C.2 Wave model

The question tests the fundamental definition of a wave: energy is transferred without permanent displacement of the medium's particles.

Water molecules in a ripple oscillate up and down about their equilibrium positions. The disturbance — and the energy it carries — propagates outward, but the molecules themselves do not travel with it.

The statement 'Energy is transferred by the wave while the water molecules oscillate about fixed positions' correctly describes this: the wave carries energy to the float, but the water does not permanently move horizontally.

We need to identify which statement correctly describes how a wave transfers energy through water.

This is incorrect — in a wave, particles do not travel with the wave. Horizontal transport of molecules would mean bulk flow of water, not a wave.

Particles are not permanently displaced in a wave. After the wave passes, each molecule returns to its equilibrium position.

The fact that the float bobs up and down demonstrates that energy has been transferred to it, even though it eventually returns to rest.

The remaining option — 'Energy is transferred by the wave while the water molecules oscillate about fixed positions' — correctly captures the essence of wave energy transfer.

The period and frequency are related by $T=\frac{1}{f}$

$T=\frac{1}{256}=3.906\times 10^{-3}\text{ s}\approx 3.91\times 10^{-3}\text{ s}$

The period is $3.91\times 10^{-3}$ s, which confirms this option is correct.

We need to find the period $T$ given frequency $f=256$ Hz, using $T=1/f$.

This would imply one cycle takes 256 seconds — clearly wrong for an audible sound wave; this confuses $f$ and $T$ without taking the reciprocal.

This is $1/100\times 2.56$, roughly $1/39$, which does not equal $1/256$. This is a factor-of-ten error.

This value ($\approx 1/64$) does not correspond to any straightforward calculation with 256 Hz and is therefore incorrect.

$3.91\times 10^{-3}$ s is the only option consistent with $T=1/256\approx 3.91\times 10^{-3}$ s.