Lab Report

Part I: Understanding the Setup

1. Describe the equipment used for the acoustic levitation experiment.
   Equipment List:

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2. Explain how standing waves are formed between two ultrasonic transducers.

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3. Write the formula to calculate the wavelength of the standing wave based on the distance between transducers and the number of nodes.
   Formula: ______________________________________________________

4. What is the relationship between the frequency of the transducers and the speed of sound?

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Part II: Data Collection and Analysis

5. Record the number of polystyrene balls levitating at different transducer distances.

1. • Compare the experimental speed of sound with the theoretical speed at room temperature (340 m/s).

     1. Experimental speed of sound (average): ______________________ m/s

     2. Percentage error: ___________________________________________ %

Part III: Oscillation and ImageJ Analysis

7. Using ImageJ, analyze the oscillation data from the video recording. Record the time intervals between peaks of the oscillation.
   Time intervals: ______________________________________________________

8. Plot the height of the polystyrene ball as a function of time.

   • Attach your plot here: ____________________

9. Identify the damping behavior (if any) in the oscillation data.

Instructions: Complete the following tasks after performing the Acoustic Levitation experiment. Use the data collected during the lab and theoretical concepts discussed in class.

1. Describe how acoustic radiation pressure leads to the levitation of small objects. Include the formula for the force due to acoustic radiation pressure.

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2. Explain the role of air resistance in the oscillation of a levitated object. How does the drag force affect the motion of the object?

3. Using your experimental data, calculate the damping coefficient of the oscillation.

4. Based on your ImageJ analysis, provide a detailed report on the oscillation behavior of the object. Include a time vs. height graph.

5. Discuss the possible sources of error in the experiment. How would you improve the accuracy of the levitation and oscillation data?

Problem Set: AIoTs Acoustic Levitation

 Problem 1. Standing Wave and Speed of Sound Calculation:
a. A distance of 5 cm separates a pair of ultrasonic transducers operating at a frequency of 40 kHz. The system creates standing waves with nodes where objects can be levitated. If three nodes are observed, calculate the wavelength of the sound wave.
b. Using the wavelength calculated in part (a), determine the speed of sound in air at room temperature.

Problem 2. Oscillation Under Air Resistance:
An object suspended at a node is perturbed and begins oscillating in the vertical direction. The air drag acting on the object is proportional to its velocity, and the equation of motion is given by:

where b is the drag coefficient, and Fac​ is the acoustic radiation pressure. If the mass of the object is 0.5 grams, the drag coefficient b is 6×10^(-5)kg/s, and the acoustic force is 0.005 N:
a. Write the differential equation governing the velocity of the object.
b. Solve for the velocity as a function of time, assuming an initial velocity of 0.

Problem 3. Damping Ratio and Natural Frequency:
During the experiment, the oscillating object exhibits damping due to air resistance. The equation of motion can be described as:

where ζ is the damping ratio, and ω0​ is the natural frequency.
a. Derive the equation for the damping ratio ζ in terms of the experimental parameters.
b. If the natural frequency is measured to be 100 Hz and the damping ratio is 0.1, calculate the oscillation period.

Problem 4 Simulating Oscillation in Python:
Write a Python program to simulate the oscillation of the levitated object with air resistance. The object starts at rest and is perturbed by a small force. Use the parameters from your experiment to simulate the motion and generate a plot of position vs. time. Compare your simulation with the experimental results obtained from ImageJ analysis.

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format