Superposition and Interference — Practice Quiz
A Physics cheat sheet for Superposition and Interference — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.
Formulas & key concepts
Diffraction (Single Slit): Angle \(\theta\) to first minimum for a slit of width \(D\).
Diffraction (Circular Aperture): Angle \(\theta\) to first minimum for a circular opening of diameter \(D\).
Transverse Standing Waves (String fixed at both ends) / Longitudinal Standing Waves (Tube open at both ends): Natural frequencies \(f_n\).
Where: \(n = 1, 2, 3, \dots\)
Longitudinal Standing Waves (Tube open at one end): Natural frequencies \(f_n\).
Where: \(n = 1, 3, 5, \dots\) (odd integers only)
Practice quiz
A laser with wavelength $632.8 \text{ nm}$ shines through a single slit of width $0.05 \text{ mm}$. What is the angle, in radians, to the first diffraction minimum?
- A) $0.0127 \text{ rad}$
- B) $0.0063 \text{ rad}$
- C) $0.0253 \text{ rad}$
- D) $0.0032 \text{ rad}$
Answer: A) $0.0127 \text{ rad}$
A telescope has an objective lens with a diameter of $10 \text{ cm}$. If it observes light with a wavelength of $550 \text{ nm}$, what is the angular radius of the first Airy disk minimum?
- A) $6.71 \times 10^{-6} \text{ rad}$
- B) $5.50 \times 10^{-6} \text{ rad}$
- C) $1.34 \times 10^{-5} \text{ rad}$
- D) $1.10 \times 10^{-5} \text{ rad}$
Answer: A) $6.71 \times 10^{-6} \text{ rad}$
An organ pipe, open at both ends, has a length of $2.4 \text{ m}$. If the speed of sound in air is $343 \text{ m/s}$, what is the frequency of its fundamental harmonic?
- A) $71.5 \text{ Hz}$
- B) $143.0 \text{ Hz}$
- C) $35.7 \text{ Hz}$
- D) $214.5 \text{ Hz}$
Answer: A) $71.5 \text{ Hz}$
A tube, open at one end and closed at the other, has a length of $0.85 \text{ m}$. If the speed of sound is $340 \text{ m/s}$, what is the frequency of its third harmonic?
- A) $100 \text{ Hz}$
- B) $200 \text{ Hz}$
- C) $300 \text{ Hz}$
- D) $400 \text{ Hz}$
Answer: C) $300 \text{ Hz}$
If the width of a single slit is decreased, what happens to the angular width of the central maximum in its diffraction pattern?
- A) It increases.
- B) It decreases.
- C) It remains the same.
- D) It depends on the wavelength of light.
Answer: A) It increases.
For the same wavelength of light and the same physical dimension $D$ (slit width or aperture diameter), how does the angular spread of the first minimum for a circular aperture compare to that of a single slit?
- A) The circular aperture has a wider angular spread.
- B) The single slit has a wider angular spread.
- C) They have the same angular spread.
- D) The comparison depends on the intensity of the light.
Answer: A) The circular aperture has a wider angular spread.
Consider two tubes of the same length $L$ and filled with the same gas (so same speed of sound $v$). Tube A is open at both ends, and Tube B is open at one end and closed at the other. How does the fundamental frequency of Tube A compare to that of Tube B?
- A) The fundamental frequency of Tube A is twice that of Tube B.
- B) The fundamental frequency of Tube A is half that of Tube B.
- C) The fundamental frequency of Tube A is equal to that of Tube B.
- D) The fundamental frequency of Tube A is four times that of Tube B.
Answer: A) The fundamental frequency of Tube A is twice that of Tube B.
A string fixed at both ends has a length of $0.75 \text{ m}$. If the wave speed on the string is $150 \text{ m/s}$, and it is vibrating at a frequency of $300 \text{ Hz}$, what harmonic is it vibrating in?
- A) First harmonic
- B) Second harmonic
- C) Third harmonic
- D) Fourth harmonic
Answer: C) Third harmonic
An astronomer is observing a distant star through a circular telescope aperture. To determine the minimum angular separation resolvable, which formula should be used?
- A) $\sin \theta = \frac{\lambda}{D}$
- B) $\sin \theta = 1.22 \frac{\lambda}{D}$
- C) $f_n = n (\frac{v}{2L})$
- D) $f_n = n (\frac{v}{4L})$
Answer: B) $\sin \theta = 1.22 \frac{\lambda}{D}$
A musical instrument produces sound by vibrating a column of air that is open at one end and closed at the other. Which of the following describes the possible natural frequencies of this instrument?
- A) All integer multiples of the fundamental frequency.
- B) Only odd integer multiples of the fundamental frequency.
- C) Only even integer multiples of the fundamental frequency.
- D) Frequencies that are independent of the length of the air column.
Answer: B) Only odd integer multiples of the fundamental frequency.
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