Wave Relationships

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

Purpose:

The purpose of this lab is to investigate some of the properties and relationships associated with wave motion. The variables effecting the speed of a wave and the energy transported by a wave will be investigated.

Getting Started:

1. Log on to the student server in the usual manner
2. Open the Math/Science folder; then open the Science Apps folder; open the Physics folder.
3. Once the Physics Explorer-Waves application; chose Open... from the File menu.
4. A directory dialogue box should appear. Open the Waves folder, and then the Exploring Waves 1 Makeup file by double-clicking on its icon.
5. Click on the button at the bottom of the monitor which is titled "Stiffness and Mass."

Part 1: Properties of the Medium:

The Physics Explorer - Waves software models the motion of a wave (or a pulse) along a medium. The medium is depicted as a string of 50 masses (representing the particles of the medium) connected by springs. As a disturbance or pulse is introduced into the medium, it moves from one mass to the next. The masses, being connected to each other by springs, interact with each other in order to transmit the energy of the disturbance along the medium. The properties of the medium (and of the wave) can be set by the user using data input boxes. In the first part of this activity you will investigate the effect of two media properties (stiffness and mass) upon wave speed.

1. The stiffness or elasticity of a medium through which a wave is moving is often measured in terms of the spring constant. The higher the spring constant, the more stiff (and the less elastic) that the medium is. If the medium is stiffer (if the spring constant of the springs connecting the individual masses is increased), do you think that the pulse will travel faster or slower along the string? __________ Explain your answer.

2. Keeping the mass m = 1 kg, you will make the necessary measurements to calculate the speed for various values of the spring constant (k). The speed can be determined by measuring the distance traveled per time. There is a timer in the window on the left. This timer can be used to measure the time for the pulse to move down the medium and back. The distance down the medium is 50 meters; so down and back would be a total distance of 100 meters.

 Sping Constant, k (N/m) Distance (m) Time (s) Speed (m/s) 1 ________ ________ ________ 4 ________ ________ ________ 9 ________ ________ ________ 16 ________ ________ ________

• Describe the relation between the spring constant (k) and the speed in the the table above? Hint: look at the SQRT(k). Explain.

3. Now consider the effect of the particles' mass on the wave's speed.
• How do you think an increase in the masses of the particles of the medium will influence the wave's speed of travel?

• To check your answer, keep k = 10 N/m and measure the speed for a particle of mass 1, 4, 9, and 16 kg. Record your measurements and calculations in the table.

 Mass, m (kg) Distance (m) Time (s) Speed (m/s) 1 ________ ________ ________ 4 ________ ________ ________ 9 ________ ________ ________ 16 ________ ________ ________

• How do the results compare with your prediction?

• Describe the relationship between mass and speed as shown in the table above. That is, does speed depend on the mass, the square of mass, the square root of mass, the inverse of mass, the inverse square of mass, the inverse square root of mass, etc.?

• What happens if you change the mass as well as the spring constant by the same factor, i.e., what happens to the speed if you multiply both k and m by, say, 2? Explain your answer fully.

Part 2: Energy in the Medium:

You have seen that a wave is a disturbance which moves along a medium. The speed at which the disturbance moves along the medium is dependent upon the stiffness and mass of the particles of the medium. Another property of the disturbance is its amplitude - the maximum displacement given to the mediumas the pulse passes through it. In the second part of this activity, you will investigate the factors which effect the amplitude of the pulse.

1. Click on the "Energy" button. The Energy Transfer window shows three bar graphs and numerical outputs giving the kinetic energy of particles P10, P25, and P40.

• Run the simulation and watch the bar graph for particle 10. When the pulse is between P10 and P25, click on the STOP tool (see diagram at right).

• Explain the motion of the bar graph for particle 10 during this simulation.

• Predict the motion of the bar graphs for P25 and P40 as the pulse passes through them.

• At what points is the kinetic energy of P10 a maximum as the pulse is passing through?

• At what points is the kinetic energy of P10 a minimum as the pulse is passing through?

1. Click on the CONTINUE tool (see diagram at right) to check your predictions. Stop the experiment after the pulse has reached the end of the medium.
• Where did the kinetic energy of P10 go after the pulse passes completely through it?

• When the pulse moved from P10 to P25 and P40, what else was transported?

2. In real media, friction forces are always present, causing energy dissipation. The variable determining how fast energy will be dissipated in a medium is its damping coefficient.

Increase the value of the damping coefficient to 0.2 and run the simulation again.

• Compared to the case of no damping, what differences do you see in the behavior of the pulse and in the bar graphs?

• What similarities are there between this most recent simulation and the simulation for the undamed motion?

3. The amount of energy transported by a pulse is related to the amplitude of the pulse.
• Predict the effect of changing amplitude on the amount of energy transported by a pulse.

The user input box titled "Amplitude" allows you to modify the amplitude of the pulse moving along the medium. Reset the damping coefficient to 0 and systematically vary the amplitude from 10 meters to 50 meters. Record values of the maximum energy of P10 in the table below.

 Amplitude (m) Max. Energy of P10 (J) 10 _____________ 20 _____________ 30 _____________ 40 _____________ 50 _____________

• How do the results compare with your prediction?

• Describe the relationship between the energy transported and amplitude as shown in the table above. That is, does energy ttransported by a pulse depend on the amplitude, the square of amplitude, the square root of amplitude, the inverse of amplitude, the inverse square of amplitude, the inverse square root of amplitude, etc.?

Conclusion:

In a well-written paragraph, summaraize the factors which effect the speed of a pulse and the amount of energy transported by a pulse. Be complete (explaining the mathematical dependence of mass and energy on the various factors which effect it) and clear. Do a bang-up job!