Ultrasonic Waves Experiment Overview

Aug 5, 2024

Notes on Ultrasonic Waves Experiment by Dr. Dudai Kumar Khan

Introduction

  • Dr. Dudai Kumar Khan introduced the experiment to determine the wavelength and velocity of ultrasonic waves in a liquid through diffraction using ultrasonic grating.

Ultrasonic Waves

  • Definition: Sound waves with frequencies higher than 20 kHz (20 kHz to 1 GHz).
  • Characteristics: Cannot be sensed by human ears; have various applications, including studying materials.

Generation of Ultrasonic Waves

Methods of Generation

  1. Mechanical generation
  2. Thermal generation
  3. Piezoelectric generation (used in this experiment)
    • Piezoelectric Crystals: Non-centrosymmetric ferroelectric crystals that expand and contract when alternating voltage is applied.
    • Example crystals: Quartz, Tourmaline.

Ultrasonic Grating

  • Formation: When a piezoelectric crystal is immersed in a medium (liquid/gas) and subjected to RF signals, it creates periodic density variations (compression and rarefaction).
  • This periodic variation results in an ultrasonic grating acting similarly to a ruled transmission grating.

Key Formulas

  1. Grating Element Calculation:
    • D = A + B (where A = length of compression and B = length of rarefaction)
    • Wavelength: ( \lambda_A = D )
  2. Diffraction Condition:
    • ( d \sin \theta = n \lambda_L )
    • Substitute: ( \lambda_A \sin \theta = n \lambda_L )
    • Rearranged: ( \lambda_A = \frac{n \lambda_L}{\sin \theta} )
  3. Velocity of Ultrasonic Wave:
    • ( V_A = \nu_A \lambda_A )
    • Where ( \nu_A ) is the frequency of the ultrasonic wave.

Experimental Arrangement

  • Setup:
    • Rectangular liquid tank (filled with white kerosene)
    • Piezoelectric crystal attached to the tank wall
    • RF oscillator connected to the crystal
    • Sodium vapor lamp for light source, collimator, and telescope for measurements
  • Procedure:
    1. Prepare the liquid tank and immerse the piezoelectric crystal.
    2. Connect the RF oscillator and adjust frequency to match the crystal's natural frequency.
    3. Observe the diffraction pattern through the telescope and measure angles for various orders.

Measurement Techniques

  • Use vernier and main scales on a spectrometer to measure the angle of diffraction.
  • Calculate the wavelength and velocity using the relevant formulas.

Experimental Considerations

  • Ensure the piezoelectric crystal is parallel to the liquid tank wall.
  • Avoid reflections that could create standing wave patterns.

Applications of the Experiment

  1. Calculate the bulk modulus of the liquid:
    • Formula: ( K = \rho V_s^2 ) (where ( V_s ) is the speed of sound in the liquid)
  2. Determine the adiabatic compressibility:
    • Formula: ( \beta = \frac{1}{\rho V_s^2} )

Conclusion

  • Understanding ultrasonic waves is crucial for various scientific applications, and this experiment allows for practical measurement of their properties.
  • Thank you for watching the demonstration!