How Does Frequency Affect Laser Diffraction Through a Phase Grating?

[franky_boy]

Homework Statement

A laser passes through a body of water and later hits a screen, as shown:

http://img80.imageshack.us/img80/7417/20478103.jpg

However, suspended in the water is a piezoelectric quartz crystal which can produce waves within the water. When set at 5.5MHz, the following is observed on the screen:

http://img207.imageshack.us/img207/3624/5x5p.jpg

At 9.5MHz:

http://img207.imageshack.us/img207/5941/9x5.jpg

And, finally, at 12MHz:

http://img14.imageshack.us/img14/178/12x0.jpg

The question is: what is happening?

Homework Equations

No equations are supplied.

The Attempt at a Solution

A little research shows that one type of diffraction grating is called a phase grating, which I assume works in roughly the following way:

http://img513.imageshack.us/img513/5749/85592676.png

Where the grey patches represent parts of the water which are in a state of compression (resulting in an altered refractive index). Given that the speed of sound in water is about 1466m/s, these bands are about 67 microns thick when at 5.5MHz, and about 31 microns when at 12MHz.

I'm unclear as to whether the resulting vibration in the water results in a standing wave, or something which propagates. And why doesn't a diffraction grating which constantly changes its properties result in a smeared image on the screen?

It makes good sense to me that 'ordinary' light would produce a diffraction pattern after passing through a phase grating, but presumably a laser is different. What is causing the light to diverge so much? Can Huygens's principle help in this case?

Any pointers in the right direction would be highly appreciated.

Many thanks in advance!

 

[Redbelly98]

The Attempt at a Solution

A little research shows that one type of diffraction grating is called a phase grating...

That is they key to what is going on; the water waves act as a diffraction grating. You can use the speed-of-sound and frequencies to calculate wavelengths, which are the period of the diffraction grating "rulings". (The 67 and 31 micron values you gave are not the correct water wavelengths, by the way.)