What is Wave motion: Definition and 56 Discussions
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities, sometimes as described by a wave equation. In physical waves, at least two field quantities in the wave medium are involved. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.
The types of waves most commonly studied in classical physics are mechanical and electromagnetic. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium. Other examples of mechanical waves are seismic waves, gravity waves, surface waves, string vibrations (standing waves), and vortices. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields which sustains propagation of a wave involving these fields according to Maxwell's equations. Electromagnetic waves can travel through a vacuum and through some dielectric media (at wavelengths where they are considered transparent). Electromagnetic waves, according to their frequencies (or wavelengths) have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.
Other types of waves include gravitational waves, which are disturbances in spacetime that propagate according to general relativity; heat diffusion waves; plasma waves that combine mechanical deformations and electromagnetic fields; reaction-diffusion waves, such as in the Belousov–Zhabotinsky reaction; and many more.
Mechanical and electromagnetic waves transfer energy, momentum, and information, but they do not transfer particles in the medium. In mathematics and electronics waves are studied as signals. On the other hand, some waves have envelopes which do not move at all such as standing waves (which are fundamental to music) and hydraulic jumps. Some, like the probability waves of quantum mechanics, may be completely static.
A physical wave is almost always confined to some finite region of space, called its domain. For example, the seismic waves generated by earthquakes are significant only in the interior and surface of the planet, so they can be ignored outside it. However, waves with infinite domain, that extend over the whole space, are commonly studied in mathematics, and are very valuable tools for understanding physical waves in finite domains.
A plane wave is an important mathematical idealization where the disturbance is identical along any (infinite) plane normal to a specific direction of travel. Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic motion at one frequency. In linear media, complicated waves can generally be decomposed as the sum of many sinusoidal plane waves having different directions of propagation and/or different frequencies. A plane wave is classified as a transverse wave if the field disturbance at each point is described by a vector perpendicular to the direction of propagation (also the direction of energy transfer); or longitudinal if those vectors are exactly in the propagation direction. Mechanical waves include both transverse and longitudinal waves; on the other hand electromagnetic plane waves are strictly transverse while sound waves in fluids (such as air) can only be longitudinal. That physical direction of an oscillating field relative to the propagation direction is also referred to as the wave's polarization which can be an important attribute for waves having more than one single possible polarization.
Solving for t' by substitution I obtained t' = 7/8. Then I substituted x= 10 and t = 7/8 in the given equation. Is that the right way to do it? My answer key says the answer is 100 but I am getting 78.5.
Homework Statement
Calculate the speed of sound in the classroom. You can use: Tuning forks, water, beaker, pvc pipe, ringstands, etc.
Homework Equations
v = f(wavelength)
For fundamental frequency: L = 1/4(wavelength)
For fundamental frequency: f = v/4L
The Attempt at a Solution
Here is...
Homework Statement
A thin card produces a musical note when it is held lightly against the spokes of a rotating wheel. If the wheel has 32 spokes, how quickly must it rotate, in revolutions per minute, in order to produce the A above middle C (i.e. 440 Hz)?
Homework Equations
ω=2πƒ; ƒ=1/T...
Homework Statement
A mass of 120 g rolls down a frictionless hill, reaching a speed of 4.2 m/s. This mass collides with another mass of 300 g that is at rest and attached to a spring with constant 30 N/m. The two masses stick together and enter into periodic motion. What is the equation for the...
The equation below (2.9) is also a linear differential equation.
This equation also describes the wave phenomena.
So, why is this equation not considered as wave equation?
I have taken it from the optics book by Chapter two Eugene Hecht,5th edition ,Pearson.
Homework Statement
3 tuning forks of frequencies 200, 203, 207 Hz are sounded together.find out the beat frequency.
Homework Equations
Beat frequency= n1-n2 (n=frequency).
The Attempt at a Solution
I know that beat frequency is the difference in the frequencies of two superposing notes. But...
1.Homework Statement
The wave function for a wave on a taunt string is:
y(x,t)=(0.350)(sin(10(π)(t)-3(pi)(x) +(π)/4)
where x and y are in meters and t is in seconds. If the linear mass density(μ) of the string is 75.0g/m, (a) what is tha average rate at which energy is transmitted along...
http://www.elateafrica.org/elate/physics/waves/traqnsversewaves.jpg
Note that :
Leaf. A has attained maximum displacement and is about to start going down .Leaves B, C and D are still going up. Each of them will finally attain its maximum displacement and then move downwards to complete the...
Dear experts,
I need to study wave motion in detail. Mainly mechanical waves on a string, reflection of mechanical waves, standing waves, resonance etc. I am looking for a book which covers these basic concepts in minute detail.
For example , I believe that the phase shifts during wave...
Hello, I am preparing for the IIT JEE exam, The toughest entrance exam in the Indian subcontinent, and i am struck in confusion about the theory regarding waves in Physics. The problem is that I can;t visualize the sine-cos functions physically , as I could visualize the movement of pulley...
For an progressive wave why the phase particle lags behind of time than it's predecessor one ? we know for a particle which is at the origin follows the equation # # y=# # A sin \omega t...
Homework Statement
A water wave traveling in a straight line on a lake is described by the equation
y(x,t)=(3.75\,\text{cm})\cos(0.450\,\text{cm}^{-1}x+5.40\,\text{s}^{−1}t)
where y is the displacement perpendicular to the undisturbed surface of the lake.
How much time does it take for one...
*Currently enrolled in University Physics 2*
We have not covered the topic pertaining to light yet, but we are working with sinusoidal waves. I would like to better understand the motion of light in space. It is my understanding that light moves in the form of waves, so what causes the wave...
If motion of an object obeys the wave equation, then it will display wave like behaviour. If you solve the wave equation, you get things like y = Asin \frac{2∏}{\lambda}(x - vt) which is a sinosodial wave. But from the second order differential equation v^{2}\frac{d^{2}y}{dx^{2}} =...
Ive been learning a lot about how similar waves and particles are at the fundamental level, but today i was assaigned to discuss the difference between the CLASSICAL physics of particles vs Classical Physics of waves.
Differences and similarities and well as how momentum is/isnt diferent as...
i'm really a beginner in this topic. So, I'm really confused even about this simple thing
an object has so many types of energies like energy due to mass in it, kinetic energy, pot. energy etc. So does the 'E' in E=mc2 give sum of all these energies or only the energy due to mass?
also...
Homework Statement
An aluminium wire of length L1=60 cm and of cross sectional area 1.00×10-2cm2 is connected to a steel wire of the same cross sectional area. The compound wire; loaded with a block of mass m=10kg is arranged so it is hanging freely from a suspended pulley so that the...
I have now in some time tried to figure out a way to calculate the peak amplitude of a water wave, after starting the wave motion by dropping an object, with a certain weight from a given height, in the water.
I am not in need of the information, but it would be nice to know.
I will hope...
Physics calculation about waves?
A wave traveling along a string is described by y(x,t)=0.00327sin(72.1x-2.72t)in which the numerical constants are in SI units (0.00327m,72.1radm^-1,and 2.72rads^-1)
A)What is the amplitude of this wave?
B)What are the wavelength,period and frequency of this...
Homework Statement
The tension in a guitar string is 21% too high. The fundamental frequency will be...
Homework Equations
V=F\lambda=\sqrt{Tension}
The Attempt at a Solution
I know the answer is 10% too high, but not sure how to get there...
If I take the square root of 1.21, I...
Homework Statement
y(x,t) = 3e-(2x-4t)^2
Consider the wave function which represents a transverse pulse that travels on a string along the horizontal x-axis.
a) Find the wave speed
b) Find the velocity of the string at x=0 as a function of time
Homework Equations
The Attempt at...
Ok so this may be an odd question but maybe there is someone here who can understand what I'm talking about.
When you have a wave of water and the water hits a wall, the waves will ripple back and causes the motion of the waves to traverse.
I was wondering if there is anything like this...
Homework Statement
1)I'm analysing a standing wave formed by superposition of Asin(kx-wt) and Asin(kx+wt) so it becomes 2Asinkxcoswt
It asks me to comment on the velocity of this wave. But I thought it was a standing wave - so it has no velocty in the x direction..
So what is its...
Hi, I was just wondering if someone can suggest an undergrad textbook which will help me understand SHM, Wave motion, interference and superposition, both mathematically and conceptually. I am having a hard time in my first year second semester course which is focused only on the topics listed...
From HRW 8 Ch 16 Q19
http://img684.imageshack.us/img684/8947/82287578.jpg
What i did:
I resolved the components of tension is each string (T cosX and T sin X) and found X to be 19.47 degrees (sin inverse of [0.25m/0.75 m]). Then i got the value of T as 20.79 N. The Tension in the...
As we know Power for transverse wave is P=(Fu)1/2 x A2w2 Sin2(kx-wt) for the wave traveling in +x direction represented by Y=ACos(kx - wt) . However for wave traveling in -x direction is P= -(Fu)1/2 x A2w2 Sin2(Kx-wt) . (Note the negative sign)
The Problem is I am not able to derive this. In...
Homework Statement
Assume that P and S (Primary and Secondary) waves from an earthquake with a focus near the Earth's surface travel through the Earth at nearly constant but different average speeds. A monitoring station that is 1000 km from the epicenter detected the S wave to arrive at 42...
Homework Statement
A block of mass M hangs from a rubber cord. The block is supported so that the cord is not stretched. The unstretched length of the cord is L0 and its mass is m, much less than M. The "spring constant" for the cord is k. The block is released and stops at the lowest point...
Homework Statement
A wave travels along a string at a speed of 261 m/s. What will be the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?
Homework Equations
v=squareroot(T/mu) (where T=tension)
mu=m/L (where m=...
Homework Statement
A large ant is standing on the middle of a circus tightrope that is stretched with tension T. The rope has mass per unit length mu (no symbl). Wanting to shake the ant off the rope, a tightrope walker moves her foot up and down near the end of the tightrope, generating a...
Homework Statement
For a sinusoidal wave:
At a certain instant, let point A be at the origin and point B be the first point along the x-axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B?
y = (15.0 cm) cos(0.157x - 50.3t)
Homework EquationsThe Attempt...
Homework Statement
A sinusoidal wave traveling in the -x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 29.0 cm, and a frequency of 15.0 Hz. The transverse position of an element of the medium at t = 0, x = 0 is y = -3.00 cm, and the element has a positive velocity...
[SOLVED] Wave Motion
Homework Statement
A transverse wave on a string is described by the following wave function.
y = (0.115 m) sin [(x/10 + 3t)]
(a) Determine the transverse speed and acceleration at t = 0.240 s for the point on the string located at x = 1.70 m.
(b) What are the...
My teacher told me that in SHM and wave motion phase refers to the argument in the corresponding function. then she said that if there is a difference of 2pi in the arguments then the phases are equal (sin ,cos function)
but isn't it wrong , i know that their effect in terms of velocity , acc...
Hi,
I was wondering if anyone could explain Simple Harmonic Motion. My physics teacher has tried and I have read the parts in the book, but I am still confused. I know how to find the amplitude from the standard form equations, but I really just don't understand how to get the period and...
Homework Statement
The displacement of particles in a string stretched in the x direction is represented by y. Which of the following expressions for y describe wave motion:
1: cos kx sin wt
2:k^2x^2-w^2t^2
3:cos^2(kx+wt)
Homework Equations
Equation of a progressive wave is of...
Homework Statement
Okay, I've got a question that's been bugging me for the longest time.
I've got a string attached to a wall at one end (the other end is free to move, though) and it has a sinusoidal wave traveling to the right and hits the wall at x = L and reflects. I'm supposed to...
I was wondering if someone would be able to help me with the following questions:
-A progessive wave has amplitude 0.40m and wave length 2.0m. At a given times the displacement y=0 at x=0. Calulate the displacement at (a)t=5sec (b) t=0.8sec
-A progessive wave has amplitude 2.5m and a time...
This may not be the best place to ask this question ... heck it isn't even homework ... I am trying to get a head start on next weeks lesson which is wave motion ... My book keeps referring to a term "wave front" , it mentions it twice/thrice during an explanation of interfernce patterns as...
Hi all,
Considering the nature of a water wave, how is the coconut going to move inland, say it is in the middle of the ocean(pacific)? Am i correct to say that the coconut bobs straight up and down.
Thx!
Any help will be appreciated
I work as an elevator constructor. part of an installation involves installing a steel tape the entire length of the shaft. it is very thin (imagine steel duct tape) and is under spring tension to keep it from moving too much. when at the top of the shaft i pulled the tape and sent a wave down...
Thats a quote from one of my physics texts, but it seems to me to contradict what I've been tought about enrergy and matter thus far, which isn't much i must add.
If wave motion can be defined as energy transfer without matter transfer, then doesn't that violate the famous equation?
If so...
when we say that speed of a wave is u we mean that with respect to the medium the wave is traveling with a speed u . now consider a sine wave traveling in positive X direction on a string . all the particles of string (these are particles of medium ) will have different speeds . The wave has the...
I have been studying sound waves, however, i have not seen in my books nor online how sound waves "move." I know that sound waves are longitudinal waves, meaning, that they move parallel to the direction of displacement, but it seems like they just travel in one direction although they reflect...
first i have a quick question, for average power of a transverse harmonic wave the equation has the quantities tension, frequency and amplitude. the question asks me to find how much i need to change each quantity to increase the power by a factor of 100, i understand all that but then it asks...
Well I am having some serious troubles with chapter 6 from French's book on vibrations and waves. Here are the things I am having trouble with.
1. Show that for a vibration of an air column an open end represents a condition of zero pressure change during oscillation and hence a place of...
Trying to start my homework and stuck on this first problem...
A point mass M is concentrated at a point on a string of characteristic impedance pc. A transverse wave of frequency w moves in the positive x direction and is partially reflected and transmitted at the mass. The boundary...
The question reads:
"Water waves in the deep part of a ripple tank have a wavelength of 5.2cm. They approach the boundary where the shallow part begins with an angle of 25degrees between the waves and the boundary, but after they have crossed the boundary, this angle has dropped to 17degrees...
I am having difficulty grasping what to do for this problem:
Two point sources located (0, +/- 2.5(lambda)) are generating waves in phase. Compute the distance from the x-axis to the first nodal line at
x=50(lambda)
I'm not sure what equations to use. My physics instructor is terrible...