Page 206 - text book form physics kssm 2020

Solving Problems Involving Refraction of Waves
Refraction of waves is caused by the change in speed of waves. For water waves, speed of wave
changes when the depth of water changes. Th is also causes wavelength to change. However, the
frequency of waves does not change because wave frequency is determined by the frequency of
vibrations at the source of the wave.
Figure 5.42 shows changes in speed and wavelength when water waves propagate from
deep region to shallow region.
v v
1 2
h h
1 2

Deep region Shallow region Deep region

Figure 5.42 Propagation of water waves from deep region to shallow region

From formula of speed of wave, v = fλ,
in deep region: v = fλ .......... (1)
1 1
in shallow region: v = fλ .......... (2)
2 2
v λ
(1) ÷ (2) gives 1 = 1 ,
v λ
v v 2 2
that is 1 = 2
λ λ
1 2
Example 1

A plane wave which has a wavelength of 2 cm and speed of 8 cm s propagates across a
–1
shallow region. When the wave enters the deep region, wave speed becomes 12 cm s .
–1
Determine the value of the wavelength in the deep region.

Solution:
Step Shallow region: λ = 2 cm, v = 8 cm s –1
1 1
List the given information in symbols. Deep region: v = 12 cm s , λ = ?
–1
2 2
14243
v v
1 = 2
Step λ λ
1 2
Identify and write down the formula used. 14243 12
8 =
2 λ
2
Step 12 × 2
λ =
Substitute numerical values into the formula 14243 2 8
and perform the calculations. = 3 cm

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200 5.4.4
5.4.4