# Exploring Waves

 Materials: Computer and School Network Time Allotment: 3 Class Days

### Introduction:

In this activity, the motion of a transverse wave on an elastic string will be investigated by using a computer simulation. The computer program simulates a string made of 50 masses connected by invisible springs. In the simulation, each mass is representative of a particle in the string. Thus, the motion of the transverse wave in a medium such as a slinky or a rope can be studied using this simulation. A simplified diagram of a section of the string with the springs displayed is shown in the top picture of the diagram. The bottom picture depicts the same string with a pulse traveling along it.

### Getting Started:

• Open the Physics Explorer application in the usual manner; open the Waves model.
• Select Open... from the File menu; navigate to the Physics 163 folder; open the Waves folder. Open the Exploring Waves - Part 1 file by double-clicking on its icon.

### EXPLORATION 1: The Nature of a Transverse Wave

Observe the window titled Wave Nature. Be sure that the Particles Not Connected option is selected. Run the simulation by clicking on the GO Tool (see diagram at right). Watch the transverse pulse as it moves down the string.

Click on the STOP Tool (see diagram at right) before the wave reaches the end. Click on the GO Tool to repeat the simulation.

• Describe the motion that you see. In which direction do the individual particles of the medium move?

### EXPLORATION 2: What Does a Wave Do?

Click in the window titled Navigation Window to make it active. Horizontal lines will appear across the top of the window's title bar. Click on the button titled Energy Transport. A new window will appear in the upper left corner of the monitor. This window is titled Energy Transport. Observe the marks in the model window above Particle #10, #25, and #40. These marks indicate that there are detectors placed upon these particles in order to measure certain quantities during the simulation. Click on the GO Tool to run the simulation. As the simulation is running, observe the bar graphs and numerical output displays in the Energy Transport window. Repeat the simulation for as many times as necessary in order to answer the following questions.

1. The bar graphs and the numerical output displays indicate the total quantity of energy detected by the detectors at Particle #10, #25, and #40. Describe the change in energy of Particle #10 as the disturbance or pulse passes through this particle of the medium.

2. Describe what happens to the energy of a pulse as time progresses. Use the model with the accompanying data in your description.

3. Must the individual particles of the medium be displaced in order for the wave to transport energy from one end of the medium the other? Explain.

4. Curly and Moe are conducting a wave experiment using a slinky. Curly introduces a disturbance into the slinky by giving it a quick back and forth jerk. Moe places his cheek (facial) at the opposite end of the slinky. Using the terminology of this unit, describe what Moe experiences as the pulse reaches the other end of the slinky.

5. Textbooks often describe a wave as "an energy transport phenomenon". Explain this statement.

### Introduction:

In the first and second explorations, it was learned that a transverse wave is an energy-tranport phenomenon in which the particles of the medium move perpendicular to the direction in which the wave travels. In this exploration, variables which effect the speed of a wave will be studied. Five variables will be investigated: the mass of particles in the medium, the "spring constant" (or amount of "springyness") of the medium, the damping coefficient of (or amount of friction in) the medium, the frequency of the wave, and the amplitude of the wave. The first three variables represent properties of the medium itself. The last two variables represent properties of the wave.

Specific questions which should be explored include: Does the speed of a wave depend upon the frequency or the amplitude? Does changing the medium through which a wave travels (without changing the frequency or amplitude) effect the speed of the wave?

• Open the folder titled Physics 163 by double-clicking on its folder icon.
• Open the folder titled Waves by double-clicking on its icon.
• Open the lab titled Wavelength-Frequency-Speed by double-clicking on its icon.

### Procedure:

The Input Variables window at the bottom of the monitor should appear as follows.

Click on the GO Tool to run the simulation. As the wave travels past Particle #10, the timer is reset. As the wave reaches Particle #30, the simulation is stopped and the time elapsed as the wave travels between Particle #10 and Particle #30 is displayed in a message window. The speed of the wave is the distance traveled per time. That is,

Speed = 20 units/time

Any variable can be changed by double-clicking on its value and typing in another value. Run the simulation for a variety of Mass, K, Damping Coefficient, Amplitude, and Frequency values in order to determine which variables will effect the speed of a wave. Each time a value is changed, the GO Tool will have to be clicked in order to run the simulation with the new variable value. Repeat the simulation as many times as necessary in order to answer the following questions.

### Post-Lab Questions:

1. Does a change in the frequency of a wave result in a significant and convincing change in the speed of the wave?

2. Does a change in the amplitude of a wave result in a significant and convincing change in the speed of the wave?

3. Does changing the properties of a medium result in a significant and convincing change in the speed of the wave? __________ If so, then what properties induce a change in a wave's speed?

4. Textbooks often state that "wave speed depends on the medium" and not upon the properties of the wave itself. Explain this statement.

### Extensions:

1. If a sound wave travels from air into water, does the speed of the sound wave change? Explain.

2. Is the speed of a sound wave in air dependent upon the temperature of the air? _______ ... the density of the air? _______ ... the frequency of the sound wave? _______ ... the intensity of the sound wave? _______ Support your answers with good logical reasoning.

### Conclusion:

Write an organized paragraph summarizing the principles which you have learned in this lab. Do a bang-up job!