Date | November 2021 | Marks available | 1 | Reference code | 21N.2.SL.TZ0.3 |
Level | Standard level | Paper | Paper 2 | Time zone | 0 - no time zone |
Command term | Calculate | Question number | 3 | Adapted from | N/A |
Question
A longitudinal wave travels in a medium with speed 340 m s−1. The graph shows the variation with time t of the displacement x of a particle P in the medium. Positive displacements on the graph correspond to displacements to the right for particle P.
Another wave travels in the medium. The graph shows the variation with time t of the displacement of each wave at the position of P.
A standing sound wave is established in a tube that is closed at one end and open at the other end. The period of the wave is TT. The diagram represents the standing wave at t=0t=0 and at t=T8t=T8. The wavelength of the wave is 1.20 m. Positive displacements mean displacements to the right.
Calculate the wavelength of the wave.
State the phase difference between the two waves.
Identify a time at which the displacement of P is zero.
Estimate the amplitude of the resultant wave.
Calculate the length of the tube.
A particle in the tube has its equilibrium position at the open end of the tube.
State and explain the direction of the velocity of this particle at time t=T8t=T8.
Draw on the diagram the standing wave at time t=T4t=T4.
Markscheme
T=4×10-3 T=4×10−3 «s» or f=250 f=250«Hz» ✓
λ=340×4.0×10-3=1.36≈1.4 λ=340×4.0×10−3=1.36≈1.4«m» ✓
Allow ECF from MP1.
Award [2] for a bald correct answer.
«±» π2/90°π2/90° OR 3π2/270°3π2/270° ✓
1.5 «ms» ✓
8.0 OR 8.5 «μm» ✓
From the graph on the paper, value is 8.0. From the calculated correct trig functions, value is 8.49.
L = «34λ=34λ=» 0.90 «m» ✓
to the right ✓
displacement is getting less negative
OR
change of displacement is positive ✓
horizontal line drawn at the equilibrium position ✓