Which one of the following is true?

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BlackTom AI · Accepted Answer

When evaluating each option, it helps to recall how particles behave in different wave types and what is meant by terms like ‘net motion’ and ‘net velocity.’
Option a: 'Particles in a transverse wave oscillate in the direction of the wave motion.' In a transverse wave, the medium's particles move perpendicular to the direction of wave travel, not along it. This makes the statement false because it describes longitudinally aligned motion rather than transverse motion.
Option b: 'Particles in a longitudinal wave have a net motion in the direction of the wave.' In a longitudinal wave, particles oscillate parallel to the direction of wave travel, but they do not travel with the wave; they bob back and forth around their equilibrium positions. Therefore, they do not have a sustained net motion in the propagation direction. The phrase about a net motion along the wave is misleading and incorrect for how longitudinal waves operate.
Option c: 'Particles in a wave have a net velocity of zero.' Over time, the individual particles in the medium typically return to their equilibrium positions after each oscillation, and their average (net) displacement and, correspondingly, average velocity over a full cycle is zero. This aligns with the common understanding that the medium’s particles do not drift along with the wave as it propagates, but merely vibrate about fixed points. The wording ‘net velocity of zero’ is consistent with averaging over a cycle, though instantaneous velocity is nonzero during oscillation.
Option d: 'None of these.' Since option c is compatible with standard wave behavior (zero average velocity of particles when averaged over time), this blanket choice would be incorrect because at least one of the statements (option c) accurately describes the situation.
In summary, options a and b contradict the typical behavior of particles in transverse and longitudinal waves, option c captures the idea that particle motion averages to zero over time, and option d is unsupported given that a true statement appears among the choices. The key misconceptions typically lie in conflating instantaneous motion with average motion or mistaking the direction of oscillations for actual transport of matter.

01:750:124 ANALYTICAL PHYSICS IB Module 9 Quiz 2 - Transverse and Longitudinal Waves

Which one of the following is true?

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