ELEKTRONIKOS
ĮTAISAI
2009
Acoustic Waves
Acoustic wave: A longitudinal wave that (a) consists of a sequence of pressure pulses or elastic displacements of the material, whether gas, liquid, or solid, in which the wave propagates. In solids, the wave consists of a sequence of elastic compression and expansion waves that travel though the solid.
In acoustic wave devices acoustic waves are transmitted on a miniature solid substrate.
In a crystalline solid a sound wave is transmitted as a result of the displacement of the lattice points about their mean position. The wave is transmitted as an elastic wave. (Elastic substance is able to return to its original shape or size after being pulled or pressed out).
The term sound wave is sometimes confined to waves with the frequency falling within the audible range of the human ear, i. e. from about 20 Hz to
20 kHz. Waves of frequency greater than 20 kHz are ultrasonic waves . Waves of frequency 10 9 –10 13 Hz are called hypersonic waves .
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ELEKTRONIKOS
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2009
Acoustic Waves
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There are various kinds of acoustic waves. Bulk acoustic waves are acoustic waves propagated through the bulk substrate material.
If the motions of the matter particles conveying the wave are perpendicular to the direction of propagation of the wave itself, we have a transverse wave.
If the motion of particles is back and forth along the direction of propagation, we have a longitudinal wave.
Surface acoustic waves propagate along the surface of a substrate. There are some types of the surface acoustic waves. In the case of the Rayleigh waves particles in the surface layer move both up and down and back and forth tracing out elliptical paths.
Acoustic waves
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ELEKTRONIKOS
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2009
Acoustic Waves
Let us consider that longitudinal vibrations are excited in a rod.
Hooke’s law:
 2 s
 t
2

E

 2 s
 x
2 d m
 
S d x d F


F
 x d x a
 d
2 s d t
2
 d F d m

1

S

F
 x d s d x

F
ES

F
 x

ES
 2 s
 x
2 s ( x , t )

A exp[ j

( t
 x / v l
)]

B exp[ j

( t
 x / v l
)] v l

E /
  
E
 s
 x
.
Here s is displacement; σ is stress .
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ELEKTRONIKOS
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2009
Acoustic Waves
Mechanical waves are described using terms such as wavelength, period, frequency, amplitude and speed of propagation.
Mechanical vibrations propagate along the rod as an elastic wave. The longitudinal displacement is given by the sum of waves that propagate in opposite directions: s ( x , t )

A exp[ j

( t
 x / v l
)]

B exp[ j

( t
 x / v l
)]
The displacement causes the longitudinal mechanical stress given by

( x , t )

E

 s x
 j
 v l
E


A exp[ j

( t

The speed of the longitudinal wave is given by x / v l
)]
 v l

B exp[
E /
 j

( t
 x / v l
)] .

The velocity is about 10 5 times less than the velocity of the electromagnetic wave . So using mechanical waves we can obtain sufficient delay time at short distances.
  v l f
 v l
T – the length of the acoustic wave at radio frequency is short .
At v = 5000 m/s and f = 1 MHz,

= 5 mm.
5
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ELEKTRONIKOS
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2009
Acoustic Waves
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Let us consider that the length of the rod is l and its left end is fixed. Then s ( 0 , t )

0 B
 
A s ( x , t )

C sin

( x , t )

C
 v l
 x e j
 t v l
E cos
 x v l e j
 t

( l , t )

0 cos
 l v l

0
 l v l

( 2 n

1 )
π
2
Natural frequencies: f l n

2 n

1 v l
4 l

( 2 n

1 )
4 l
E

 l n
 v l f

2 n
4

1 l l

( 2 n

1 )
 l n
4
At natural frequency odd number of wavelength quarters fit in the length of the rod.
Vibrations of a rod Vibrations of a rod 1
VGTU EF ESK stanislovas.staras@el.vgtu.lt

ELEKTRONIKOS
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2009
Acoustic Waves
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VGTU EF ESK l

( 2 n

1 )
 l n
4 stanislovas.staras@el.vgtu.lt
l
 n
λ l n
2

ELEKTRONIKOS
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2009
Flexural Bending Mode Shapes and Boundary Conditions
Dan Russell, Ph.D.
, Applied Physics , Kettering University
All text and images on this page are ©2006 by Daniel A. Russell and may not used in other web pages or reports without permission
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VGTU EF ESK
Dan Russell, Ph.D.
, Applied Physics , Kettering University stanislovas.staras@el.vgtu.lt

ELEKTRONIKOS
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2009
Acoustic Waves and Mechanical Resonators
1. Mechanical resonators are small and have high quality (to 10 7 ).
2. Because resonant frequency is dependent on the resonator dimensions and elasticity modulus, materials having small thermal expansion coefficient and stable elasticity modulus must be used for mechanical resonators.
3. The velocity of acoustic wave is dependent on the type of the wave.
4. The natural frequencies depend on the types of acoustic wave.
5. A mechanical resonator have many resonant frequencies dependent on the number n , type of the acoustic wave and other factors. This property is not desirable in electronic applications.
6. The desirable type of vibrations may be selected by the selection of the form of a resonator and the method used for excitation of vibrations.
Rectangular Circular
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VGTU EF ESK
Dan Russell, Ph.D.
, Applied Physics , Kettering University stanislovas.staras@el.vgtu.lt

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ĮTAISAI
2009 12
VGTU EF ESK
Dan Russell, Ph.D.
, Applied Physics , Kettering University stanislovas.staras@el.vgtu.lt

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2009 13
VGTU EF ESK stanislovas.staras@el.vgtu.lt