Experiment: Wave Speeds

Experiment: Wave Speeds

Try this investigation of the effect of the medium on wave speeds. OBJECTIVES Make quantitative observations and measurements at the appropriate level of precision. Analyze, evaluate and predict trends from data. Communicate conclusions for peer review.

These supplies are needed: Slinky® stopwatch or sweep second hand meter stick. Follow these directions and answer the question. On the floor, or a large flat surface, fix one end of the Slinky® and extend it approximately 5 meters (Note: this is for an average full size Slinky® ). Generate a pulse by making a quick wave with the free end of the Slinky®. You will use the stopwatch to time how long it takes the wave to travel to the far end and back. Repeat this several times to obtain an average. Extend the Slinky® by about 1 additional meter (you still want to be able to make a wave). Repeat Step 2. Extend the Slinky® by about 1 more additional meter (you still want to be able to make a wave). Repeat Step 2. Calculate the velocities, using d/t. Make sure you accurately measure exactly how far you stretched your slinky for each wave. Complete the lab and answer the following questions.

Why does stretching the slinky change the density of the medium carrying the pulse? How did the different stretches (densities) affect the velocity of the pulse?

Sample Paper For Above instruction

Analysis of Wave Speeds in a Slinky: Effects of Medium Density

Understanding the influence of medium properties on wave propagation is fundamental in physics, particularly in the study of mechanical waves such as those in a Slinky. This investigation explores how varying the length—and consequently the density—of a Slinky affects wave speed, thereby providing practical insight into the physical principles governing wave motion.

The experiment involved creating pulses in a Slinky extended over varying lengths—5 meters, approximately 6 meters, and approximately 7 meters—and measuring the time taken for each wave to travel to the end and back. By timing these pulses with a stopwatch and calculating the velocities, the relationship between the medium's properties and wave behavior was examined.

Impact of Stretching on Medium Density

Stretching the Slinky increases the length of the medium, which directly influences the linear density of the material. In the context of wave physics, the linear density (mass per unit length) is a critical factor—an increase in length while maintaining the same mass results in a lower density, whereas a decrease in length results in a higher density. Since the Slinky is stretched to vary the length, it effectively modifies the mass distribution along its length, thereby changing its density.

According to the wave equation, the speed of a wave (v) on a medium such as a string or Slinky is given by:

v = √(T/μ)

where T is the tension in the medium and μ is the linear mass density. As μ decreases with increased stretching (longer length for the same mass), the wave speed should increase assuming tension remains constant. Conversely, reducing the length (thereby increasing density) should decrease wave speed.

Effects of Different Stretches on Wave Velocity

The experimental data demonstrated that as the Slinky was extended further, the wave speeds increased. This confirms the theoretical expectation based on the wave equation. With longer extensions, the linear density (μ) decreases because the same mass is distributed over a greater length, reducing inertia and allowing the wave to travel faster.

Furthermore, tension in the Slinky remained approximately constant during the experiment, as the string was held steady during pulse generation. Therefore, the primary factor affecting wave speed was the linear density. The observed increase in wave speed with greater extension aligns with the equation v = √(T/μ), as a lower μ results in a higher v.

Conclusion

This investigation illustrates the direct relationship between the physical properties of a medium and the speed of wave propagation. Specifically, reducing the linear density by extending the Slinky enhances wave velocity, highlighting the importance of medium density in wave dynamics. These findings have broader implications in fields such as acoustics, materials science, and seismic studies, where understanding how medium properties influence wave behavior is essential for interpretation and application.

Future studies could explore the effect of varying tension levels or employing different materials to observe their impact on wave speed, further enriching the understanding of wave-medium interactions.

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