# GRE Subject Test: Physics : Waves

## 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?

Explanation:

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?

Explanation:

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).

Explanation:

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?

Explanation:

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?

Explanation:

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?