DP Physics (last assessment 2024)

Question 21N.2.SL.TZ0.3

Date	November 2021	Marks available	[Maximum mark: 9]	Reference code	21N.2.SL.TZ0.3
Level	SL	Paper	2	Time zone	TZ0
Command term	Calculate, Draw, Estimate, Explain, Identify, State	Question number	3	Adapted from	N/A

[Maximum mark: 9]

21N.2.SL.TZ0.3

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.

(a)

Calculate the wavelength of the wave.

[2]

Markscheme

$T = 4 \times 10^{- 3}$ «s» or $f = 250$ «Hz» ✓

$λ = 340 \times 4.0 \times 10^{- 3} = 1.36 \approx 1.4$ «m» ✓

Allow ECF from MP1.
Award [2] for a bald correct answer.

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.

(b.i)

State the phase difference between the two waves.

[1]

Markscheme

«±» $\frac{π}{2} / 90 °$ OR $\frac{3 π}{2} / 270 °$ ✓

(b.ii)

Identify a time at which the displacement of P is zero.

[1]

Markscheme

1.5 «ms» ✓

(b.iii)

Estimate the amplitude of the resultant wave.

[1]

Markscheme

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.

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 $T$ . The diagram represents the standing wave at $t = 0$ and at $t = \frac{T}{8}$ . The wavelength of the wave is 1.20 m. Positive displacements mean displacements to the right.

(c.i)

Calculate the length of the tube.

[1]

Markscheme

L = « $\frac{3}{4} λ =$ » 0.90 «m» ✓

(c.ii)

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 $t = \frac{T}{8}$ .

[2]

Markscheme

to the right ✓

displacement is getting less negative

change of displacement is positive ✓

(c.iii)

Draw on the diagram the standing wave at time $t = \frac{T}{4}$ .

[1]

Markscheme

horizontal line drawn at the equilibrium position ✓