All Free Physics MCQs with Answers

91. 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.

92. 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.

93. 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.

94. A stationary wave is formed when

• A. two identical waves travel in the same direction
• B. two identical waves travel in opposite directions and superpose
• C. a wave is absorbed by a wall
• D. a single wave travels through a very long medium

Explanation: Usually the incident wave and its own reflection interfere, producing a pattern with fixed nodes of zero displacement and antinodes of maximum displacement. No energy is transported along a stationary wave, unlike a progressive wave, which is the essential difference between them. The distance between two adjacent nodes is half a wavelength.

95. The distance between two consecutive nodes in a stationary wave is

• A. one wavelength
• B. half a wavelength
• C. a quarter of a wavelength
• D. two wavelengths

Explanation: Nodes recur every half wavelength, with an antinode midway between each pair, so measuring the node separation is the standard way of finding the wavelength in a laboratory experiment. The distance from a node to the neighbouring antinode is therefore a quarter of a wavelength. Doubling the node separation gives the full wavelength.

96. In a pipe closed at one end, the fundamental note has

• A. a node at the closed end and an antinode at the open end
• B. antinodes at both ends
• C. nodes at both ends
• D. an antinode at the closed end

Explanation: The air cannot move at a closed end, so a node forms there, while the open end is free to vibrate and carries an antinode. The pipe therefore holds a quarter of a wavelength at its fundamental, so the wavelength is four times the length. A pipe open at both ends holds half a wavelength and sounds an octave higher for the same length.

97. A closed organ pipe produces

• A. all harmonics
• B. only even harmonics
• C. only odd harmonics
• D. no harmonics at all

Explanation: The node and antinode boundary conditions can only be satisfied by odd multiples of the fundamental, so a closed pipe gives the first, third, fifth and so on. An open pipe supports every harmonic, which is why it sounds richer. This difference in harmonic content is a large part of why a clarinet and a flute have such different tone.

98. Simple harmonic motion is defined as motion in which the acceleration is

• A. constant in magnitude and direction
• B. proportional to the displacement and directed towards the mean position
• C. proportional to the speed
• D. always zero at the extreme positions

Explanation: The restoring force is proportional to the displacement and always points back to equilibrium, which produces sinusoidal motion in time. Acceleration is therefore greatest at the extremes, where displacement is maximum, and zero at the mean position, where the speed is greatest. A mass on a spring and a simple pendulum at small angles are the standard examples.

99. In simple harmonic motion, the speed of the body is maximum

• A. at the extreme positions
• B. at the mean position
• C. midway between mean and extreme
• D. everywhere, since it is constant

Explanation: At the mean position the displacement is zero, so all the energy is kinetic and the speed peaks, while at the extremes the body is momentarily at rest with all the energy stored as potential. The total energy stays constant throughout, simply exchanging between the two forms twice every cycle. Acceleration follows the opposite pattern to speed.

100. The time period of a simple pendulum depends on

• A. its mass and length
• B. its length and the acceleration due to gravity
• C. its amplitude, for all amplitudes
• D. the material of the bob

Explanation: The period is 2 pi times the square root of length divided by g, so it is independent of the mass entirely and of the amplitude provided the swing is small. Lengthening the pendulum four times doubles the period. This independence from mass is what makes the pendulum a reliable timekeeper and a good way to measure g.