\tag{1} A_G(x,y,z) = \frac{A_1}{q(z)} e^{-ik \frac{x^2 + y^2}{2q(z)}} $$ where $$ q(z) = z+iz_0 $$ ...
0
votes
1answer
83 views

Percentage increase in the length of pendulum

I'm struggling with a physics question : What should be the percentage increase in the length of the chord of a pendulum for the period increased by 1%? The answer is 2%. I tried with $w = 2 \pi/T ...
0
votes
1answer
349 views

How do we find the frequency of wave propagated along the x-axis?

I don't know how to solve question like this: A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by:y = 0.006 cos π(46t - 12x). ...
3
votes
3answers
381 views

waves on water generated by a falling object

Let an object of mass $m$ and volume $v$ be dropped in water from height $h$, and $a$ be the amplitude of the wave generated. What is the relation between $a$ and $h$. How many waves are generated? ...
6
votes
2answers
1k views

Galilean transformation of wave equation

I have this general wave equation: \begin{equation} \dfrac{\partial^2 \psi}{\partial x^2}+\dfrac{\partial^2 \psi}{\partial y^2}-\dfrac{1}{c^2}\dfrac{\partial^2 \psi}{\partial t^2}=0 \end{equation} ...
0
votes
2answers
287 views

So where is mistake in the formula of wave number (magnitude of wave vector)?

I have following form for wave vector $k_2=n_2 \omega/c_0$. Now because $\omega=2 \pi c/ \lambda$, then $k_2=n_2 \omega/c_0=\frac{n_2 2 \pi c_0}{c_0 \lambda}=\frac{n_2 2 \pi}{\lambda}$. But problem is ...
0
votes
0answers
79 views

Can a wave propagate in an elastic fluid in the absence of volume forces?

A motion (wave) $\mathbf{x}: \mathcal{B}_0 \times [t_0,t_1] \to \mathcal{E}:$ such that $q-o = \mathbf{x}(p,t)=(p-o)+\mathbf{a}_0 cos(\mathbf{k}_0\cdot(p-o) - \omega_0 t)$ can propagate in an elastic ...
2
votes
1answer
227 views

Confusion concerning the use of wavenumber in exercise about Fabry-Perot etalon

In the exercise we are given that the spectrum of a light source consists of two spectral lines, which both have wavelengths around $500 \text{ nm}$ and the separation between them - given in ...