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Date	May 2019	Marks available	2	Reference code	19M.2.SL.TZ2.3
Level	Standard level	Paper	Paper 2	Time zone	2
Command term	Calculate	Question number	3	Adapted from	N/A

Question

The diagram shows the direction of a sound wave travelling in a metal sheet.

The frequency of the sound wave in the metal is 250 Hz.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

[2]

The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s^–1 and the speed of sound in air is 340 m s^–1. Calculate the angle between the normal at Q and the direction of the wave in air.

[2]

State the frequency of the wave in air.

[1]

ci.

Determine the wavelength of the wave in air.

[1]

cii.

The sound wave in air in (c) enters a pipe that is open at both ends. The diagram shows the displacement, at a particular time T, of the standing wave that is set up in the pipe.

On the diagram, at time T, label with the letter C a point in the pipe that is at the centre of a compression.

[1]

Markscheme

Expression or statement showing acceleration is proportional to displacement ✔

so « $7.9 \times \frac{{2.3}}{{3.2}} » = 5.7 « {\text{m }}{{\text{s}}^{ - 2}}$ » ✔

$\sin \theta = \frac{{340}}{{6010}} \times \sin 54^\circ$ ✔

θ = 2.6° ✔

f = 250 «Hz» OR Same OR Unchanged ✔

ci.

$\lambda = « \frac{{340}}{{250}} =» 1.36 \approx 1.4 «{\text{m}}$ » ✔

cii.

any point labelled C on the vertical line shown below ✔

eg:

Examiners report

This was well answered at both levels.

Many scored full marks on this question. Common errors were using the calculator in radian mode or getting the equation upside down.

Many used a ratio of the speeds to produce a new frequency of 14Hz (340 x 250/6010). It would have helped candidates if they had been aware that the command term ‘state’ means ‘give a specific name, value or other brief answer without explanation or calculation.’

ci.

[N/A]

cii.

This was answered well at both levels.

Syllabus sections

Core » Topic 4: Waves » 4.1 – Oscillations

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