A fiber-optic Michelson interferometer is a device that detects changes in optical paths. In a fiber-optic interferometer, a coherent light source (usually a laser) is sent through a beam splitter that splits the light along two paths. These beams are coupled into fiber optic cables that can be arranged and manipulated more freely than mirrors. The two beams are finally recombined by a second beam splitter and superimposed on a screen. If there is a phase difference between the two waves, interference fringes will be viewed on the screen.

By observing fringe shifts, one can quantify the change in optical path difference between the two fibers using the following equation:

where m is the number of fringe shifts, x is the difference between the optical paths of the two beams, and  is the change in the optical path difference.

Experiment 1:

A student sets up a fiber-optic Michelson interferometer and heats one of the fibers with various resistors and power supplies, fans air over one of the fibers, and then bends one of the fibers. The resulting fringe shifts, as well as the change in optical path difference (OPD), are shown below.

Why is it necessary to use a second beam splitter in this setup?

A scientist is exploring the nature of energy and work in two experimental systems.

Experiment 1

She first sets up a system with a ball on an inclined plane, and calculates the potential and kinetic energies of the ball at three positions. She places the ball at position 1, stops the ball after rolling to position 2, and then again allows it to roll to position 3. The measured kinetic and potential energies are shown in the table, along with measurements of the force of friction acting on the ball.

Experiment 2

The same scientist then sets up another experiment with the same ball, again at three positions.  The ball is provided a slight push, and then allowed to roll down three levels without any additional external input of energy.

She uses the following formulae to calculate the energy levels of the ball:

Potential Energy = Mass of the Ball x Acceleration Due to Gravity x Height of the Ball

Kinetic Energy = (1/2) x Mass of the Ball x (Velocity of the Ball)²

She also measures the internal energy of the ball, a value that she defines as the amount of energy contained in the motion of the molecules that make up the matter of the ball.

A second scientist is examining this data and wants to test if introducing an electric field around the ramp in Experiment 1 changes the measured energy values. To do this, he sets up another system, identical to that in Experiment 1, but with the addition of an electric field. He compares data generated by both the original system in Experiment 1 and the new system with the electric field. Experiment 1 is now serving as what?

Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so.  

Study 1
A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.

Study 2
The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.

Assume that density of a substance is the only contributing factor to velocity of sound through that substance. If the students' hypothesis in Study 1 is correct, what might they have predicted for the velocity of sound through lead? (Assume all other values in Table 1 remained the same.)

Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so.  

Study 1
A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.

Study 2
The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.

Jackie read about this experiment and decided to recreate Study 1. She found that each of the velocities she measured are higher than those in the original experiment. What is one possible explanation for this difference?

A student is doing an experiment relating force and distance to work and work and time to power. She is given the following table:

She is also told that:

Power = Work/ Time           

Work is in Joules and Time is in seconds. Power is measured in Watts.

If the Watts of power equals the amount needed to light the light bulb attached then the bulb will be lit. If more Watts of power are present, an attached light bulb will burn brighter.

If the student were to do an experiemt with a force of 6 Newtons and a distance of 1 meter, how much work would the student be doing?

A student is doing an experiment relating force and distance to work and work and time to power. She is given the following table:

She is also told that:

Power = Work/ Time           

Work is in Joules and time is in seconds. Power is measured in Watts.

If the Watts of power equals the amount needed to light the light bulb attached then the bulb will be lit. If more Watts of power are present, an attached light bulb will burn brighter.

What is a Joule equal to according to the table?

A student is doing an experiment relating force and distance to work and work and time to power. She is given the following table:

She is also told that:

Power = Work/ Time           

Work is in Joules and time is in seconds. Power is measured in Watts.

If the Watts of power equals the amount needed to light the light bulb attached then the bulb will be lit. If more Watts of power are present, an attached light bulb will burn brighter.

If the student is trying to light a 2 Watt Bulb, which of the following experimental scenarios would work?

A student is doing an experiment relating force and distance to work and work and time to power. She is given the following table:

She is also told that:

Power = Work/ Time           

Work is in Joules and time is in seconds. Power is measured in Watts.

If the Watts of power equals the amount needed to light the light bulb attached then the bulb will be lit. If more Watts of power are present, an attached light bulb will burn brighter.

The student tried the experiment again, but this time she moved the object over a distance of 40 meters, but in a circle so she ended up in the same place. She thinks that the distance would be 0 meters because she didn't change locations, so she cannot light a bulb because no power would be created. Is this true?

A student is doing an experiment relating force and distance to work and work and time to power. She is given the following table:

She is also told that:

Power = Work/ Time           

Work is in Joules and time is in seconds. Power is measured in Watts.

If the Watts of power equals the amount needed to light the light bulb attached then the bulb will be lit. If more Watts of power are present, an attached light bulb will burn brighter.

The student repeats the experiment at home and finds out that the light bulb burns brighter if she pushes the object up an incline rather than a flat surface of the same distance in the same amount of time. What would explain this?

A physicist wishes to study the trajectory of a ball launched horizontally. She varies parameters such as the launching velocity, starting height, and mass of the ball. For each trajectory, she records the time of flight (in seconds) and horizontal displacement (in meters). She assumes air resistance is negligible.

Figure 1

Using all of the data she collects, she constructs the following table:

Table 1

Which of the following variables were controlled in Trial 2?