Double-Slit Interference and Diffraction Gratings AP Physics 2 MCQ – Exam Style Questions etc.
Double-Slit Interference and Diffraction Gratings AP Physics 2 MCQ
Unit 14: Waves , Sound , and Physical Optics
Weightage : 15–18%
Exam Style Practice Questions ,Double-Slit Interference and Diffraction Gratings AP Physics 2 MCQ
Question
Coherent monochromatic light of wavelength λ in air is incident on two narrow slits, the centers of which are 2.0 mm apart, as shown above. The interference pattern observed on a screen 5.0 m away is represented in
the figure by the graph of light intensity I as a function of position x on the screen.
a. What property of light does this interference experiment demonstrate?
b. At point P in the diagram, there is a minimum in the interference pattern. Determine the path difference between the light arriving at this point from the two slits.
c. Determine the wavelength, λ, of the light.
d. Briefly and qualitatively describe how the interference pattern would change under each of the following separate modifications and explain your reasoning.
i. The experiment is performed in water, which has an index of refraction greater than 1.
ii. One of the slits is covered.
iii. The slits are moved farther apart.
Answer/Explanation
Ans:
All portions of this problem have been done in the physical optics section besides d-i highlighted in bold,
d) i Based on n1 λ1 = n2 λ2 … nair λair = nwater λwater. The λwater is less in comparison to the air. So the λ has been decreased. In the equation m λ = d x / L, for decreased λ there will be decreased x, which means the location of spots is smaller, compressing the pattern.
Question
Your teacher gives you two speakers that are in phase and are emitting the same frequency of sound, which is between 5000 and 10,000 Hz. She asks you to determine this frequency more precisely. She does not have a frequency or wavelength meter in the lab, so she asks you to design an interference experiment to determine the frequency. The speed of sound is 340 m/s at the temperature of the lab room.
(a) From the list below, select the additional equipment you will need to do your experiment by checking the line next to each item.
___ Speaker stand ___ Meterstick ___ Ruler ___Tape measure
___ Stopwatch ___ Sound-level meter
(b) Draw a labeled diagram of the experimental setup that you would use. On the diagram, use symbols to identify what measurements you will need to make.
(c) Briefly outline the procedure that you would use to make the needed measurements, including how you would use each piece of equipment you checked in (a).
(d) Using equations, show explicitly how you would use your measurements to calculate the frequency of the sound produced by the speakers.
(e) If the frequency is decreased, describe how this would affect your measurements.
c) Set the speakers a fixed distance d apart, pointing perpendicular to the line along which d is measured. Determine a line parallel to the speaker line and a distance L away. Use the sound meter to locate the maxima of the interference pattern along this line. Record the locations of these, y values, maxima along the line. d) With the values obtained above, plug into m λ = d x / L, with m = 1 for the first maxima and other variables as defined above to determine the λ of the sound. Assuming angle θ is small. It not, determine theta and use m λ = d sin θ. Then, with the λ plug into v = f λ with v as speed of sound to determine f. e) Decreasing frequency results in increasing wavelength for constant velocity. Based on mλ = d x / L, larger wavelength means a larger x value and thus the distance between successive maxima will increase.
Answer/Explanation
Ans:
This is basically the same as 2005B4 but with sound.
a) Meterstick, tape measure, sound level meter
b) 
c) Set the speakers a fixed distance d apart, pointing perpendicular to the line along which d is measured. Determine a line parallel to the speaker line and a distance L away. Use the sound meter to locate the maxima of the interference pattern along this line. Record the locations of these, y values, maxima along the line.
d) With the values obtained above, plug into m λ = d x / L, with m = 1 for the first maxima and other variables as defined above to determine the λ of the sound. Assuming angle θ is small. It not, determine theta and use m λ = d sin θ. Then, with the λ plug into v = f λ with v as speed of sound to determine f.
e) Decreasing frequency results in increasing wavelength for constant velocity. Based on mλ = d x / L, larger wavelength means a larger x value and thus the distance between successive maxima will increase.