AP Physics Physics: Waves & Optics 3 — Questions and Answers
Question 1: A string fixed at both ends vibrates in its third harmonic. If the string length is 0.9 m, what is the wavelength of the standing wave?
- 0.3 m
- 0.6 m (Correct answer)
- 0.9 m
- 1.8 m
Correct answer: 0.6 m
In the nth harmonic, λ = 2L/n = 2(0.9)/3 = 0.6 m.
Question 2: Light of wavelength 600 nm passes through a single slit of width 0.1 mm. What is the angle to the first diffraction minimum?
- 0.17°
- 0.34° (Correct answer)
- 0.60°
- 1.20°
Correct answer: 0.34°
sin θ = λ/a = 600×10⁻⁹/10⁻⁴ = 6×10⁻³, so θ ≈ 0.34°.
Question 3: A convex mirror has a focal length of −20 cm. An object is placed 30 cm in front of it. What is the image distance?
- −12 cm (Correct answer)
- 12 cm
- −60 cm
- 60 cm
Correct answer: −12 cm
Using 1/v = 1/f − 1/u = 1/(−20) − 1/30 = −0.0833, so v ≈ −12 cm.
Question 4: Two sound waves of frequencies 440 Hz and 444 Hz are played simultaneously. How many beats per second are heard?
- 2
- 4 (Correct answer)
- 440
- 884
Correct answer: 4
Beat frequency = |f1 − f2| = |440 − 444| = 4 beats per second.
Question 5: A transverse wave has amplitude A = 0.02 m and angular frequency ω = 10 rad/s. What is the maximum transverse speed of a particle on the string?
- 0.002 m/s
- 0.02 m/s
- 0.2 m/s (Correct answer)
- 2 m/s
Correct answer: 0.2 m/s
Maximum transverse speed vmax = Aω = 0.02 × 10 = 0.2 m/s.
Question 6: Which color of visible light has the highest frequency?
- Red
- Green
- Yellow
- Violet (Correct answer)
Correct answer: Violet
Violet light has the shortest wavelength (~380–420 nm) and therefore the highest frequency in the visible spectrum.
Question 7: A plane wave strikes a small circular obstacle. According to Huygens' principle, what appears directly behind the obstacle?
- A region of complete darkness
- A bright spot at the center of the shadow (Correct answer)
- A series of bright and dark fringes only at the edges
- No diffraction pattern
Correct answer: A bright spot at the center of the shadow
Each point on the wavefront acts as a secondary source; waves diffract around the obstacle and constructively interfere at the center, creating a bright Poisson spot.
AP Physics Physics: Waves & Optics 3
A string fixed at both ends vibrates in its third harmonic.
If the string length is 0.9 m, what is the wavelength of the standing wave?