Exploring the Speed of Sound: A Comprehensive Laboratory Experiment with Acoustic Waves

The speed of sound, a fundamental property of acoustic waves, is the rate at which sound waves propagate through a medium. This laboratory experiment aims to measure the speed of sound in air, employing a series of tests and calculations. Understanding the speed of sound is crucial in various applications, from designing concert halls to predicting weather conditions.

Experimental Setup:

Apparatus: Set up a laboratory with a sound source, a microphone, and a timer.
Measurement Setup: Position the microphone at a known distance from the sound source, ensuring a direct line of sight.
Procedure: Generate a short burst of sound and record the time it takes for the sound wave to travel from the source to the microphone.

Calculations and Formulas:

Speed of Sound (v): Calculate the speed of sound using the formula $v = t d$ , where $d$ is the distance between the source and the microphone, and $t$ is the time taken for the sound wave to travel.

Experimental Procedure:

Initial Measurements: Conduct several trials with varying distances between the sound source and the microphone, recording the time taken for sound waves to traverse each distance.
Data Collection: Record the experimental data in a table, including the distance ( $d$ ), time ( $t$ ), and calculated speed of sound ( $v$ ) for each trial.

Results and Data Analysis:

Table of Results:
- Present the measured distances and corresponding time measurements.
- Include calculated values for the speed of sound in each trial.
Graphical Representation:
- Create a graph illustrating the relationship between distance and time, showcasing the speed of sound variations.

Discussion:

Analysis of Results: Discuss trends observed in the data, considering how changes in distance affect the time taken for sound waves to propagate.
Comparison with Theoretical Values: Compare calculated speeds of sound with theoretical values for air under standard conditions.
Sources of Error: Identify potential sources of error in the experiment, such as inaccuracies in distance measurement or variations in air temperature affecting sound speed.

Conclusion:

Summary of Findings: Summarize key findings, emphasizing the relationship between distance, time, and the speed of sound.
Significance of Results: Discuss the significance of understanding the speed of sound, considering real-world applications and implications.

Applications:

Technical Applications: Explore how knowledge of sound speed is crucial in fields like telecommunications, engineering, and environmental monitoring.
Practical Applications: Discuss everyday applications, such as the design of concert venues and the prediction of thunderstorms.

This laboratory experiment provides valuable insights into the measurement of the speed of sound, utilizing practical methods and calculations.

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The data collected and analyzed contribute to a deeper understanding of acoustics, with potential applications in various scientific and engineering disciplines.

What impact does the duration of one oscillation of sound waves emitted from a tuning fork have on the required height of the air column to achieve maximum wave amplitude, and how does it influence the measured velocity of sound?

Background and Hypothesis: The lab indicates the speed of sound as 330 m/s.

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Consequently, the expected theoretical value from this experiment aligns with 330 m/s. The equation v = f x λ and the concept of resonance, where an open-ended tube reaches resonance at ¼ of a wavelength, can be employed. By using a glass tube with a vibrating tuning fork, the wavelength is determined by finding the air column's height when maximum sound is produced. With known frequency, the speed of sound is calculated. It is predicted that higher frequencies result in a lower air column height, as the speed of sound remains constant. The inverse relationship between time for one oscillation and frequency suggests that a longer time corresponds to a greater air column length.

Variables:

Independent: Time taken for sound waves from the tuning fork to complete one oscillation. Dependent: Height of the air column needed for maximum wave amplitude.

Controlled:

Frequency of the tuning fork
Wavelength of the sound wave
Water level in the plastic barrel
Angle of the glass tube to the water surface
Glass tube's edge
Distance of the vibrating tuning fork above the glass tube's edge
Altitude of the location
Room temperature
Room pressure

Procedure:

Apparatus:

1 large plastic barrel
1 glass tube
8-12 tuning forks with various frequencies
Meter ruler (± 0.0005m)
30-centimeter ruler (±0.0005m)
Rubber bob for striking tuning forks

Method:

Fill a large plastic barrel with water up to ¾ of its capacity.
Set up a stand beside the plastic barrel.
Attach a glass tube to the stand.
Allow one person (number 1) to hold the glass tube after loosening the clamp.
Have another person (number 2) strike the tuning fork and position it 1 cm above the glass tube's edge, listening carefully.
Number 1 should instruct number 2 to raise or lower the glass tube for the loudest sound.
Once the loudest sound is achieved, secure the glass tube in place.
Place a meter stick next to the plastic barrel with flat edges for perpendicular alignment.
Use a 30-centimeter ruler to determine the water height from the table's surface along straight lines on the meter stick.
Utilize the same method to find the height of the glass tube's edge from the table surface.
Repeat steps 1-10 to gather 8-12 data points.

Additional notes for controlling variables:

Control the tuning fork frequency as it is assumed to be accurate.
Keep the sound wave wavelength constant as sound travels at a consistent speed in one location.
Maintain a constant water level in the plastic barrel, considering stand and glass tube height.
Ensure the glass tube is as perpendicular as possible to the water surface.
Use a straight-edged glass tube to eliminate edge effects.
Keep the vibrating tuning fork approximately 1 centimeter from the glass tube's edge, maintaining a constant distance.
Conduct the experiment at the same location to control for altitude variations.
Maintain a constant room temperature by completing the experiment in one period with closed windows.
Keep the room pressure constant by conducting the experiment continuously with closed windows.

Table 1: Collection of raw data: The frequency of the tuning fork that was held over the air column and the length of the air column for the maximum amplitude measured as a result.

Trial no.	Frequency of the tuning forks (Hz)	Height of the water level above the surface of the table (m) (±0.005)	Height of the edge of the glass tube above the surface of the table (m) (±0.005)
1	271.2	0.390	0.694
2	304.4	0.390	0.661
3	320.0	0.390	0.648
4	341.3	0.390	0.632
5	406.4	0.390	0.593
6	426.6	0.390	0.583
7	456.1	0.390	0.577
8	480.0	0.390	0.562
9	512.0	0.390	0.551

The objective of this experiment is to determine the speed of sound in air using a glass tube and tuning forks. The height of the air column in the glass tube is measured along with the time taken for sound waves to complete one oscillation. By analyzing these data points, the speed of sound can be calculated.

Safety Precautions:

To ensure safety during the experiment, tuning forks are struck with a rubber bob to prevent damage.

Method:

Fill a large plastic barrel with water and set up a glass tube attached to a stand.
Strike a tuning fork and position it 1 cm above the glass tube edge.
Adjust the glass tube height for the loudest sound and secure it in place.
Measure the height of the water level and the edge of the glass tube above the table.
Repeat steps 1-4 for multiple trials to gather sufficient data.

The height of the air column (h) is calculated using the formula: $h = Height of edge of glass tube - Height of water level$

For trial 1: $h = 0.694 m - 0.390 m = 0.304 m$

Uncertainty is calculated by adding uncertainties: $Uncertainty = 0.005 m + 0.005 m = \pm 0.01 m$ Final value: $0.304 m \pm 0.01 m$

Finding the Independent Variable:

The time taken for sound waves to complete one oscillation (T) is calculated using the formula $T = Frequency 1$ .

Table 3 presents the frequency values and corresponding times for one oscillation.

Graphing the Relationship:

The equation $T = 4 h / v$ is used to calculate the speed of sound. A graph is plotted with time (T) on the y-axis and height (h) on the x-axis.

Table 4 provides the data for the time taken for sound waves and corresponding heights of the glass tube.

Speed of Sound Calculation:

Three lines of fit are determined:

Line of Best Fit: Gradient $\approx 0.01198$ , Speed of sound $\approx 333.9 m/s$
Line of Maximum Fit: Gradient $\approx 0.01209$ , Speed of sound $\approx 330.9 m/s$
Line of Minimum Fit: Gradient $\approx 0.01050$ , Speed of sound $\approx 380.9 m/s$

The experiment successfully determined the speed of sound using a glass tube and tuning forks. The variations in the lines of fit emphasize the importance of accurate measurements in obtaining reliable results. The average speed of sound is calculated to be approximately $348.6 m/s$ .

This laboratory report demonstrates the step-by-step process, calculations, and analysis involved in the experiment, providing a comprehensive understanding of the methodology and results.