Exercise 5 (Wave phenomena) Suggested Answers
1.
2.
3.
4. (a) (i) To generate circular waves.
(ii) To produce a region of slower wave speed so that refraction occurs.
(b) (i) 2.5 cm behind the reflecting surface.
(ii) Destructive interference.
Path difference = (5 2 +12 2 ) 1/2 – 12 = 1 cm = 1
2
(2) = 1
2
λ , so destructive interference occurs.
5. (a) A = 0.2 cm, T = 0.1 s, so f = 1/T = 10 Hz, v = s / t = 0.12 / 0.5 = 0.24 m s -1 , λ = v / f = 0.24 / 10 = 0.024 m
(b) Fit the edge of the tank with spongy lining.
(c) (ii) Diffraction
(d) (i) Constructive : A/C Destructive : D
(ii) No. At point of constructive interference, if trough meets trough, a bigger trough is formed. The statement is wrong.
6. (a) 3

= 0.06 =>
 f = v /

= 0.02 m
= 0.4 / 0.02 = 20 Hz
(b) (i) At P : Path difference = 2 λ
(ii) At Q : Path difference = 1
1
2
λ
So constructive interference occurs at P and destructive interference occurs at Q.
(c) If the frequency of vibration is doubled, the wavelength of the water waves is reduced by half. The path difference at Q equals to 3 times the wavelength of the water waves, so the interference at Q becomes constructive.
(d) Place a barrier with two small slits in front of the dipper as shown.
․ S
7. (a) Node
(b) Wavelength =
1 .
2
2 .
5
= 0.48 m
Speed = f

= 75

0.48 = 36 m s

1
(c) A stationary wave with two loops on the string has wavelength equal to 1.2 m.

By v = f

, frequency = v
λ
36
=
1 .
2
= 30 Hz
8. (a) 2 waves travel in opposite directions.
The 2 waves should have similar amplitude.
Stationary wave forms only at certain frequencies.
(b) The displacement of a point on the string is perpendicular to the mean position of the string.
(c) The amplitude of the oscillation of point A is larger than that of point B , and they are in antiphase.
(d) Wavelength = 1.2 m
By v = f

, frequency = v
λ
6 .
2
=
1 .
2
= 5.17 Hz
(e) (i)
(ii) (P, Q and R located appropriately, i.e. they are not in neighbouring loops of each other.)
9. (a) (i) Wavelength = 0.6 x 2 / 3 = 0.4 m
(ii) Both are at rest
(iii)
(iv)
(v)
WAVES IN STRING
Stationary wave
WAVES IN AIR
Travelling wave
Transverse wave Longitudinal wave
They have different speeds / wavelengths
MC 1-5 C E B C E 6-10 D E C C D 11-15 C D C C C 16-17 A D

Explanations
2. The waves bend toward normal.
3. Decreasing the size of slit would increase the diffraction degree.
6. 4

= 10 cm =>

= 2.5 cm v = f

= 25 x 0.025 = 0.625 m s -1
7. The refracted waves should converge to focus because of the convex shape of the boundary. So A, B and D are incorrect. In case C, the waves bend to normal (because the refracted wavefronts have the same curvature as the boundary), but not bend towards normal .
8. Path difference = 31- 28 = 3 cm
3 cm = 1.5

for

= 2 cm,
and also 3 cm = 0.5

for

= 6 cm.
9. If the waves emitted are in phase, at P, path difference = 3
2 
4
2 
4

1 m = 0.5 wavelength, so destructive interference occurs at P. at Q, path difference = 3
2 
4
2 
4

1 m = 0.5 wavelength, so destructive interference occurs at Q.
However, the waves emitted are exactly out of phase, so the interference results are reverse, i.e. constructive interference occurs at both P and Q.