Determination of velocity of ultrasonic waves in liquid - Acoustic Grating Method

DETERMINATION OF VELOCITY OF ULTRASONIC WAVES IN LIQUID ‒ ACOUSTIC GRATING METHOD

Principle

When ultrasonic waves are passed through a liquid, the density of the liquid varies layer by layer due to the variation in pressure and hence the liquid will act as a diffraction grating, so called acoustical grating. Under this condition when a monochromatic source of light is passed through the acoustical grating, the light gets diffracted. Then by using the condition for diffraction, the velocity of ultrasonic waves can be determined.

Construction

It consists of a glass tank, filled with the liquid (say kerosene). A piezo‒ electric crystal (Quartz) is fixed at the top of the glass tank and is connected to a piezo‒electric oscillatory circuit as shown in Fig.5.7.

An incandescent lamp is used as a monochromatic source of light(S) and a telescope arrangement is made to view the diffraction pattern. A collimator consisting of two lens L₁ and L₂ is used to focus the light effectively onto the glass tank.

Working

i) When the piezo‒electric crystal is at rest

Initially the piezo‒electric crystal is kept at rest and the monochromatic source of light is switched ON. When the light is focused onto the glass tank filled with the liquid, a single image (or) a vertical peak is observed on the telescope, which shows that there is no diffraction.

ii) When the piezo‒electric crystal is set into vibration

The piezo‒electric crystal (quartz) is set into vibrations using piezo‒electric oscillatory circuit. At resonance, ultrasonic waves are produced and is passed through the liquid.

These ultrasonic waves are reflected by the walls of the glass tank and forms a stationary wave pattern with nodes and antinodes, in the liquid.

At nodes the density of the liquid becomes more and at the antinodes the density of the liquid becomes less. Thus the liquid behaves as a diffracting element called acoustical grating element.

Now when the monochromatic source of light is passed through the acoustical grating, the light gets diffracted and a diffraction pattern consisting of central maximum (C_m) and principle maxima (P_m) on either side is viewed through the telescope as shown in Fig. 5.8.

The velocity of ultrasonic waves can be found using the diffraction condition

i.e., 2d sin θ = nλ                 ………………(1)

Where 'd' is the distance between successive nodes (or) antinodes.

θ is the angle of diffraction.

n on is the order of spectrum.

λ is the wavelength of the monochromatic source of light.

If λ_u is the wavelength of ultrasonics, then

we can write from Fig.5.9 as λ_u = 2d                   ......(2)

Equation (1) becomes λ_u sin θ = nλ

 (or) Wavelength of ultrasonics λ_u = nλ / sin θ

We know,

Velocity of ultrasonics = (Frequency of ultrasonics) × (Wavelength of ultrasonics)

Frequency of ultrasonics produced by piezo‒electric oscillator will be the same as that of the frequency of the oscillatory circuit. So if v_u is the frequency of the ultrasonics produced using piezo‒electric oscillator then,

Velocity of Ultrasonics (v) = V_uλ_u                  ……………….(4)

Substituting equation (3) in (4), we get

Velocity of ultrasonics v = v_unλ / sin θ

Thus the velocity (or) wavelength of the ultrasonics can be determined using acoustical grating.

NOTE: Using this method we can determine the velocity of any liquids (or) gases, even at various temperatures.