Ultrasonic Interferometer

Aim:

• To calculate the velocity of ultrasonic sound through different liquid media.
• To calculate the adiabatic compressibility of the given liquid.

Apparatus:

Ultrasonic interferometer, sample liquids, high frequency generator etc.

Theory:

Ultrasonic interferometer is a simple device which yields accurate and consistent data, from which one can determine the velocity of ultrasonic sound in a liquid medium.

Ultrasonics:

Ultrasonic sound refers to sound pressure with a frequency greater than the human audible range (20Hz to 20 KHz). When an ultrasonic wave propagates through a medium, the molecules in that medium vibrate over very short distance in a direction parallel to the longitudinal wave. During this vibration, momentum is transferred among molecules. This causes the wave to pass through the medium.

Generation of ultrasound:

Ultrasonic can be produced by different methods. The most common methods include:

1.  Mechanical  method:       In this, ultrasonic frequencies up to 100 KHz are produced. But this method is rarely used due to its limited frequency range.
2. Piezoelectric generator:    This is the most common method used for the production of ultrasound. When mechanical pressure is applied to opposite faces of certain crystals which are cut suitably, it get contracted and expanded. i.e., a rapid alternating electric field causes the piezoelectric crystal to vibrate. This vibration is largest at resonance, and is then passed through the medium as a longitudinal wave. i.e., a sound wave is produced.
3. Magnetostriction generator:   In this method, the magnetostriction method is used for the production of ultrasonic. Frequencies ranging from 8000 Hz to 20,000Hz can be produced by this method.

Ultrasonic Interferometer:

The schematic diagram of an ultrasonic interferometer is shown below.

In an ultrasonic interferometer, the ultrasonic waves are produced by piezoelectric method. In a fixed frequency variable path interferometer, the wavelength of the sound used is measured, and from this one can calculate its velocity through that medium. The apparatus consists of an ultrasonic cell, which is a double walled brass cell with chromium plated surfaces and has a capacity of 10ml. The schematic diagram of an ultrasonic interferometer is shown below. The micrometer screw has a least count of 0.001cm and pitch scale has a length of 25mm. Ultrasonic waves of known frequency are produced by a quartz crystal which is fixed at the bottom of the cell. There is a movable metallic plate parallel to the quartz plate, which reflects the waves. These waves superimpose and if the separation between the plates is exactly a whole number multiple of wavelength of sound, standing waves are produced in the liquid medium. At this point, acoustic resonance occurs and this give rise to an electrical reaction on the generator driving quartz plate. Now the anode current of the generator becomes maximum.

If we increase or decrease the distance and the variation is exactly one half of the wavelength (λ/2) or its multiple, the anode current again becomes maximum. If ‘d’is the   separation between successive adjacent maximum anode current, then,

d = λ/2.

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We have, the velocity (v) of a wave is related to its wavelength (λ) by the relation,

                                   v=fλ, where f is the frequency of the wave.

                                   Then,   v= λf= 2df.

The velocity of ultrasound is determined principally by the compressibility of the material of the medium. For a medium with high compressibility, the velocity will be less. Adiabatic compressibility of a fluid is a measure of the relative volume change of the fluid as a response to a pressure change. Compressibility is the reciprocal of bulk modulus, and is usually denoted by the Greek word beta (β).The adiabatic compressibility of the material of the sample can be calculated using the equation,

  where ρ is the density of the material of the medium and v is the velocity of the sound wave through that medium.