Chapter 1: WavesChapter 1: Waves1.3 Analysing Refraction of Waves

1.3 1.3 Analysing Refraction Analysing Refraction of Wavesof WavesAny 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 Refraction of Plane Water WavesWaves1 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 Refraction of Plane Water WavesWaves2 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 Refraction of Plane Water WavesWaves3 After refraction, the wave has the

same frequency, but a different speed, wavelength and direction.

Refraction of Plane Water Refraction of Plane Water WavesWaves4 When a water wave transmitted from

deer water into shallow water, the wave is refracted towards the normal.

Refraction of Plane Water Refraction of Plane Water WavesWavesConversely, 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 Refraction of Plane Water WavesWaves

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 Refraction of Plane Water WavesWavesHypothesisRefraction occurs and the direction of

propagation is influenced by the shapes of the Perspex plates.

Refraction of Plane Water Refraction of Plane Water WavesWaves

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 Refraction of Plane Water WavesWavesApparatus/MaterialsRipple tank, wooden bar, perspex plates of

different shapes, mechanical stroboscope and white paper.

Refraction of Plane Water Refraction of Plane Water WavesWavesProcedure1 A ripple tank is set up as shown in

Figure 1.30.

Refraction of Plane Water Refraction of Plane Water WavesWavesProcedure2 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 Refraction of Plane Water WavesWavesProcedure3 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 Refraction of Plane Water WavesWavesProcedure4 The dipper with the wooden bar

attached is switched on to produce plane waves.

Refraction of Plane Water Refraction of Plane Water WavesWavesProcedure5 The directions of the water waves in

the areas of deep and shallow water are observed with a stroboscope.

Refraction of Plane Water Refraction of Plane Water WavesWavesProcedure6 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 Refraction of Plane Water WavesWavesProcedure7 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 Refraction of Plane Water WavesWavesProcedure7 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 Refraction of Plane Water WavesWavesProcedure7 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 Refraction of Plane Water WavesWavesProcedure7 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 Refraction of Plane Water WavesWavesProcedure7 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 Refraction of Plane Water WavesWavesDiscussion1 Refraction occurs when a water wave

passes from one area to another area with a

different depth of water.

Refraction of Plane Water Refraction of Plane Water WavesWavesDiscussion2 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 Refraction of Plane Water WavesWavesDiscussion3 If the wave strikes the Perspex plate

at a certain angle of incidence, the water wave is refracted.

Refraction of Plane Water Refraction of Plane Water WavesWavesDiscussion4 The water wave is refracted towards

the normal the wave travels to a shallower area, and vice versa.

Refraction of Plane Water Refraction of Plane Water WavesWavesConclusionThe 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 Refraction of Plane Water WavesWavesExample 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 Refraction of Plane Water WavesWavesCalculate (a) the frequency of the dipper,

Refraction of Plane Water Refraction of Plane Water WavesWavesSolution (a) Frequency of dipper = Number of slits x Frequency of

stroboscope = n x p = 3 x 4 = 12Hz

Refraction of Plane Water Refraction of Plane Water WavesWavesCalculate (b) the wavelength in the deep area and in

the shallow area,

Refraction of Plane Water Refraction of Plane Water WavesWavesSolution (b) Area of deep water: Wavelength ,

Area of shallow water: Wavelength

cm23

61

cm8.03

4.22

Refraction of Plane Water Refraction of Plane Water WavesWavesCalculate (c) the speeds of the waves in the two

areas.

Refraction of Plane Water Refraction of Plane Water WavesWaves

Solution (c) Area of deep water: Speed

Area of shallow water: Speed = 9.6 cm s-1

111 24212 cmsfv

122 8.012 cmsfv

Refraction of Plane Water Refraction of Plane Water WavesWavesExample 8A 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 Refraction of Plane Water WavesWavesSolution (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 Refraction of Plane Water WavesWavesExample 8A 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 Refraction of Plane Water WavesWavesSolution (b) Frequency of wave, f = = 4 Hz

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

v

Refraction of lightRefraction of light1 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 lightRefraction of light2 Figure 1.37 shows that a light ray is

bent or refracted when passing from air to

the glass.

Refraction of lightRefraction of light3 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 lightRefraction of light4 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 Refraction of Sound WavesWaves1 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 Refraction of Sound WavesWaves2 At night-time, the layers of air close to

the ground are cooler than the layers further from the ground.

Refraction of Sound Refraction of Sound WavesWaves3 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 Refraction of Sound WavesWavesExperiment 1.5 To investigate the refraction

of sound wavesWhat happens to a sound wave as it passes

through a balloon filled with carbon dioxide?

Refraction of Sound Refraction of Sound WavesWavesHypothesisA sound wave of greater amplitude is

produced after it passes through the balloon filled with carbon dioxide.

Refraction of Sound Refraction of Sound WavesWavesVariables (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 Refraction of Sound WavesWavesApparatus Audio signal generator, loudspeaker, balloon

fillet with carbon dioxide, microphone and cathode-ray oscilloscope.

Refraction of Sound Refraction of Sound WavesWavesProcedure1 The apparatus is set up as shown

in Figure 1.39.

Figure 1.39

Refraction of Sound Refraction of Sound WavesWaves

Procedure2 The experiment is started without the

balloon.

Refraction of Sound Refraction of Sound WavesWavesProcedure3 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 Refraction of Sound WavesWavesProcedure4 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 Refraction of Sound WavesWavesResults

Refraction of Sound Refraction of Sound WavesWavesResultsThe 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 Refraction of Sound WavesWavesDiscussionA 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 Refraction of Sound WavesWavesDiscussionWhen 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 Refraction of Sound WavesWavesConclusionSound 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.