2
votes
0answers
28 views

How to calculate the dispersion relation for a wave equation with non-constant speed of wave propagation?

Specifically, it is a one-dimensional wave equation for waves on a string with a non-constant cross-section, i. e. $$S(x)=S_1+S_2 \cos{2x}; \qquad c(x)=\sqrt{F/\rho\, S(x)}.$$ Separating the variables ...
2
votes
1answer
52 views

Pulse Reflection

I wanted to ask why a pulse that reaches to a free end will reflect off and return with the same direction of displacement that it had before reflection. I am looking for explanation with forces.
0
votes
1answer
111 views

Electric field generated by a point charge moving at the speed of light

As you see, this is the electric field generated by a point charge moving at constant speed v. I know that when $v$ -> 0, $E$ is just the Coloumb Law. But how do you interpret $E$ when $v$ -> $c$ ? ...
0
votes
1answer
233 views

Relationship between amplitude and frequency of a wave

I wanted to ask what is the relationship between amplitude and frequency of a wave. Some say there isn't , some say that there is , but from their answers the relationship is still unclear.
0
votes
1answer
205 views

What is the difference between a pulse and a wave?

I wanted to ask what is the difference between a pulse and a wave. According to the definitions of them , they are almost the same. In the websites I looked at , the difference between them was ...
2
votes
0answers
27 views

Normal modes of two wires fastened together

The problem is to find the normal frequencies of the system formed by two fastened wires of length L, and different mass per unit length. I already wrote the boundary conditions, but I need to know ...
-1
votes
2answers
87 views

What is the lenght of the rope?

The $E$ string of a violin has a linear density of $0.5 g / m$ and is subjected to a $80\text{N}$ of tension, tuned for a frequency $u = 660 \text{Hz}$: What is the length of the rope? I know ...
0
votes
1answer
59 views

What can cause a change in wave's shape - One dimensional wave

what can cause a change in wave's shape of one dimensional wave moving through a rope? It's velocity ? or the wave's length ? What can cause him change his shape.
0
votes
1answer
68 views

Spring Constant - Waves

I tried to prove that for the same length of spring , a one dimensional wave that moves faster in spring 2 than spring 1, its spring constant will be lower than the spring constant of spring 1. ...
2
votes
1answer
33 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
42 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
46 views

Properties of 3D waves [closed]

I have a few questions about 3D waves: Are all 3D waves types of electromagnetic radiation? Are all 2D waves mechanical?
1
vote
0answers
36 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 ...
3
votes
2answers
87 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 ...
1
vote
0answers
55 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
50 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
195 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
27 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
88 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 ...
-1
votes
2answers
2k 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
256 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
257 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
97 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
160 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
187 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
65 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
348 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
240 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
768 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
195 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
203 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
511 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
525 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
191 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
192 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
108 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
213 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
536 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
200 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
52 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
78 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
182 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?
2
votes
3answers
384 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
182 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
948 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
300 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
259 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
147 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 $$ q(z) = z+iz_0 $$ ...