MEE ….MEE ….WAVE PROPAGATION IN WAVE PROPAGATION IN

SOLIDS SOLIDS Week 1

Assoc. Prof. Dr. Abdullah SeçginAssoc. Prof. Dr. Abdullah Seçgin

A Harmonic wave.. Wavelength..

Wave Speed

1[ ] c[ ]T[ ]m ms s c[ ]

[ ]m

f Hz

2

3

[ / ]c

ρ[ / ]

E N m

kg m

For solids:

For gas (not for liquids):

0c= [ ]ρ

pRT K

Example: Speed of sound

Ex.1.1: Compute the speed of sound waves for air at 20 0C, and for steel?

c= 1.4 287 (20 273.2) 343.2 /RT m s For air:

For steel:11c= / ρ 2.1 10 / 7900 5155.8 /E m s

0airc =20.0457 ( C+273.2) 343.2 /m s

or simply

Particle velocity

Surface of the source expands and contracts sinusoidally

During the first half of the motion, it pushes the particles near its surface outward

During the second half of the motion, it pulls the particles near its surface inward.

It is the velocity of the oscillation of the particle, so not be confused with wave speed which is the velocity of the propagating wave.

Particle velocity can be longitudinal (compression), or transverse

Particles

Source

Longitudinal-Transverse waves

Propagation of Waves in 1D

to the leftto the rightWave propagates

( / )1/

( / )

r sk m

c m s

Wavenumber

( , ) ( ) ( )p x t F kx t G kx t

The wave propagates with k in space and with in time

2

2

T

k

A little math..Gradient, Divergence, Curl, Laplacian

321

321

321

zyxf)fcurl(

z

f

y

f

x

ff)fdiv(

z

f

y

f

x

ffgrad(f)

fff

kji

kfjfiffLet

kji

zyyzxf sin22

Examples

Derive the followings

ivfradf

Laplacianffe

fd

fc

fb

fa

dg)

)

curldiv)

)

)

)

2