THIS LECTURE
Sponsored Links
This presentation is the property of its rightful owner.
1 / 19

Waves on a string PowerPoint PPT Presentation


  • 83 Views
  • Uploaded on
  • Presentation posted in: General

THIS LECTURE. Waves on a string. Standing waves. Dispersive and non-dispersive waves. Travelling waves. No boundaries. x. With boundaries. Standing waves. Two ends fixed. One end fixed. Standing waves. Two ends fixed. Standing waves. Two ends fixed. x. x. Travelling waves.

Download Presentation

Waves on a string

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


THIS LECTURE

Waves on a string

  • Standing waves

  • Dispersive and non-dispersive waves


Travelling waves

No boundaries

x

With boundaries

Standing waves

Two ends fixed

One end fixed


Standing waves

Two ends fixed


Standing waves

Two ends fixed


x

x

Travelling waves

Standing waves

Boundaries

No boundaries

2

2

Each section of the string vibrates with same frequency w

Each section of the string vibrates

with same amplitude A

Each section of the string vibrates

with different phase f = kx


x

x

Travelling waves

Standing waves

Boundaries

No boundaries

2

2

Each section of the string vibrates with same frequency w

Each section of the string vibrates with same frequency w

Each section of the string vibrates

with same amplitude A

Each section of the string vibrates

with different amplitude 2Asin(knx)

Each section of the string vibrates

with different phase f = kx

Each section of the string vibrates

with phase 0 or out of phase by p


Standing waves

One end fixed


Superposition of standing waves


Relative intensities of the harmonics

for different instruments


Playing different instruments

x

x


Dispersive wave: it changes shape

t = 0

t > 0

Dispersive and non-dispersive waves

Non-dispersive wave: it does not change shape

t = 0

t > 0


Two velocities to describe the wave

Group velocity, Vg

Velocity at which the envelope

of wave peaks moves

Phase velocity, Vp

Velocity at which successive

peaks move

For non-dispersive waves Vg =Vp

For dispersive waves VgVp

http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-further-dispersive.htm


Group velocity

If VpVg  dispersive wave

If Vp=Vg  non-dispersive wave

Group and phase velocity

Phase velocity

Relation between Vg and Vp


Superposition

Wave-packet

Superposition of sinusoidal waves

Sinusoidal waves

w1, k1

w2, k2

w3, k3


Dispersive wave

Sinusoidal waves have different speed

w1/ k1= c1

w2/ k2= c2

w3/ k3= c3

Non-dispersive wave

Sinusoidal waves have the same speed

Wave propagates

with speed c

maintaining its shape

w1/ k1= c

w2/ k2= c

t = 0

w3/ k3= c

t > 0

Wave

changes its shape

t = 0

t > 0


Dispersion relation

c= slope

Real string (e.g. a piano string)

c2

c1

Waves on a string

Ideal string

Vp=w/k=c does not

depend on k

Non-dispersive wave

Vp=w/k=c

depends on k

Dispersive wave


Dispersion relation

Group velocity

Phase velocity

Real string

Ideal string


Problem

Determine phase and group velocity for waves whose dispersion relation is described by :


The resulting wave is given by

Group velocity

2p/Dk

Phase velocity

2p/k

Superposition of sinusoidal waves


  • Login