Date | May 2016 | Marks available | 3 | Reference code | 16M.2.HL.TZ0.4 |
Level | Higher level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Demonstrate and Describe | 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.
(i) Calculate the speed of this wave.
(ii) Show that the angular frequency of oscillations of a particle in the medium is ω=1.3×103rads−1.
One particle in the medium has its equilibrium position at x=1.00 m.
(i) State and explain the direction of motion for this particle at t=0.
(ii) Show that the speed of this particle at t=0.882 ms is 4.9ms−1.
The travelling wave in (b) is directed at the open end of a tube of length 1.20 m. The other end of the tube is closed.
(i) Describe how a standing wave is formed.
(ii) Demonstrate, using a calculation, that a standing wave will be established in this tube.
Markscheme
(i)
ALTERNATIVE 1
«distance travelled by wave =» 0.30 m
v=≪distancetime=≫340ms−1
ALTERNATIVE 2
evaluates T=0.882×10−3×1.60.3«=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
ω=≪2πf=≫2π×3401.60=1.3×103 or 1.34×103rads–1
ALTERNATIVE 2
«0.882 ms is 0.31.6 of cycle so whole cycle is» 2π×316×0.882×10−3
1.35×103rads–1
Allow ECF from (b)(i).
(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 OR on the graph displacement moves towards equilibrium/0
to the left
Do not allow “moving downwards”.
(ii)
y=–1.5mm
v=2π×212×√(4.0×10−3)2−(1.5×10−3)2
«v=4.939≈4.9ms-1»
Allow ECF from (b)(ii).
Do not allow 4.3mm0.882ms=4.87ms−1.
(i)
the superposition/interference of two oppositely moving/reflected «identical travelling» waves
(ii)
the allowed wavelengths in the tube are λ=4Ln=480n, n = 1, 3, 5,…
OR
diagram showing 34 of a standing wavelength in the tube
1.6=4.80n⇒n=3
OR
justification that 34×1.6=1.2m
Allow diagram showing 34 of a wavelength for MP1.