What is Mechanical waves: Definition and 41 Discussions
A mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a medium. While waves can move over long distances, the movement of the medium of transmission—the material—is limited. Therefore, the oscillating material does not move far from its initial equilibrium position. Mechanical waves transport energy. This energy propagates in the same direction as the wave. Any kind of wave (mechanical or electromagnetic) has a certain energy. Mechanical waves can be produced only in media which possess elasticity and inertia.
A mechanical wave requires an initial energy input. Once this initial energy is added, the wave travels through the medium until all its energy is transferred. In contrast, electromagnetic waves require no medium, but can still travel through one.
One important property of mechanical waves is that their amplitudes are measured in an unusual way, displacement divided by (reduced) wavelength. When this gets comparable to unity, significant nonlinear effects such as harmonic generation may occur, and, if large enough, may result in chaotic effects. For example, waves on the surface of a body of water break when this dimensionless amplitude exceeds 1, resulting in a foam on the surface and turbulent mixing.
There are three types of mechanical waves: transverse waves, longitudinal waves, and surface waves, etc. Some of the most common examples of mechanical waves are water waves, sound waves, and seismic waves.
Using the equation above I know that I have to find parameters k ##\omega## and ##\phi##.
$$k = \frac{2\pi}{\lambda}$$
and
$$\omega = 2\pi f$$
The problem I've been having is how you would go about finding ##\phi## since by solving:
$$y(0,0)=0 \rightarrow sin(\phi)=0 \rightarrow \phi = 0...
Based on Maxwell's Law, the speed of light can be defined by:
$$c= \frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$
Based on that, can we find a medium where a mechanical wave travels faster than a electromagnetic one? If so, how does that works?
Homework Statement
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 0.381m. The maximum transverse acceleration of a point at the middle of the segment is 8600 m/s and the max. transverse velocity is...
Suppose a ocean wave encountered a section of ocean which had a higher level of aeration from gas such as methane escaping from the seafloor.
Due to the aerated sections apparent lower density would the wave travel slower through the aerated section than its propagation speed thru pure seawater ?
The D'Alembert equation for the mechanical waves was written in 1750. It is not invariant under a Galilean transformation.
Why nobody was shocked about this at the time? Why we had to wait more than a hundred years (Maxwell's equations) to discover that Galilean transformations are wrong...
Homework Statement
A 1.60-m string of weight 1.30 N is tied to the ceiling at its upper end, and the lower end supports a weight W. When you pluck the string slightly, the waves traveling up the string obey the equation y(x,t)=(8.50mm)cos(172rad⋅m−1(x)−2730rad⋅s−1(t))
a) How much time does it...
Homework Statement
The linear mass density of a non-uniform wire under constant tension gradually decreases along the wire while ensuring an incident wave is transmitted without reflection. The wire has constant density μ for x ≤ 0. In this region a transverse wave has the form y(x,t) =...
Homework Statement
Do waves travel faster in dense or less dense mediums?
As a wave moves from a less dense to a denser medium at a boundary end what properties change? (Wavelength, speed, frequency, amplitude...)
If waves travel faster in solids then why do we hear better through air, and if...
In deriving wave equation or power transmission of wave transmitted by a string, it is usually stated (with some assumptions) that the transverse force on a point of the string is proportional to the slope at that point. An example is given in p.20 of this notes...
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...
I wanted to ask the following question: If we change the medium of the wave (lighter or heavier) , how it will affect the particles velocity of the standing mechanical wave ?
In my exam , there was a function's graph of one of the particles (of the standing wave) described with the...
Suppose we send a single mechanical pulse down a wire from one side and an identical one with the top down from the other side - like on the picture. Now suppose these two pulses interfere destructively. Then there is a specific time at which the string is completely at rest. My question is...
Hello,
I am having issues understanding all the waves, there are a lot of equations involving sine and cosine..and then all the various ways frequencies are looked at. I'm talking about pendulums, oscillators, standing waves, and sound waves. They all look similar in there form, but it is a...
Homework Statement
A string whose linear density is 0.00500 kg/m is stretched to produce a wave speed of 85 m/s. What tension was applied to the string.
Homework Equations
v=√(F/(m/L))
The Attempt at a Solution
v=0.00500 kg/m m/L= 85 m/s
I can't seem to re-arrange the...
Homework Statement
A string of mass 38.5g and length 5.60m is secured so that it is under tension of 220N. A wave with frequency 178 Hz travels on the string. Find the speed of the wave and the amplitude of the wave if it transmits power of 140 Watts.
The Given answers are: 179 m/s and 1.35 cm...
I have known for many years that the speed of sound (usually quoted ≈340 m/s) and the speed of light (usually quoted ≈3*10^8 m/s) are vastly different. Doing some reading, I would seem to conclude that part of the reason for this is the fact that sound is a mechanical wave, propagated through...
Homework Statement
When a mass M hangs from a vertical wire of length L, waves travel on this wire with a speed V.
a) What will be the speed of these waves in terms of V if we double M without stretching the wire?
V=?
Good morning, could someone please tell me why my answer of rad...
As a hobby, I have been researching the different aspects of modeling the sounds produced by musical instruments. Particularly, I want to create as accurate a model as possible, and not something very simple (to which many may ask "why?" if complexity will reduce the likeliness of real time...
Hi All,
I have Physics Homework that must be done during my holidays.
The homework is I have to solve 30 questions about Mechanical Waves. I can do any questions, but the rules is:
10 questions about Transvesal Waves
10 questions about Stasioner Waves
10 questions about Melde's...
Homework Statement
A 403 Hz wave travels at 200 m/s along a wire.
a)At a given time, the distance between points that differ in phase by 1.9 rad is ___ m.
b)At a given position, the change in phase during an interval of 4.8 ms is ___ rad.
Homework Equations
V=w/k
w=2pif
The Attempt at...
Homework Statement
a uniform rope with length L and mass M is held at one end and whirled in a horizontal circle with angular velocity \omega. you can ignore the force of gravity on the rope. find the time required for a transverse wave to travel from one end of the rope to the other...
Homework Statement
The figure shows a snapshot of three waves traveling along a string, where x,t are in SI units. The phases for the waves are given by... the picture and problem is in this link
http://img339.imageshack.us/img339/2407/phys1prob.th.png
Homework Equations
(kx-wt)...
Homework Statement
show, using the propagating wave y = Ae^[i(wt - kx)] that the average power transmitted across any point on the string in a complete full cycle is given by P = vE (P and E are both vectors). v is the phase velocity and E the total average energy density per cycle. also show...
1. Homework Statement
At the Winter Olympics, an athlete rides her luge down the track while a bell just above the wall of the chute rings continuously. When her sled passes the bell, she hears the frequency of the bell fall by the musical interval called a minor third. That is, the...
Hello all!
I'm trying to understand and in detail analyse how transverse mechanical waves work, and have had troubles finding anything on the net, except for the link below. Let's begin with a water wave. The following questions then:
1) Firstly, I wonder if it's possible to find, buy or...
Homework Statement
The ultrasonic motion sensor sends pulses of the ultrasound toward a cart on the low-friction track and determines the distance by the time an echo takes to return. The temperature in the lab is equal to 20 °C. What is the distance between the motion sensor and the cart, if...
[SOLVED] Mechanical waves
Homework Statement
Hi all.
Please see the last page in this .ppt (problem 15.66):
http://web.utk.edu/~kamyshko/P232/Problems_13_15.pdf
The Attempt at a Solution
Here are my answers - I would be grateful, if you would read them through and comment/help where...
Homework Statement
A piano wire with mass 3.25 g and length 84.0 cm is stretched with a tension of 27.0 N. A wave with frequency 100 Hz and amplitude 1.30 mm travels along the wire.
Homework Equations
The only equation that I think applies to this one is P = .5*Sqrt(μ*F)*(omega^2)*A^2...
Homework Statement
A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners at x = -7.0 m and x = 3 m
a) What is the x-coordinate of the source?
b) A third listener is positioned along the positive y-axis. What is her...
Homework Statement
I just have a question; what's the main difference between light waves and mechanical waves? I know that light waves are transverse. I also know that water waves are transverse, but sound waves are longitudinal. I know that light has a dual nature, and travels in both wave...
Hey Guys,
We have been studying mechanical waves, using the mathematical description of a wave, however, I am not quite sure how to solve the following, so if anyone has any pointers or hints that would be great!
You are told that two points x=0 and x=0.0900m are within one wavelength of...
Ok, so the velocity of mechanical waves through a medium is equal to the square root of some elastic property divided by some inertial property...
I did a quick search on google and a couple of textbooks and cannot find any actual explanation as to why this is. It is intuitive, yes, but...
Hi, I'm having a little bit of difficulty understanding exactly what to do to get to an answer in section a of this problem. It asks to show that the given function satisfies the wave equation... I have the wave equation. How do I go about 'showing' that it satisfies the wave equation?
Do I...
I would like to understand exactly how to principle of superposition works. I don’t think its so simple that you could imagine as first.
A mechanical wave doesn’t need a physical movement to spread thorough a medium, and it can not be stopped by physically stopping the movement of some of...
This is a question about mechanical waves. As i understand it, there can be many different types of mechanical waves, but its is not allways necessary to actually make a physically motion of one harmonic oscillator (a particle, or a part of the medium that the mechanic waves travels throw) to...
Hello again! I have a few questions regarding mathematical descriptions of waves.
what does it mean when a wave is propagating to the left? and how would i go about drawing that? do i just put a negative sine in front of the function? (for example sin(x) is original, -sin(x) is...