Ultrasonic grating

An ultrasonic wave is a sound wave having a frequency greater than 20 kHz. Because of the very small wavelength of ultrasonic waves compared to X-rays they have considerable penetrating power. The human ear can not recognize ultrasonic waves, but animals such as bats and dogs can easily sense the ultrasonic wave. It is produced by the phenomena of the Piezo-electric effect and magnetostriction.

When ultrasonic waves are generated in a liquid kept in rectangular vessel, the wave can be reflected from the walls of the vessel. The direct and reflected waves get superimposed, which causes a standing wave to be formed. The density of the liquid at the node will be more than the density at an antinode. Under these conditions, if a beam of light is passed through the liquid at right angles to the wave the liquid acts as a diffraction grating. Such a grating is known as an "acoustical grating". The grating element is equal to the wavelength of the ultrasonic waves. Let it be denoted by $d$. If $lambda$ is the wavelength of the light passed through the grating which is diffracted by an angle $heta$, then the nth order of the maximum is given by:

$d\; sin\; heta\; =\; n\; lambda$

or,$d\; =\; n\; lambda/sin\; heta$

If v is the velocity of the ultrasonic wave in the liquid we can calculate the velocity of the wave with:

$v/\; u\; =\; n\; lambda/sin\; heta$

or, $v\; =\; u\; n\; lambda/sin\; heta$

where $u$ is the frequency of the wave.