### All GRE Subject Test: Physics Resources

## Example Questions

### Example Question #32 : Gre Subject Test: Physics

A particle traveling through glass (index of refraction 1.33) emits Cherenkov radiation. Which of the following is a possible speed of the particle?

**Possible Answers:**

**Correct answer:**

Cherenkov radiation is emitted by a particle traveling faster than the phase velocity of light in that medium. Because , the phase velocity of light in the glass is:

This is the minimum velocity of a particle to be emitting Cherenkov radiation in glass. This eliminates all answers except * *and *. *The latter is impossible because it is greater than the speed of light in a vacuum, therefore the answer is *.*

### Example Question #1 : Electromagnetics, Waves, And Optics

A monochromatic beam of light travels through a material with a phase velocity of . What is the refractive index of the material?

**Possible Answers:**

**Correct answer:**

The phase velocity of light through a medium with refractive index is given by:

Solving this for and substituting our given value of _{:}

### Example Question #1 : Interference

A double slit experiment is set up with the following parameters: two slits are a separated by a distance . A beam of light with wavelength shines through the two slits, and is projected onto a screen a distance from the slits. What is the distance on the screen between the central band and the next band on either side? (This distance is marked '' on the figure).

**Possible Answers:**

**Correct answer:**

The condition for constructive interference with double slit diffraction is given by:

Where is 0, 1, 2, ...

Solving for the angle and using the small angle approximation, we get;

The distance in the diagram can be related to the other quantities by simple geometry:

Again, with the help of the small angle approximation. Setting the two thetas equal to each other and solving for , we get:

For the central band, , so the position is also zero. The next band, , yields a distance of:

### Example Question #1 : Waves

Two waves with frequencies: are combined. What is the frequency of the resulting beat?

**Possible Answers:**

**Correct answer:**

The beat from two combined sound waves is:

### Example Question #1 : Electromagnetics, Waves, And Optics

A beam of light, with wavelength , is normally incident on a transmission diffraction grating. With respect to the incident beam, the first order diffraction maximum occurs at an angle of . What is the number of slits per centimeter on the grating?

**Possible Answers:**

**Correct answer:**

The equation describing maxima of a diffraction grating is:

Where d is the separation of slits, which can also be expressed as:

Substituting d into the first equation and making the small angle approximation, one can solve for (lines per length):

Note that the angle had to be converted from degrees to radians. Finally, the question asks for lines per centimeter, not meter, so the answer becomes .

### Example Question #1 : Electromagnetics, Waves, And Optics

A car's horn has a frequency of . As the car drives away from you, you hear the horn at a frequency of . What is the speed of the car?

**Possible Answers:**

**Correct answer:**

The equation for the Doppler effect with frequency for a moving source is given by:

Where is the speed of sound, is the speed of the source, is the stationary frequency and * *is the Doppler frequency. Substituting the known values and solving gives us the speed of the car.

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