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.
My physics book says the following:
"If the waves in the smaller spring have a greater speed because the spring is stiffer, then the reflected wave will be inverted"
This indicates that a stiffer/denser spring results in a greater speed and vice versa
Now Google, ChatGPT, and an online source...
Since the period is 0.025s, I think the frequency is 1/0.025s = 40 Hz. I don't know how can I proceed solving the problem from here. I'm assuming I will have to try to find the velocity and wavelength, but idk how.
We can derive the constancy of the speed of light from Maxwell equations. My questions are: 1. Why it is then need to postulate it when we can obtain it from Maxwell equations?
2. It is stated in many books that gravity wave also propagates with the same speed, c. How do we conclude that? Is...
My textbook is deriving wave speed on a string under tension with confusing thetas. It assumes ##\tan \theta_1 = \frac{-F_1}{F_T}## and ##\tan \theta_2 = \frac{F_2}{F_T}## which confuses me. I know for sure theta is the angle due to the position of y and x, ##\tan \theta = \frac{y}{x}##, but I...
Homework Statement
A uniform rope of length 12cm and mass 6kg hangs vertically from a rigid support.A block of mass 2kg is attached to the free end of the rope.A transverse pulse of wavelength 0.06m is produced at the lower end of the rope.What is the wavelength of the rope ,when it reaches...
Homework Statement
y(x,t)=0.8/{(4x+5t)^2+5 }represents a moving pulse,where x and y are in metre and tin second.Then choose the options.
(a)Pulse is moving in positive X axis
(b)In 2 secs,it will travel a displacement of 2.5m
(c)It's maximum displacement is 0.16m
(d)It is a symmetric pulse...
In the wave equation## \frac {\partial^2 \psi} {\partial x^2}=\frac{1}{v^2}\frac{\partial^2 \psi}{\partial t^2}\tag{1}##, v is the speed of the wave propagation.
With respect to which reference frame is this speed measured( in general)?
Hi could someone please explain to me what is meant by the term wave speed because I am confused by the definition which states "how fast a point moves on the wave".
Homework Statement
A long rope with mass m = 10 kg is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope and the pulse travels up the rope.
(a) Explain why the speed of the wave pulse change as it moves up the rope; does it increase or...
Homework Statement
A sinusoidal wave is propagating along a stretched string that lies along the x-axis. The displacement of the string as a function of time is graphed in the figure (attachment) for particles at x=0m and x=0.0900m.
(A) What is the amplitude of the wave?
4mm
(B) What is the...
Homework Statement
[/B]
Consider a long chain of mass m and length L suspended from a tall ceiling. Like any string if one end is disturbed waves will travel along the string. However, the tension in the string is due to its own weight and is not uniform. As such the speed of the wave will be...
Homework Statement
The wavelength of a water wave is 4.4m and it's period is 1.5s.
(a) what is the speed of the wave.
(b) the time required for the wave to travel 100m.
(c) the distance traveled by the wave in 1min.
Homework Equations
v=λ/T
The Attempt at a Solution
(a) v=λ/T
v= 4.4m x 1.5s...
Homework Statement
A certain pedestrian bridge in England resonates like a string fixed at both ends. If the bridge is 73.0 m long and its fundamental resonance is at 0.600 Hz, what is the wave speed in the bridge?
Homework Equations
Velocity = (frequency)(wavelength)
The Attempt at a...
Homework Statement
I need to write an equation for the at rest at a stoplight. Each car bumps into the one in front of it until the first car in line gets bumped.
Homework Equations
I found these equations for wave speed:
V=√(T/(m/L)), where T is tension, m is mass, L is length
and of...
I had a thought experiment related to wave speed and frequency.
Lets say we had a wave emitter that emitted transverse plane waves at a regular frequency. Of course we could imagine this as a radio tower, but I wanted it the thought experiment to be more general. Say the emitter is sending...
Homework Statement
A rope of mass m is hanging down from the ceiling. Nothing is attached to the loose end of the rope. As a transverse wave travels upward on the rope, does the speed of the wave increase, decrease, or remain the same?
Homework Equations
$$v=\sqrt{\frac{F}{m/L}}$$
$$F=-ma$$...
Homework Statement
Just wanted to check my work on this one.
An aluminum wire is clamped at each end under zero tension at room temperature. The tension in the wire is increased by reducing the temperature which results in a decrease in the wire's equilibrium length. What strain (ΔL/L) will...
Homework Statement
A geologist is at the bottom of a mine shaft next to a box suspended by a vertical rope. The geologist sends a signal to his colleague at the top by initiating a wave pulse at the bottom of the rope that travels to the top of the rope. The mass of the box is 20.0 kg and the...
Homework Statement
So in my textbook it says
"The speed of the wave depends on properties of the medium, not on the motion of source or observer. An explosion causes pressure variations in the air around it. This "deformation" propagates outward as a sound wave at a speed dependent only on...
Hi,
I'm trying to wrap my head around the derivation of the wave equation and wave speed.
For starters I'm looking at the derviation done on this site: http://www.animations.physics.unsw.edu.au/jw/wave_equation_speed.htm
I could maybe explain what I understand at this point
Given a string with...
Homework Statement
A hanging cord is attached to a fixed support at the top and is 78.0m long. It is stretched taut by a weight with mass 21.0kg attached at the lower end. The mass of the cord is 2.20kg . A device at the bottom oscillates the cord by tapping it sideways (Do not neglect the...
Homework Statement
A bit confused here as to what wave speed is dependent on. At first I learned that v = λƒ, and a couple of pages later in my textbook I find that v = √(τ/μ). Also, I found that speed is only dependent on the properties of the medium, specifically its elasticity and mass...
A bit confused here as to what wave speed is dependent on. At first I learned that v = λƒ, and a couple of pages later in my textbook I find that v = √(τ/μ). Also, I found that speed is only dependent on the properties of the medium, specifically its elasticity and mass. Where does wavelength...
Homework Statement
A violin string with a mass of 0.35g is 33 cm long. The frequency of a wave supported by the string is 196 Hz.
What is the speed of the wave?
Homework Equations
Ln = n/2 *lambda
v = f*lambda
The Attempt at a Solution
1. Solve for wave length [/B]
L1 = 1/2 *lambda
0.33 =...
Homework Statement
A long string with a mass/length of 500g/m is placed under a tension of 400N. The string is then vibrated up and down with a period of .425sec.
What is the wave speed?
What is the wavelength of the resulting wave?
I have no idea where to beginI would really...
The wave on the string could be described with wave equation.
Wave equation has a factor v^2 = Tension/linear density.
It has dimensions of speed, but from where exactly does it follow that this is actually speed of propagation of the wave?
Homework Statement
The displacement due to a wave moving in the positive x-direction is given by ##y=\frac{1}{1+x^2}## at time t=0 s and by ##y=\frac{1}{1+(x-1)^2}## at t=2 s, where x and y are in meters. Find the velocity of the wave in m/s.Homework Equations
##...
Homework Statement
A wire with an alternating current flowing through it is placed in a magnetic field. This causes the wire to oscillate with a frequency equal to the frequency of the current (you will learn about this when we study electromagnetism). The wire has a length (length is...
Does d'Alembert's formula hold if the wave speed is not constant?
For example, if the speed c in the link is not a constant, but instead a function of the coordinate x. Is the formula still valid?
Why do sound waves travel faster in incompressible material (such as water (water vs air)) and why do light waves travel faster in less dense (such as air (air vs water))?
I know that sound waves are longitudinal waves and light waves are transverse waves. What is the relationship between...
Homework Statement
A musician frets a guitar string of length 1.5 m at x = 0.34 m with one finger, and simultaneously plucks the string at x = 0.17 m with another finger (raising it to a height h = 2.1 mm. Both fingers are simultaneously removed from the string, and it is allowed to vibrate...
With reference to this diagram, my textbook tells me the following:
I am able to follow the rest of the derivation after this point, but I do not understand where equation 15.14 came from? I'm trying to think in terms of small angle approximations, but nothing is really coming of that...
My Friend and I were discussing standing waves and I made problem about speed, inspired off a concept taught in my Physics book: v = \sqrt {\frac {F_T}{m/L}}. My Friend asked a very valid question: "How in the whole can you defined speed of a standing wave when it's not changing position?" - He...
A wave on a string is described by the equation y = 0.150 m sin(1.795 x + 2010.6 t).
Two questions:
1. How do I find wave speed?
velocity = λ * f
My pathway λ → (2pi/λ) = 1.795 ... λ = 3.50m
My pathway f → f = (ω/2pi) ... ω = 2010.6 ... f = 320 Hz
velocity = λ * f ... velocity =...
I have always thought that the speed of oscillations of a particle in a wave = wave traveling velocity - is that not correct? In addition, when light passes through a medium, does only part of it go through and the rest reflected? Or does that only happen when it is going from a denser medium to...
Dear physics forum, I am doing an experiment on the vibrational behavior of beams and a question has come up that I can't answer. How does compression affect wave speed?
Brief overview of the experiment:
studying the change in vibrational behavior of a beam that is gradually tapered...
Homework Statement
A rubber string when unstretched has length L0 and mass per unit length μ0. It is clamped by its ends and stretched by ΔL. The tension is T=κΔL / L0.
Show that the wave speed on the rubber string when stretched by ΔL is
1/L0 √( (κ/μ0) ΔL(L0+ΔL) )
Homework...
Homework Statement
A sinusoidal wave is propagating along a stretched string that lies along the x-axis. The displacement of the string as a function of time is graphed in the figure (attachment) for particles at x=0m and x=0.0900m.
(A) What is the amplitude of the wave?
4mm
(B) What is the...
For a sound wave: A car is moving towards a person at 50m/s and toots its horn. Let's say the speed of sound relative to the air is 340m/s. Does the person measure the speed of the sound to be 390m/s or does it remain at 340m/s?
Homework Statement
the speed of waves on a lake depends on frequency. For waves of frequency 1.0 Hz the wave speed is 1.56 m/s; for 2.0 Hz waves the speed is .78 m/s. the 2.0 Hz waves reach you 120 seconds after the 1.0Hz waves generated by the same boat. How far away is the boat...
Homework Statement
A fierce winter storm blows across a large fetch of the South Pacific near the Antarctic. The waves it generates have a wavelength of 1500 feet with a 15-second period. They originate at a distance of 5000 miles from your favorite Hawaiian surfing beach. How many days will...
I tried finding lambda:
.03 = wavelength/2 --> wavelength = (.03)(2) = .06
Then plugging that into the equation
v = (frequency)(wavelength) --> v = (11996)(.06) = 719.76
But that didn't work.
Homework Statement
When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 64.6 cm wide tub is 0.835 Hz. What is the...
Homework Statement
What is the wave speed in a brass wire with a radius of 3.35×10-4 m stretched with a tension of 120 N? The density of brass is 8.60×103 kg/m^3.
Homework Equations
v = sqrt( T/ mu )
The Attempt at a Solution
I have no clue about this problem. It gives me regular density...
To increase wave speed on a string i would have to decrease the frequency and the string thickness correct? the string thickness would not make an impact correct?
I am studying for an upcoming test, and it is known that there are hiccups in our study guide. I am stuck on two problems.
Homework Statement
1. What is the frequency, in Hz, of a sound wave (v=340 m/s) with a wavelength of 10 m?
2. A series of ocean waves, each 8 m from crest to...
Homework Statement
A wave is moving through a string at 450 m/s. The wavelength is 0.18 m and the amplitude is 2.0 mm. What is the time required for a particle on the string to move through 1.0 km? (The answer given is 5.0x10 s).
Homework Equations
The only equations I can think of are...
Homework Statement
A block of mass 3.1 kg rests on a frictionless inclined plane, held in place by a string of mass 0.023 kg. The angle of the plane from the horizontal is 32°, and the string length is 1.5 m. How long does it take a wave to travel from one end of the string to the other? Note...
Homework Statement
The wave speed in a guitar string of length 62.9 cm is 278 m/s. you pluck the center of the string by pulling it up and letting go. Pulses move in both directions and are reflected off the ends of the string. If you plucked the string 25.1 cm from the left end of the string...
Hi, I'm completely stuck on a homework question and I really don't even know where to start...
A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.382 m. The maximum transverse acceleration of a...