mee …. wave propagation in solids week 1 assoc. prof. dr. abdullah seçgin
DESCRIPTION
Wave Speed For solids: For gas (not for liquids):TRANSCRIPT
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[ ][ ]
mf Hz
2
3
[ / ]cρ[ / ]E N mkg m
For solids:
For gas (not for liquids):
0c= [ ]ρp RT 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
22
Tk
A little math..Gradient, Divergence, Curl, Laplacian
321
321
321
zyxf)fcurl(
zf
yf
xff)fdiv(
zf
yf
xffgrad(f)
fff
kji
kfjfiffLet
kji
zyyzxf sin22
Examples
Derive the followings
ivfradf
Laplacianffe
fdfcfbfa
dg))
curldiv))))
2