where expertise comes together - since 1996 -

# The Largest Open Access Portal of Nondestructive Testing (NDT)

Conference Proceedings, Articles, News, Exhibition, Forum, Network and more

where expertise comes together
- since 1996 -

 AT-Automation Technology GmbHAT -Automation Technology is a systems house for industrial image processing. AT offers thermographic ndt systems as well as high-speed 3D sensors.

 9210 views
Career Discussions
Sandy
Sandy
07:22 Dec-03-2003
Resonance and crystal thickness

Resonance frequency (Fr)= (speed of sound in crystal)/(2xthickness of the crystal)

I can't really believe this because what I understand is that the crystal vibrates via voltage and then produces vibration,
or do they mean the impedance of the material?

Also I read:The so-called "fundamental resonant frequency" of an ultrasound transducer is the transmit frequency that corresponds to the half-wavelength crystal thickness.
So that:
Fr = 2 x christal thickness

So my question is:
Is the Fr of the crystal obtained when the crystal has a diameter equal to exactly half the wavelength of the ultrasound that is produced by the crystal.

Or does this depend on the acoustic impedance, or speed of sound in the crystal? Do does the Fr depend on the material?

Can someone please give me the correct information on this
or point me in the good direction?

Many thanks!

Paul A. Meyer
R & D,
GE Inspection Technologies, USA, Joined Nov 1998, 47

Paul A. Meyer

R & D,
GE Inspection Technologies,
USA,
Joined Nov 1998
47
09:21 Dec-03-2003
Re: Resonance and crystal thickness
Hello Sandy,
The fundamental mechanical resonance occurs when the thickness of the crystal is 1/2 wavelength thick.
Let
lambda = wavelength
c = acoustic velocity
f = frequency

thickness = lambda/2 (at fundamental resonance)

and

lambda = c/f

then

thickness= c/(2*f)

solving for f

f=c/(2 * thickness)

This refers to the mechanical free resonance of the crystal which is achieved by deforming it and allowing it to resonate...much like striking a tuning fork or a piano string.

If you drive the crystal with an electrical signal, the response will be at the driving frequency. The amplitude of the output will vary with driving frequency...as you approach the resonant frequency of the crystal, the output amplitude will increase.

The piezoelectric element used in a transducer has many resonances, some related to the thickness, and some related to the lateral dimensions. Most transducers are designed so that the unwanted resonances are suppressed and the fundamental dominates theoutput.

So, to answer your question, Fr depends on the thickness and and the acoustic velocity of the crystal.

Paul
----------- Start Original Message -----------
: Resonance frequency (Fr)= (speed of sound in crystal)/(2xthickness of the crystal)
: I can't really believe this because what I understand is that the crystal vibrates via voltage and then produces vibration,
: or do they mean the impedance of the material?
: Also I read:The so-called "fundamental resonant frequency" of an ultrasound transducer is the transmit frequency that corresponds to the half-wavelength crystal thickness.
: So that:
: Fr = 2 x christal thickness
: So my question is:
: Is the Fr of the crystal obtained when the crystal has a diameter equal to exactly half the wavelength of the ultrasound that is produced by the crystal.
: Or does this depend on the acoustic impedance, or speed of sound in the crystal? Do does the Fr depend on the material?
: Can someone please give me the correct information on this
: or point me in the good direction?
: Many thanks!
------------ End Original Message ------------

Sandy
Sandy
05:30 Dec-09-2003
Re: Resonance and crystal thickness
Thank you very much Paul, forgot to thank you,it answers perfectly well my question,
and still another little question(S)

It is stated that for a gaussian pulse shape the bandwidth;
df x t pulse = 1

what do they mean with gaussian?
So the bandwidth x the pulse time = 1

hz x time = 1 ?

Sandy

----------- Start Original Message -----------
: Hello Sandy,
: The fundamental mechanical resonance occurs when the thickness of the crystal is 1/2 wavelength thick.
: Let
: lambda = wavelength
: c = acoustic velocity
: f = frequency
:
: thickness = lambda/2 (at fundamental resonance)
: and
: lambda = c/f
: then
: thickness= c/(2*f)
: solving for f
: f=c/(2 * thickness)
: This refers to the mechanical free resonance of the crystal which is achieved by deforming it and allowing it to resonate...much like striking a tuning fork or a piano string.
: If you drive the crystal with an electrical signal, the response will be at the driving frequency. Theamplitude of the output will vary with driving frequency...as you approach the resonant frequency of the crystal, the output amplitude will increase.
: The piezoelectric element used in a transducer has many resonances, some related to the thickness, and some related to the lateral dimensions. Most transducers are designed so that the unwanted resonances are suppressed and the fundamental dominates the output.
: So, to answer your question, Fr depends on the thickness and and the acoustic velocity of the crystal.
: Paul
: : Resonance frequency (Fr)= (speed of sound in crystal)/(2xthickness of the crystal)
: : I can't really believe this because what I understand is that the crystal vibrates via voltage and then produces vibration,
: : or do they mean the impedance of the material?
: : Also I read:The so-called "fundamental resonant frequency" of an ultrasound transducer is the transmit frequency that corresponds to the half-wavelength crystal thickness.
: : So that:
: : Fr = 2 x christal thickness
: : So my question is:
: : Is the Fr of the crystal obtained when the crystal has a diameter equal to exactly half the wavelength of the ultrasound that is produced by the crystal.
: : Or does this depend on the acoustic impedance, or speed of sound in the crystal? Do does the Fr depend on the material?
: : Can someone please give me the correct information on this
: : or point me in the good direction?
: : Many thanks!
------------ End Original Message ------------

Paul A, Meyer
R & D,
GE Inspection Technologies, USA, Joined Nov 1998, 47

Paul A, Meyer

R & D,
GE Inspection Technologies,
USA,
Joined Nov 1998
47
01:01 Dec-10-2003
Re: Resonance and crystal thickness
Hi Sandy,

A continuous wave signal has only one frequency component and that signal will continue for all time. A pulse can be represented as a summation of continuous wave signals of various frequency and amplitude. The Fourier or frequency spectrum of a pulse shows the distribution of energy as a function of frequency necessary to create the prescribed pulse. The Gaussian shape you reference means that the frequency spectrum has a Gaussian, or "normal", distribution with frequency. This is the same "normal" distribution you encounter in statistics.

However, if I understand your question, it refers to a different situation. You can calculate the frequency spectrum of a pulse through the use of a mathematical process called a Fourier Transform. With the advent of digital computers an approximation algorithm was developed that calculates the transform at discrete frequencies rather that as a continuous function. For practical purposes, this is sufficient and much quicker computationally. In thatresult, the frequency increment (df) calculated is equal to 1/(length of pulse in time). Rearranging this equation yields: df x t pulse = 1 I do not believe that a Gaussian spectrum shape is necessary for this equation to be true.

Thanks,
Paul

----------- Start Original Message -----------
: Thank you very much Paul, forgot to thank you,it answers perfectly well my question,
: and still another little question(S)
: It is stated that for a gaussian pulse shape the bandwidth;
: df x t pulse = 1
: what do they mean with gaussian?
: So the bandwidth x the pulse time = 1
: hz x time = 1 ?
: Sandy
: : Hello Sandy,
: : The fundamental mechanical resonance occurs when the thickness of the crystal is 1/2 wavelength thick.
: : Let
: : lambda = wavelength
: : c = acoustic velocity
: : f = frequency
: :
: : thickness = lambda/2 (at fundamental resonance)
: : and
: : lambda = c/f
: : then
: : thickness= c/(2*f)
: : solving for f
: : f=c/(2 * thickness)
: : This refers to the mechanical free resonance of the crystal which is achieved by deforming it and allowing it to resonate...much like striking a tuning fork or a piano string.
: : If you drive the crystal with an electrical signal, the response will be at the driving frequency. The amplitude of the output will vary with driving frequency...as you approach the resonant frequency of the crystal, the output amplitude will increase.
: : The piezoelectric element used in a transducer has many resonances, some related to the thickness, and some related to the lateral dimensions. Most transducers are designed so that the unwanted resonances are suppressed and the fundamental dominates the output.
: : So, to answer your question, Fr depends on the thickness and and the acoustic velocity of the crystal.
: : Paul
: : : I read somewhere:
: : : Resonance frequency (Fr)= (speed of sound in crystal)/(2xthickness of the crystal)
: : : I can't really believe this because what I understand is that the crystal vibrates via voltage and then produces vibration,
: : : or do they mean the impedance of the material?
: : : Also I read:The so-called "fundamental resonant frequency" of an ultrasound transducer is the transmit frequency that corresponds to the half-wavelength crystal thickness.
: : : So that:
: : : Fr = 2 x christal thickness
: : : So my question is:
: : : Is the Fr of the crystal obtained when the crystal has a diameter equal to exactly half the wavelength of the ultrasound that is produced by the crystal.
: : : Or does this depend on the acoustic impedance, or speed of sound in the crystal? Do does the Fr depend on the material?
: : : Can someone please give me the correct information on this
: : : or point me in the good direction?
: : : Many thanks!
------------ End Original Message ------------

Product Spotlight

#### AIS229 - Multipurpose Real Time System

Latest standard & automatic real time system developed by Balteau. The AIS229 has been designed to
...
do series inspection in a wide variety of industry. Composed of a shielded cabinet, 5 axis manipulator, x-ray generator and tubehead from 160kV to 225kV, a fl at panel & much more, the AIS229 is most certainly one of the most multipurpose RTR system available on the market.
>

#### Research and Application Development For NDT

Acuren’s Research and Application Development specializes in the development of advanced ultraso
...
nic inspection techniques and systems for challenging inspection applications, with an emphasis on practical solutions which are field deployable. Services include manual and automated ultrasonic inspection system development, inspection technique optimization using laboratory scale studies and ultrasonic modeling (CIVA, BeamTool), preparing technical justification for technique evaluation and qualification (Probability of Detection and sizing accuracy studies), inspection/calibration/analysis procedure preparation to support field deployment of custom techniques, and development of custom imaging algorithms to support challenging inspection applications.
>

#### Immersion systems

ScanMaster ultrasonic immersion systems are designed for high throughput, multi shift operation in a
...
n industrial or lab environment. These fully integrated systems provide various scanning configurations and incorporate conventional and phased arrays technologies to support diverse applications, such as inspection of disks, bars, shafts, billets and plates. All of ScanMaster immersion systems are built from high accuracy scanning frames allowing for scanning of complex parts and include a multi-channel ultrasonic instrument with exceptional performance. The systems are approved by all major manufacturers for C-scan inspection of jet engine forged discs. Together with a comprehensive set of software modules these flexible series of systems provide the customer with the best price performance solutions.
>

#### VeeScan AirCraft Wheel Inspection

The VEESCAN offers maximum flexibility, has a proven mechanical design and records of breakdown-fr
...
ee operation of over 365 days. Appealing to companies in the Aerospace industry, the VEESCAN is ideal for all wheel-testing environments. With a wide selection of probes, the VeeScan allows your wheel testing facility the flexibility to select the most compatible configurations with their workload.
>

Share...
We use technical and analytics cookies to ensure that we will give you the best experience of our website - More Info
Accept
top
this is debug window