# What is Wave velocity: Definition and 29 Discussions

The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group.

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1. ### Propagation Wave Expressions and Wave Velocity

Hello everyone, I would really appreciate some help on the following problem on plane waves and propagation. Not too sure if my attempt at writing the propagation wave expressions are correct, and how to handle the arbitrary function f(u). For the velocity, the wavelength is not specified, so is...
2. ### Temperature and Sound Wave Velocity: Exploring the Proportional Relationship

Apologies if this is a question with a basic answer, I'm coming back to physics after many years of being away from it! I read somewhere that for longitudinal sound waves traveling through air, if the temperature increases by 1 degree celsius then the velocity of the wave will increase y 0.6...
3. ### Non-constant wave velocity in a ripple tank system

Hi. We tried to make some quantitative measurements with a Pasco ripple tank system, a video camera and software for video analysis. We generated circular waves and tracked the propagation of a crest, from which the software computed the phase velocity: We used 5 Hz, 10 Hz and 20 Hz...
4. ### What will the wave velocity be in this string?

Homework Statement What will be the wave velocity, if a string of 100 cm length is in a 10 kg-wt tension forms 9 nodes when vibrated and becomes symphonic to a 50 Hz tuning fork. Given, Cross sectional area of string, $$A=4.95 mm^2$$ & density, $$d = 0.25 g/cc$$? Homework Equations ...
5. ### Longitudinal Wave Velocity: Why it's Greater in Solids

Why the velocity of longitudinal wave in solid is greater than transverse wave
6. ### Understanding the Longitudinal Wave Velocity of a Helical Spring

v = [sqrt(D/m)] * L, where D is spring constant, m is mass of spring, L is length of the spring My lecturer give me this formula to find the longitudinal wave velocity on an helical spring. May i know how to derive this formula? < Mentor Note -- this is not technically a homework question, but...
7. ### Phase velocity and wave velocity

Numerically, speed of wave propagation(defined as wave velocity) = ω/k = phase velocity But, conceptually is there any difference between phase velocity and wave velocity?
8. ### Hooke's law and wave velocity related problem

Homework Statement The extension in a string, obeying hooke’s law is Y when wave velocity in it is V. if extension is increased to 1.5Y, then wave velocity V’ becomes? 1) V' =V. 2)V'= 1.22V . 3)V'=1.5V. 4) V'=0.75V. Homework Equations wave velocity= frequency*wave length. The Attempt at a...
9. ### Finding the velocity of a wave

I am currently studying a course on waves, which has a real ambiguity in the lecture notes. Essentially, I don't know how the professor got from equation \ref{eq:surf_x-y} to equations \ref{eq:vel_u} and \ref{eq:vel_w}. I have tried to work backwards to find a method but am not sure of its...
10. ### Mastering physics Problem 20.58 tension and wave velocity

Homework Statement The figure shows two masses hanging from a steel wire. The mass of the wire is 60.5 g . A wave pulse travels along the wire from point 1 to point 2 in 24.0 ms . https://session.masteringphysics.com/problemAsset/1383975/6/knight_Figure_20_80.jpg //What is mass m? Homework...
11. ### String Wave Velocity and Tension

Homework Statement The length of a stretched string is 1m. Its mass per length is 2x10-3kg/m. The string resonates at its 4th harmonic at 400Hz. (a) Calculate the velocity of the string wave. (b) Calculate the string tension. Homework Equations fn = nv / 2L v² = F / μ The...
12. ### What is the equation of wave velocity for an extended spring?

For a free spring, the wave velocity is v = √(k / m) x L, where L is the displacement of one end right? And what if I have a spring which both of its end is extended and held by "oscillator" to produce standing wave. In this case how would I find the wave velocity? I see some sources state...
13. ### Direct Measurement of Gravitational Wave Velocity

http://www.spacedaily.com/reports/Chinese_scientists_find_evidence_for_speed_of_gravity_999.html Done by the Institute of Geophysics at the Chinese Academy of Sciences using Earth tide measurements. The conclusion is that it is the speed of light. http://en.wikipedia.org/wiki/Earth_tide...
14. ### Solving Phase Change & Spatial Separation with Wavelength & Velocity

Homework Statement A wave of wavelength 75 cm has velocity 375 m/s. a. What is the spatial separation between two points that are 30° out of phase at a particular time? b. What is the phase change at a particular position for a time change of 0.5 ms? Homework Equations u = λ / T...
15. ### Wave Velocity: Improper approach, or incorrect differentiation?

Homework Statement A transverse wave on a cord is given by D(x, t) = 0.19sin(2.9x - 35t), where D and x are in m and t is in s. 1) At t = 8.6*10^-2 s, what is the displacement of the point on the cord where x = 0.62 m? 2) At t = 8.6*10^-2 s, what is the velocity of the point on the cord...
16. ### What Is the Maximum Transverse Velocity at x=0 for a Moving Wave Pulse?

Homework Statement I'll try to translate the problem as faithfully as I can: A wave pulse moves along the positive OX axis. Its form when t=0 is f(x) = y0/[1 + (x/a)^2] Find the expression for the transverse velocity as a function of x and t. At the point x=0, what will be its max...
17. ### Calc group velocity and wave velocity for a wave

Homework Statement a wave function \Psi=Aei(px-Et)/h where p is momentum and E=p2/2m calc group and wave velocityHomework Equations group vel=dw/dk wave v=w/kThe Attempt at a Solution I just have no idea what they did here to solve it. i(px-Et)/h=i(kx-wt) than somehow got k=p/h than...
18. ### Wave velocity in a free-hanging rope

Homework Statement A uniform rope of length L hangs freely from the ceiling. Show that the time for a transverse wave to travel the length of the rope is t0 = 2\sqrt{L/g}. Homework Equations v = \sqrt{\tau/\mu}. (Where \tau is the tension and \mu the linear density of the rope.)...
19. ### Exploring Standing Wave Velocity: Human Error or Physics?

I just completed a lab in which we created standing waves in a fixed length of pipe using a function generator. An oscilloscope was used to measure the amplitude of the waves. The frequency was changed until a resonant condition was met, and then the location of all the nodes/antinodes was...
20. ### Calculating Wave Velocity in a Stadium

Football season's comming up, so here we go. Assume a circular stadium. A "Human wave" travels around the stadium. T = period a = distance to first row d = distance between rows n = row number (may need to be converted from a letter or double letter) Wave velocity v = wr v =...
21. ### Wave Velocity, Amplitude & Phase change

Hi All, I am having trouble trying to understand & calculate the effects that magnetic soils have on a pulsed induction metal detector, in particular soils containing iron. I have read this: The section on Soil Magnetic Properties...
22. ### What is the Velocity and Acceleration of a Transverse Wave on a Stretched Cord?

Homework Statement The left-hand end of a long horizontal stretched cord oscillates transversely in SHM with frequency f = 250 Hz and amplitude 2.6 cm. The cord is under a tension of 140 N and has a linear density \mu = 0.12 kg/m. At t = 0, the end of the cord has an upward displacement 1.6...
23. ### Wave velocity on a taut string

Consider the flexible string under tension T passing through a fixed wiggly tube at speed v. At any point, the tube's wiggly curve has a well-defined centre of curvature, and associated radius r. The acceleration of the string is v^2/r, and the force due to tension T is T*dl/r where dl...
24. ### Wave Velocity in Terms of Tension

A few friends and I built a wave "machine." It's made by laying out brass "rods" about a foot long next to each other about an inch or so apart on tape, and then taping the top side. When holding both sides of this "machine," when one strikes one rod at one end, it makes the rod in front of it...
25. ### Calculating Wave Velocity, Mass, and Wavelength of a Guitar String

Homework Statement A. A typical steel B-string in a guitar resonates in its fundamental frequency at 240 Hz. The length of the string is 0.680 m. What is the wave velocity in the string? B. The tension in the above string is 86.8 N. Calculate the mass of a 2 m long piece of the steel...
26. ### Calculating Wave Velocity with Frequency and Amplitude

Anyone know how to calculate the wave velocity if you know the frecuency, but not the wavelength? We were also given the amplitude.
27. ### Transverse Wave Velocity (speed)

Prof gave us this equation and question: The equation of a transverse wave traveling in a rope is: y=10sin*pi(0.01x-2.00t) He said that x and y are expressed in cm, and time in seconds. We are to: A. find the amplitude, frequency(Hz), velocity(cm) and wavelength(cm) of the wave. B...
28. ### Wave Velocity along X-Axis: 4m/s

a wave moving along the x-axis is described by y(x,t) = Ae^(-(x+vt)^2/b) where x is in meters and t is in seconds. Given A=4m, v=3 m/s, and b=4 m^2. Determine the speed of the wave. Answer in units of m/s. i tried using partial differentiation with respect to t. i got dy/dt =...
29. ### Calculating Wave Velocity & Wavelength

A sound wave of velocity 600 m/s has a wavelength of 3 m. At a certain instant one of the molecules of the medium is at its normal position. How long will it be before this same molecule is again at its normal position? v=f&lambda;, f=v/&lambda; =(600m/s)/3m = 200Hz T=1/f=1/200=.005s...