| Date | May 2016 | Marks available | 1 | Reference code | 16M.2.SL.TZ0.4 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 0 |
| Command term | State | Question number | 4 | Adapted from | N/A |
Question
A longitudinal wave is travelling in a medium from left to right. The graph shows the variation with distance x of the displacement y of the particles in the medium. The solid line and the dotted line show the displacement at t=0 and t=0.882 ms, respectively.
The period of the wave is greater than 0.882 ms. A displacement to the right of the equilibrium position is positive.
State what is meant by a longitudinal travelling wave.
Calculate, for this wave,
(i) the speed.
(ii) the frequency.
The equilibrium position of a particle in the medium is at x=0.80 m. For this particle at t=0, state and explain
(i) the direction of motion.
(ii) whether the particle is at the centre of a compression or a rarefaction.
Markscheme
a wave where the displacement of particles/oscillations of particles/movement of particles/vibrations of particles is parallel to the direction of energy transfer/wave travel/wave movement
Do not allow “direction of wave”.
(i)
ALTERNATIVE 1
«distance travelled by wave =» 0.30 m
\(v = \ll \frac{{{\rm{distance}}}}{{{\rm{time}}}} = \gg 340{\rm{m}}{{\rm{s}}^{ - 1}}\)
ALTERNATIVE 2
evaluates \(T = \frac{{{\rm{0.882}} \times {{10}^{ - 3}} \times 1.6}}{{{\rm{0.3}}}}\)«=4.7ms» to give f = 210 or 212 Hz
uses λ=1.6 m with v=fλ to give 340ms–1
(ii)
ALTERNATIVE 1
λ=1.60m
f=\(\frac{{340}}{{1.60}}\)=212 or 213Hz
ALTERNATIVE 2
\(T = \frac{{0.882 \times {{10}^{ - 3}} \times 1.6}}{{0.3}}\)«=4.7ms»
\(F = \ll \frac{1}{T} = \gg {\rm{ 210Hz}}\)
(i)
the displacement of the particle decreases OR «on the graph» displacement is going in a negative direction OR on the graph the particle goes down
to the left
Do not allow “moving downwards” unless accompanied by reference to graph.
(ii)
molecules to the left of the particle have moved left and those to the right have moved right
«hence» the particle is at the centre of a rarefaction
