ADDITIONAL TOPIC 4 ANSWERS 1PHYSICS FOR THE IB DIPLOMA © CAMBRIDGE UNIVERSITY PRESS 2014

Measurement and uncertainties 1Measurement and uncertainties 1Measurement and uncertainties 1Measurement and uncertainties 1Measurement and uncertainties 1Additional Topic 4 answers

Topic 4 Waves

4.1 Oscilliations1 b V at the origin c same graph but from x = –1 cm to xv= 1 cm2 a i 6.9 m s–1

ii 1.5 J b

4.2 Travelling waves5 a 3.16 m s−1

b K at any point where x = 06 a i 0.6 cm ii 4.0 m iii 5.0 m s−1

iv 1.25 Hz b no8 a 5.0 × 103 m s−1

b i 0 mm ii –2.00 mm9 a 3.0 m s−1 b T = 1.5 s; f = 0.667 Hz c 4.5 m d 12 cm 10 a 0.66 m b 2.98 m 11 a 2400 m b 0.050 m c 30

4.3 Wave characteristics 12

EP/J

x/cm–4 –2 0 2 4

1

2

3

4

5

6

3 a i V at any maximum or minimum of the graph ii A at any maximum or minimum of the graph iii K at any point where x = 0 iv P at any maximum or minimum of the graph b i a negative cosine curve ii a negative sine curve4 a i Z at any maximum or minimum of the graph ii M at any point where v = 0 b

0

5

–5

2 4 6 8t /s

a /ms–2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8t /s

EK/J c

x/cm–2 0 2 4 6 8

1

2

3

4d /cm

x/cm–2 0 2 4 6 8

0.2

–0.2

–0.4

0.4

0.6

0.8

1.0d /cm 13

2 PHYSICS FOR THE IB DIPLOMA © CAMBRIDGE UNIVERSITY PRESS 2014ADDITIONAL TOPIC 4 ANSWERS

14 4.4 Wave behaviour 22

16 I08

17 128 additional polarisers 19 45°

4 cm4 cm

t = 1.0 ms

4 cm4 cmt = 2.0 ms

2 cm10 cmt = 2.5 ms

4 cm

t = 4.0 ms

12 cmt = 3.0 ms

t = 1.5 ms

45°

45°

29.87°glass

air

plastic

air

31.59°

24 Re� ection and di� raction of sound; absence of these for light. P could see Q by using a mirror at the corner.

25 b 8.0 m 26 0.83 m 27 a The path di� erence is two wavelengths, so

the observer hears a loud sound because of constructive interference.

b The path di� erence is one and a half wavelengths, so the observer hears no sound because of destructive interference.