Free Waves MCQs with Answers

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. Resonance occurs when

• A. the driving frequency equals the natural frequency of the system
• B. the driving frequency is much higher than the natural frequency
• C. the amplitude is very small
• D. there is no damping present at all

Explanation: At resonance energy is transferred most efficiently to the oscillator and the amplitude builds to a large value, limited only by damping. It explains why a radio can be tuned to one station, why a wine glass can be shattered by a sung note, and why marching troops break step on a bridge. Damping reduces the peak amplitude but does not abolish the effect.

19. The Doppler effect explains why the pitch of an approaching ambulance siren sounds

• A. lower than the true pitch
• B. higher than the true pitch, because the waves reach the observer more frequently
• C. unchanged
• D. louder but of the same pitch

Explanation: Motion towards the observer crowds the wavefronts together, shortening the observed wavelength and raising the frequency, and the pitch drops abruptly as the source passes and begins to recede. The speed of sound in the air is unchanged throughout; only the observed frequency shifts. The same effect on light gives the red shift used to measure the recession of galaxies.

20. Only transverse waves can be polarised because polarisation restricts

• A. the speed of the wave
• B. the frequency of the wave
• C. the plane in which the vibrations occur
• D. the amplitude of the wave

Explanation: A transverse wave vibrates in any plane perpendicular to its direction of travel, so a filter can select one of those planes, whereas a longitudinal wave vibrates only along the direction of travel and there is nothing to select. This is why sound cannot be polarised but light can. The fact that light can be polarised is direct evidence that it is a transverse wave.