Principle of Superposition

Q1. Which of the following correctly states the principle of superposition?

Multiple Choice · 1 point

• · When two waves meet, the faster wave cancels the slower wave
• · When two waves meet at a point, the resultant displacement is the vector sum of the individual displacements
• · When two waves meet, they reflect off each other
• · When two waves meet, the resultant displacement equals the product of the individual displacements

Q2. Two waves meet at a point. Wave A has a displacement of +5 mm and wave B has a displacement of +3 mm at that instant. What is the resultant displacement?

Multiple Choice · 1 point

• · +2 mm
• · +15 mm
• · +8 mm
• · −8 mm

Q3. Two waves meet at a point. Wave A has a displacement of +6 mm and wave B has a displacement of −6 mm at that instant. What is the resultant displacement?

Multiple Choice · 1 point

• · +12 mm
• · +6 mm
• · −6 mm
• · 0 mm

Q4. Constructive interference occurs when two waves meet with a phase difference of:

Multiple Choice · 1 point

• · π radians
• · π/2 radians
• · 0 or 2π radians
• · 3π/2 radians

Q5. Destructive interference occurs when two waves of equal amplitude meet with a phase difference of:

Multiple Choice · 1 point

• · 0 radians
• · π radians
• · 2π radians
• · π/4 radians

Q6. Two coherent waves of equal amplitude interfere constructively. If each wave has an amplitude of 4 μm, what is the amplitude of the resultant wave?

Multiple Choice · 1 point

• · 0 μm
• · 4 μm
• · 8 μm
• · 16 μm

Q7. A path difference of one full wavelength (λ) between two coherent waves produces:

Multiple Choice · 1 point

• · Destructive interference, as the waves are in antiphase
• · Constructive interference, as the waves are in phase
• · Partial interference, as the path difference is too large
• · No interference, as the waves have travelled different distances

Q8. Which of the following path differences produces destructive interference for two coherent waves of wavelength λ?

Multiple Choice · 1 point

• · 0
• · λ
• · 2λ
• · λ/2

Q9. Two coherent waves of wavelength 600 nm meet with a path difference of 1800 nm. What type of interference occurs?

Multiple Choice · 1 point

• · Destructive interference, path difference = 2.5λ
• · Constructive interference, path difference = 3λ
• · Destructive interference, path difference = 3λ
• · No interference occurs at this path difference

Q10. Which of the following correctly links path difference to phase difference for waves of wavelength λ?

Multiple Choice · 1 point

• · Phase difference (rad) = (λ / 2π) × path difference
• · Phase difference (rad) = (2π / λ) × path difference
• · Phase difference (rad) = path difference × λ
• · Phase difference (rad) = path difference / λ

Q11. Two waves of wavelength 0.40 m meet with a path difference of 0.10 m. What is the phase difference between them?

Multiple Choice · 1 point

• · π/4 radians
• · π/2 radians
• · π radians
• · 2π radians

Q12. For a stable and observable interference pattern to form, the two wave sources must be:

Multiple Choice · 1 point

• · Incoherent, so the phase difference varies over time
• · Coherent, maintaining a constant phase difference
• · Unpolarised, so both planes of oscillation contribute
• · Of different frequencies, to produce a beat pattern

Q13. When two waves undergo ____ interference, the resultant amplitude is at a minimum. This occurs when the path difference is an odd multiple of ____, giving a phase difference of ____ radians.

Fill In Blanks · 3 points

• · destructive
• · λ/2
• · π
• · constructive
• · λ
• · 2π

Q14. Two loudspeakers emit coherent sound waves of wavelength 0.80 m. A listener stands at a point where the path difference from the two speakers is 2.0 m. What type of interference does the listener experience, and why?

Multiple Choice · 1 point

• · Destructive, because 2.0 m = 2.5λ, which is an odd multiple of λ/2
• · Constructive, because 2.0 m = 2.5λ, which is an odd multiple of λ/2
• · Constructive, because 2.0 m = 2.5λ, which is a whole number multiple of λ
• · Destructive, because 2.0 m = 2.5λ, which is an odd multiple of λ/2