Waves - GRE Subject Test: Physics
Card 0 of 6
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?
A beam of light, with wavelength
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 
.
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
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
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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?
A car's horn has a frequency of
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.
The equation for the Doppler effect with frequency for a moving source is given by:
Where
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A particle traveling through glass (index of refraction 1.33) emits Cherenkov radiation. Which of the following is a possible speed of the particle?
A particle traveling through glass (index of refraction 1.33) emits Cherenkov radiation. Which of the following is a possible speed of the particle?
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 .
Cherenkov radiation is emitted by a particle traveling faster than the phase velocity of light in that medium. Because
This is the minimum velocity of a particle to be emitting Cherenkov radiation in glass. This eliminates all answers except
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A monochromatic beam of 
light travels through a material with a phase velocity of 
. What is the refractive index of the material?
A monochromatic beam of
The phase velocity of light through a medium with refractive index 
is given by:
Solving this for 
and substituting our given value of 
:
The phase velocity of light through a medium with refractive index
Solving this for
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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).
A double slit experiment is set up with the following parameters: two slits are a separated by a distance
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:
The condition for constructive interference with double slit diffraction is given by:
Where
Solving for the angle and using the small angle approximation, we get;
The distance
Again, with the help of the small angle approximation. Setting the two thetas equal to each other and solving for
For the central band,
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Two waves with frequencies: 
are combined. What is the frequency of the resulting beat?
Two waves with frequencies:
The beat from two combined sound waves is:
The beat from two combined sound waves is:
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