The important concept being tested in this question is the Doppler effect. When a source of sound waves (or any other wave) is emitted from a source and is moving relative to some observer, the actual frequency of the wave will be different for the observer.

For starters, we'll need to use the Doppler equation.

The trickiest part about this question is to decide whether to add or subtract in both the numerator and denominator. To find the right sign orientation, it's helpful to do a quick thought experiment. Imagine that only one of them is moving and the other is stationary. Decide how that will affect the observed frequency; will it increase it or decrease it? Then repeat for the other one.

First, let's consider the detector (aka observer). We're told that car B, the detector, is traveling ahead of car A and also in the same direction. This means that car B is driving away from car A. So in this situation, is the frequency that car B hears expected to increase or decrease? The answer is that it will decrease. Since car B is traveling away from car A, each successive wave will take longer to reach car B. Hence, we will use subtraction in the numerator because that will make the observed frequency smaller.

Now let's apply this same logic to the denominator, which deals with the source of the sound waves. We know that car A is traveling in the same direction as car B and is behind. This means that car A is traveling toward car B. So from this perspective, each successive wave is expected to get closer together, thus making the time between each wave smaller and the frequency bigger. In the denominator, will adding or subtracting make the observed frequency bigger? The answer is subtraction. By making a smaller number in the denominator, the entire fraction becomes larger.

Keeping this information in mind, we'll need to use subtraction in both the numerator and denominator. Once we plug in the values given in the question stem, we have everything we need to solve for the answer.

A conductor is defined as a object free to move charges. In particular, valence electrons, which are the outer most electron in each atom and the most free to move, travel inside the conductor until the net electric field inside the conductor is zero. These electrons will move until this condition has been met. Because of the presents of charged particles at the surface and the condition that they are no longer moving, any electric field at the surface must be perpendicular to that surface.

Because of the principles of superposition, each electric force that acts from the charges at the corners on to the charge at the center can be broken into components. Since all the charges are positive, all the forces will be repulsive. The forces acting from the top left and bottom right corners will cancel, leaving only the repulsive force coming from the bottom left corner.

Ohm's law is .

In this case, and .

Solving for the resistance, , we get:

Substitute known values and solve for the unknown resistance:

So this is all about the magnetic field strength around a current carrying wire.

The equation for this is:

But you must use Ohm's Law in order to find the current in the wire.

Since the wire has of resistance and the voltage through the wire is , that means the current in the wire is .

Being sure to change into , plug everything in and get the answer, which is

The important concept being tested in this question is the Doppler effect. When a source of sound waves (or any other wave) is emitted from a source and is moving relative to some observer, the actual frequency of the wave will be different for the observer.

For starters, we'll need to use the Doppler equation.

The trickiest part about this question is to decide whether to add or subtract in both the numerator and denominator. To find the right sign orientation, it's helpful to do a quick thought experiment. Imagine that only one of them is moving and the other is stationary. Decide how that will affect the observed frequency; will it increase it or decrease it? Then repeat for the other one.

First, let's consider the detector (aka observer). We're told that car B, the detector, is traveling ahead of car A and also in the same direction. This means that car B is driving away from car A. So in this situation, is the frequency that car B hears expected to increase or decrease? The answer is that it will decrease. Since car B is traveling away from car A, each successive wave will take longer to reach car B. Hence, we will use subtraction in the numerator because that will make the observed frequency smaller.

Now let's apply this same logic to the denominator, which deals with the source of the sound waves. We know that car A is traveling in the same direction as car B and is behind. This means that car A is traveling toward car B. So from this perspective, each successive wave is expected to get closer together, thus making the time between each wave smaller and the frequency bigger. In the denominator, will adding or subtracting make the observed frequency bigger? The answer is subtraction. By making a smaller number in the denominator, the entire fraction becomes larger.

Keeping this information in mind, we'll need to use subtraction in both the numerator and denominator. Once we plug in the values given in the question stem, we have everything we need to solve for the answer.

In order to answer this question, it's important to understand the factors that determine the magnetic force experienced by a charge. We can begin by writing out the equation for magnetic force.

As shown in the above equation, the magnetic force is directly proportional to the particle's charge, its velocity, and the strength of the magnetic field itself. But, for the purposes of the this question, the most important factor is the angle of the particle's velocity with respect to the magnetic field.

Notice that if theta is equal to zero, then the sine of theta will be equal to zero as well. This, in turn, will cause the magnetic force to also be zero. This is also true if we were to define theta as .

Since the particle is moving in a direction that is parallel to the magnetic field lines but in the opposite direction, we have a situation in which theta is equal to . This means that the magnetic force on the particle is zero. As a result, the particle will continue to move through the magnetic field without changing its direction.

In order to answer this question, it's important to understand the factors that determine the magnetic force experienced by a charge. We can begin by writing out the equation for magnetic force.

As shown in the above equation, the magnetic force is directly proportional to the particle's charge, its velocity, and the strength of the magnetic field itself. But, for the purposes of the this question, the most important factor is the angle of the particle's velocity with respect to the magnetic field.

Notice that if theta is equal to zero, then the sine of theta will be equal to zero as well. This, in turn, will cause the magnetic force to also be zero. This is also true if we were to define theta as .

Since the particle is moving in a direction that is parallel to the magnetic field lines but in the opposite direction, we have a situation in which theta is equal to . This means that the magnetic force on the particle is zero. As a result, the particle will continue to move through the magnetic field without changing its direction.

For this question, we're given the definition of near point. We're told what the near point is in the average person, and also the near point for a certain person who can't see well and needs glasses. We're asked to find the refractive power of a lens that will bring this individual's near point to the average, healthy value.

As was stated in the question stem, the near point is the closest distance of an object from the eye where that object can still be seen clearly. In the question, we're told that the normal value for this is . Moreover, a person with a near point of means that the object will need to be twice as far away, and no closer, to be seen clearly. Thus, in order to correct for this, a lens will be needed.

The idea is to be able to make the individual see things clearly when objects are located away. To accomplish this, a lens will need to diffract the light coming from an object away. This diffracted light will then need to form an image away, which is where this particular individual's near point is.

With this information in hand, we can use the lens-makers equation to solve for the refractive power of the lens.

We know that the object will be located a distance of away. Moreover, the image will need to form at a distance of away. However, since the image is forming on the same side of the lens that the object is located, the image will be virtual. Thus, the value used in the equation will be .

Also, remember that to find refractive power, we'll need to have our units be in meters.

Furthermore, recall that refractive power is equal to the inverse of focal length.

Hence, the power of the refractive lens will need to be diopters to correct this person's near point.

For this question, we're told that a standing wave is contained within a pipe closed at both ends. We're also given the wavelength for the fifth harmonic, and are asked to find the length of the pipe.

The first step to solve this problem is to use the equation for a pipe closed at both ends.

Since we're told which harmonic the wave is on, as well as its wavelength, we have everything we need to solve for the length of the pipe.