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Chapter 1: Waves 1.3 Analysing Refraction of Waves

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Chapter 1: Waves1.3 Analysing Refraction of Waves

1.3 Analysing Refraction of

Waves Any type of wave can be refracted, which means a

change of direction. Refraction occurs when the

speed of a wave changes, as it moves from one

medium to another. We shall look at the refraction

of water waves, light waves and sound waves.

Refraction of Plane Water

Waves 1 Water waves undergo refraction (bending)

when they are slow down. Refraction is

accompanied by a change in speed and

wavelength of the waves.

Refraction of Plane Water

Waves 2 Water waves travel faster (with higher velocity,

v) on the surface of deep water than they do on

shallow water. Thus, if water waves are passing

from deep water into shallow water, they will slow

down. This decrease in speed will also be

accompanied by a decrease in wavelength. The

change in speed of the wave causes refraction.

Figure 1.31

Refraction of Plane Water

Waves 3 After refraction, the wave has the same

frequency, but a different speed, wavelength

and direction.

Refraction of Plane Water

Waves 4 When a water wave transmitted from deer

water into shallow water, the wave is refracted

towards the normal.

Refraction of Plane Water

Waves Conversely, the wave is refracted away from the

normal when the water wave transmitted from

shallow water into deep water. The effects of

refraction of water waves are shown in Figures

1.32 (a) and (b).

Refraction of Plane Water

Waves

Experiment 1.4: To investigate the

refraction of water waves

What are the effects on the

direction of propagation of a water

wave passing over Perspex plates

of different shapes?

Refraction of Plane Water

Waves Hypothesis

Refraction occurs and the direction of propagation

is influenced by the shapes of the Perspex plates.

Refraction of Plane Water

Waves Variables:

(a) Manipulated : Shapes of Perspex plates

(b)Responding : Wavelength and direction of propagation of the water wave

(c) Fixed : Frequency

Refraction of Plane Water

Waves Apparatus/Materials

Ripple tank, wooden bar, perspex plates of different

shapes, mechanical stroboscope and white paper.

Refraction of Plane Water

Waves Procedure

1 A ripple tank is set up as shown in Figure 1.30.

Refraction of Plane Water

Waves Procedure

2 The tank is filled with water and the legs of the tank are adjusted until the depth of the water in the tank is uniform.

Refraction of Plane Water

Waves Procedure

3 A Perspex plate in the shape of a trapezium, as

shown in Figure 1.31, is immersed in the centre of

the tank to create an area of shallow water in the

tank.

Refraction of Plane Water

Waves Procedure

4 The dipper with the wooden bar attached is

switched on to produce plane waves.

Refraction of Plane Water

Waves Procedure

5 The directions of the water waves in the areas of deep and shallow water are observed with a stroboscope.

Refraction of Plane Water

Waves Procedure

6 Steps 3 to 5 are repeated with the orientation

of the trapezium plate changed so that the wave is

incident at an acute angle on a side of the plate as

shown in Figure 1.32.

Refraction of Plane Water

Waves Procedure

7 Steps 3 to 5 are repeated using Perspex plates

in the shapes of a triangle, convex lens and

concave lens.Position Observation

(a) Trapezium Perspex

plate with the vertical

side of the plate

facing the incident

wave.

Refraction of Plane Water

Waves Procedure

7 Steps 3 to 5 are repeated using Perspex plates

in the shapes of a triangle, convex lens and

concave lens.Position Observation(b) Trapezium Perspex

plate with the slant

side of the plate facing

the incident wave.

Refraction of Plane Water

Waves Procedure

7 Steps 3 to 5 are repeated using Perspex plates

in the shapes of a triangle, convex lens and

concave lens.Position Observation(c) Triangular Perspex

plate

Refraction of Plane Water

Waves Procedure

7 Steps 3 to 5 are repeated using Perspex plates

in the shapes of a triangle, convex lens and

concave lens.Position Observation(d) Perspex plate in the

shape of a convex

lens

Refraction of Plane Water

Waves Procedure

7 Steps 3 to 5 are repeated using Perspex plates

in the shapes of a triangle, convex lens and

concave lens.Position Observation(e) Perspex plate in the

shape of a concave

lens

Refraction of Plane Water

Waves Discussion

1 Refraction occurs when a water wave passes

from one area to another area with a different

depth of water.

Refraction of Plane Water

Waves Discussion

2 If the wave strikes the perspex plate at an

angle of incidence of 0°, the direction of

propagation of the wave remains unchanged. The

water wave is not refracted, i.e. the angle of

refraction is zero.

Refraction of Plane Water

Waves Discussion

3 If the wave strikes the Perspex plate at a

certain angle of incidence, the water wave is

refracted.

Refraction of Plane Water

Waves Discussion

4 The water wave is refracted towards the

normal the wave travels to a shallower area, and

vice versa.

Refraction of Plane Water

Waves Conclusion

The direction of propagation of a wave changes if

the angle of incidence of the wave is not zero. The

shape, of the refracted wave depends on the shape

of the area of shallow water over which the wave is

passing.

Refraction of Plane Water

Waves Example 7:

Figure 1.35 shows water ripples in two areas of

water with different depths. The observation is

made with a stroboscope with 3 slits. The

frequency of the stroboscope is 4 rotations per

second

Refraction of Plane Water

Waves Calculate

(a) the frequency of the dipper,

Refraction of Plane Water

Waves Solution (a) Frequency of dipper

= Number of slits x Frequency of stroboscope

= n x p

= 3 x 4

= 12Hz

Refraction of Plane Water

Waves Calculate

(b) the wavelength in the deep area and in the

shallow area,

Refraction of Plane Water

Waves Solution

(b) Area of deep water:

Wavelength ,

Area of shallow water:

Wavelength

cm23

61

cm8.03

4.22

Refraction of Plane Water

Waves Calculate

(c) the speeds of the waves in the two areas.

Refraction of Plane Water

Waves Solution

(c) Area of deep water:

Speed

Area of shallow water:

Speed

= 9.6 cm s-1

1

11 24212 cmsfv

1

22 8.012 cmsfv

Refraction of Plane Water

Waves Example 8

A plane wave has a wavelength of 2 cm and a velocity of 8 cm s-1 as it moves over the surface of shallow water. When the plane wave moves into an area of greater depth, its velocity becomes 12 cm s-1. What is

(a) the wavelength

(b) the frequency of the wave in the area of greater depth?

Refraction of Plane Water Waves

Solution

(a) Area of shallow water:

v1=8 cm s-1 and 1=2cm

Area of deeper water:

v2=12 cm s-1 and 2=?

For refraction, frequency, f = remains the same.

Substituting in the relationship:

v

Refraction of Plane Water

Waves Example 8

A plane wave has a wavelength of 2 cm and a velocity of 8 cm s-1 as it moves over the surface of shallow water. When the plane wave moves into an area of greater depth, its velocity becomes 12 cm s-1. What is

(b) the frequency of the wave in the area of greater depth?

Refraction of Plane Water

Waves Solution

(b) Frequency of wave, f = = 4 Hz

The frequency of the wave is the same in all the areas.

v

Refraction of light

1 A swimming pool seems much shallower than it

actually is; a spoon appears bent when part of it is

in water and a boy's legs look shorter when

immersed in a pool. All these effects are due to the

refraction of light.

Refraction of light

2 Figure 1.37 shows that a light ray is bent or

refracted when passing from air to the glass.

Refraction of light

3 When a ray propagates from one medium to an

optically denser medium, the ray refracts towards

the normal. Conversely, a ray propagating from one

medium to an optically less dense medium is

refracted away from the normal.

Refraction of light

4 The speed of the light decreases as it

propagates in the glass block, causing it to alter the

direction of propagation. Since the incidence ray

and the refracted ray are from the same source

(ray box), the frequency remain the same. Hence,

the wavelength of the ray in the glass is shorter

than the ray in the air.

Refraction of Sound Waves

1 The sound of a moving train at a distance is

clearer at night than that in the day time. This is

due to the effects of the refraction of sound

waves.

Refraction of Sound Waves

2 At night-time, the layers of air close to the

ground are cooler than the layers further from the

ground.

Refraction of Sound Waves

3 Sound travels at a slower speed in cold air. As

a result, the sound waves are refracted in front

path of a curve (due to total internal reflection)

towards the ground instead of disappearing into the

upper layers of the air.

Refraction of Sound Waves

Experiment 1.5 To investigate the refraction of

sound waves

What happens to a sound wave as it passes

through a balloon filled with carbon dioxide?

Refraction of Sound Waves

Hypothesis

A sound wave of greater amplitude is produced

after it passes through the balloon filled with

carbon dioxide.

Refraction of Sound Waves

Variables

(a) Manipulated : Balloon filled with carbon dioxide

(b) Responding : Amplitude of the sound wave

displayed on the screen of the cathode-ray

oscilloscope

(c) Fixed : Frequency of the sound wave

Refraction of Sound Waves

Apparatus

Audio signal generator, loudspeaker, balloon fillet

with carbon dioxide, microphone and cathode-ray

oscilloscope.

Refraction of Sound Waves

Procedure

1 The apparatus is set up as shown in

Figure 1.39.

Figure 1.39

Refraction of Sound Waves

Procedure

2 The experiment is started without the

balloon.

Refraction of Sound Waves

Procedure

3 The audio signal generator and the

cathode-ray oscilloscope are switched on.

The wave form displayed on the screen of

the oscilloscope is observed and drawn.

Refraction of Sound Waves

Procedure

4 A balloon filled with carbon dioxide is placed between the audio signal generator and the oscilloscope.

5 The wave form displayed on the screen is observed and drawn.

Refraction of Sound Waves

Results

Refraction of Sound Waves

Results

The wave form displayed on the oscilloscope shows that the amplitude is larger when the balloon is placed between the audio signal generator and the oscilloscope. The larger amplitude indicates that a louder sound is received by the microphone.

Refraction of Sound Waves

Discussion

A sound wave is refracted towards the normal when the wave passes from the air to the carbon dioxide in the balloon. This is because carbon dioxide is denser than air and the speed of sound in carbon dioxide is reduced.

Refraction of Sound Waves

Discussion

When the sound wave emerges from the balloon, the wave is refracted away from the normal. The balloon acts as a biconvex lens which converge the sound waves to the microphone.

Refraction of Sound Waves

Conclusion

Sound waves are refracted when they travel from one medium to another of different density. The sound waves are refracted away from the normal after passing through the balloon filled with carbon dioxide. The result is a sound wave with larger amplitude.

The hypothesis is valid.