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Date	November 2018	Marks available	1	Reference code	18N.2.SL.TZ0.4
Level	Standard level	Paper	Paper 2	Time zone	0 - no time zone
Command term	Demonstrate	Question number	4	Adapted from	N/A

Question

A pipe is open at both ends. A first-harmonic standing wave is set up in the pipe. The diagram shows the variation of displacement of air molecules in the pipe with distance along the pipe at time t = 0. The frequency of the first harmonic is f.

A transmitter of electromagnetic waves is next to a long straight vertical wall that acts as a plane mirror to the waves. An observer on a boat detects the waves both directly and as an image from the other side of the wall. The diagram shows one ray from the transmitter reflected at the wall and the position of the image.

An air molecule is situated at point X in the pipe at t = 0. Describe the motion of this air molecule during one complete cycle of the standing wave beginning from t = 0.

[2]

The speed of sound c for longitudinal waves in air is given by

$c = \sqrt {\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine, in kg m^–1 s^–2, the value of K for air.

[3]

Demonstrate, using a second ray, that the image appears to come from the position indicated.

[1]

c.i.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

[2]

c.ii.

Markscheme

«air molecule» moves to the right and then back to the left ✔

returns to X/original position ✔

wavelength = 2 × 1.4 = «2.8 m» ✔

c = «f λ =» 120 × 2.8 «= 340 m s⁻¹» ✔

K = «ρc² = 1.3 × 340² =» 1.5 × 10⁵ ✔

construction showing formation of image ✔

Another straight line/ray from image through the wall with line/ray from intersection at wall back to transmitter. Reflected ray must intersect boat.

c.i.

interference pattern is observed

interference/superposition mentioned ✔

maximum when two waves occur in phase/path difference is nλ

minimum when two waves occur 180° out of phase/path difference is (n + ½)λ ✔

c.ii.