Free Superposition and Interference MCQs with Answers

1. The principle of superposition states that when two waves meet, the resultant displacement at any point is

• A. the vector sum of the individual displacements
• B. always zero
• C. always double one of them
• D. the larger of the two displacements

Explanation: Displacements add algebraically, so waves in phase reinforce and waves in antiphase cancel, and afterwards each wave continues unchanged. This single principle underlies interference, beats and stationary waves alike. Cancellation is only complete when the two amplitudes are equal as well as opposite.

2. For two sources to produce a steady, observable interference pattern they must be

• A. of different frequencies
• B. coherent, keeping a constant phase relationship
• C. very far apart
• D. of unequal amplitude

Explanation: If the phase difference between the sources drifts, the positions of the bright and dark fringes shift too fast to be seen and the pattern washes out. Coherence in practice means the same frequency and a fixed phase relationship, which is why Young used a single source split into two rather than two separate lamps. Equal amplitudes are not required, but they give the greatest contrast.

3. Constructive interference occurs when the path difference between two coherent waves is

• A. an odd number of half wavelengths
• B. a whole number of wavelengths
• C. always zero
• D. one quarter of a wavelength

Explanation: A path difference of a whole number of wavelengths brings the waves back into phase, so the crests coincide and the amplitude is a maximum. An odd number of half wavelengths puts them in antiphase and gives destructive interference. Zero path difference is simply the special case of the central maximum.

4. Beats are produced when two sound waves

• A. of exactly the same frequency overlap
• B. of slightly different frequencies overlap
• C. travel in opposite directions
• D. have very different amplitudes

Explanation: The two waves drift in and out of phase, so the loudness rises and falls at a rate equal to the difference between the two frequencies. A piano tuner uses this directly, tightening a string until the beats slow to nothing and the note matches the fork. Waves of exactly the same frequency give a steady sound rather than beats.

5. Two tuning forks of 256 Hz and 260 Hz are sounded together. The beat frequency is

• A. 4 Hz
• B. 258 Hz
• C. 516 Hz
• D. 0.5 Hz

Explanation: The beat frequency is simply the difference between the two frequencies, so 260 minus 256 gives 4 beats per second. Their average, 258 Hz, is the pitch actually heard, which is why it appears as a distractor. Beats become too rapid to distinguish once the difference exceeds about 10 Hz.

6. If two speakers emit sound at same frequency and phase, maximum loudness occurs when path difference equals:

• A. half a wavelength
• B. one whole wavelength
• C. a quarter of a wavelength
• D. three quarters of a wavelength

Explanation: A path difference of a whole number of wavelengths brings the two waves back into phase so their crests coincide, giving constructive interference and maximum loudness. An odd number of half wavelengths puts them in antiphase and produces a quiet point instead. The Greek symbol for wavelength did not print cleanly in the original paper.