## velocity of ultrasonic waves in liquids (accoustic grating method)

Aim

To  determine the velocity of ultrasonic waves in the given liquids (kerosene,ccl4) using accoustic grating method & hence to find its compressibility.

Apparatus

spectrometer, monochromatic light source, ultrasonic transducer, rectangular cup containing test liquid.

Principle

velocity of ultrasonic waves is given by

V = fλ

Where

v-à velocity

f-à frequency

λ à wavelength

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.

Here, the node acts as the transmitting slit and the antinode acts as the opaque part…thus resembling a normal ruled diffraction grating. This is obvious because the nodes have points of minimum density and hence allow more amount of light to pass through them than those at antinodes. Thus, the nodes act like slits.

If this SLITs whose element grating is equal to the wavelength of the ultrasonic waves ,are illuminated with monochromatic light,. Let it be denoted by d. If λ is the wavelength of the light passed through the grating which is diffracted by an angle θ, then the nth order of the maximum is given by

d sinθ= nλ

d-à distance between slits produced by nodes and antinodes.

Θ –à diffraction angle

λ-à wavelength of monochromatic light.

If frequency given and we found ‘d’ then.

Velocity v = fd

f-à frequency of ultrasonic wave

d-à grating element

now, if  ‘ρ’ is the frquency of liquid, v its velocity,

then, bulk modulus K= v2ρ

compressibility is the reciprocal of bulk modulus :

compressibility= 1/K

procedure

• 2.   Rectangular cup containing liquid is placed on the prism table.
• 3.   An ultrasonic transducer connected to RF oscillator is put to that cup which is illuminated by monochromatic light of wavelength λ
• 4.   A diffraction pattern is observed by looking through telescope.
• 5.   Set crosswire to coincide with  nth order (say 3rd order) of the diffraction pattern on one side of the central bright line and take the readings of vernier.
• 6.   Take readings of 2nd, 1st order on the same side and 1st,2nd and 3rd order of the other side.
• 7.   Repeat the experiment for the other liquid
• 8.   Difference between the vernier readings of same order on the opposite sides give 2θ, substitute in the equations given.

Warning:

Telescope should be rotated only in one direction.