GRE Subject Test: Physics : Interference

Study concepts, example questions & explanations for GRE Subject Test: Physics

varsity tutors app store varsity tutors android store

All GRE Subject Test: Physics Resources

33 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Interference

A double slit experiment is set up with the following parameters: two slits are a separated by a distance \(\displaystyle d\). A beam of light with wavelength \(\displaystyle \lambda\) shines through the two slits, and is projected onto a screen a distance \(\displaystyle L\) 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 '\(\displaystyle x\)' on the figure).

Slit

Possible Answers:

\(\displaystyle x=\frac{2L\lambda}{d}\)

\(\displaystyle x=\frac{L^2\lambda}{d^2}\)

\(\displaystyle x=\frac{L\lambda}{d}\)

\(\displaystyle x=\frac{L^2\lambda}{2d^2}\)

\(\displaystyle x=\frac{2L^2\lambda}{d^2}\)

Correct answer:

\(\displaystyle x=\frac{L\lambda}{d}\)

Explanation:

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

\(\displaystyle d\sin(\theta)=m\lambda\)

Where \(\displaystyle m\) is 0, 1, 2, ...

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

\(\displaystyle \sin(\theta)=\frac{m\lambda}{d}\approx \theta\)

The distance \(\displaystyle x\) in the diagram can be related to the other quantities by simple geometry:

\(\displaystyle \tan (\theta)=\frac{x}{L}\approx \theta\)

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

\(\displaystyle x=\frac{Lm\lambda}{d}\)

For the central band, \(\displaystyle m=0\), so the \(\displaystyle x\) position is also zero. The next band, \(\displaystyle m=1\), yields a distance of:

\(\displaystyle x=\frac{L\lambda}{d}\)

Example Question #1 : Interference

Two waves with frequencies: \(\displaystyle f_1=6 \textup{ MHz}, \ f_2=2 \textup{ MHz}\) are combined. What is the frequency of the resulting beat?

Possible Answers:

\(\displaystyle 4\textup{ MHz}\)

\(\displaystyle 2\sqrt{10} \textup{ MHz}\)

\(\displaystyle 8 \textup{ MHz}\)

\(\displaystyle 12\: \textup{MHz}\)

\(\displaystyle 3 \textup{ MHz}\)

Correct answer:

\(\displaystyle 4\textup{ MHz}\)

Explanation:

The beat from two combined sound waves is:

\(\displaystyle f_{beat}=|f_1-f_2|\)

\(\displaystyle f_{beat}=|6000-2000|=4\textup{ MHz}\)

All GRE Subject Test: Physics Resources

33 Practice Tests Question of the Day Flashcards Learn by Concept
Learning Tools by Varsity Tutors