Wednesday, August 11, 2010

velocity of ultrasonic waves in liquids

Aim



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


Apparatus



SODIUM VAPOUR LAMP


TRANSDUCER IMMERSED IN LIQUID






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




Principle

velocity of ultrasonic waves is given by

                                                        V = fλ

Where

v- velocity

f- frequency

λ  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->  distance between slits produced by nodes and antinodes.


Θ -> diffraction angle


λ-> wavelength of monochromatic light


If frequency given and we found ‘d’ then.






Velocity v = fd


f->frequency of ultrasonic wave

d-> 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




1. initial adjustments are made and telescope is properly focussed.


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.












 






3 comments:

  1. great going guys (and gals!)...we need such proactive efforts to make our learning real..
    good luck with your work!
    PS: just an advice, you could try putting it all in word or corel draw or some other application and then upload it to scribd for further reaching out to people...

    ReplyDelete
  2. from begining I was thinking that you all are indian...........your way of teaching practical is very good keep it up.........any communication wants wanna from me then u can mail me at "utkarshsrivastava0@gmail.com"

    ReplyDelete
  3. in the theory it has been said that "the node acts as the transmitting slit and the antinode acts as the opaque part..." but as far as i think it should be the other way round... since higher the density lower the transmission...

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