1. 1Wave phenomena Waves show reflection, refraction, diffraction and interference. The reflection, refraction and dispersion of waves can be explained by Huygen’s principle.

2. Huygen’s principle (Essay) Every point on a wavefrontsource Every point on a wavefront may be regarded as a source of secondary spherical wavelets which spread out with the wave velocity. new wavefrontenvelope The new wavefront is the envelope of these secondary wavelets. Constructed wavefront First position of wavefront Secondary source First position of wavefront Constructed wavefront Secondary wavelet simulation

3. Explanation of law of reflection by Huygen’s principlereflection Consider  AA’B’ and  B’BA. AA’ = BB’ (provided)  AA’B’ =  ABB’ = 90 o AB’ = AB’ (common side)  AA’B’   B’BA (R.H.S.) a = b (corr. ,   ) ∵ i = a, a = b and b = r ∴ i = r (law of reflection) Incident Incident wavefront Secondary wavelet from A Reflected Reflected wavefront i ab r

4. Explanation of law of refraction by Huygen’s principlerefraction Secondary wavelet from A Refracted wavefront Incident wavefront a i b r Medium 1 Medium 2 Consider  AA’B’ and  ABB’ ∵ i = a and r = b ∴ (constant) the constant is called the refractive index, 1 n 2 for waves passing from medium 1 to medium 2. (Snell ’ s law)

5. Explanation of dispersion by Huygen’s principle speed of waves dispersive medium If the speed of waves in a given medium depends on the frequency of the waves, the medium is called a dispersive medium. Vacuum is a non-dispersive medium since the velocity of light for different colours (or frequencies) in vacuum is the same. Glass is a dispersive medium because when white light enters glass, the velocity is not the same for different colours (or frequencies).

6. Dispersion The secondary wavelet of blue light travels slower than that of red light in glass. Blue light is refracted more than red light and the refracted waves travel in slightly different direction. This phenomenon is called dispersion Waves of frequency f 1 and f 2 travelling with same speed Medium 1 Medium 2 White light Blue wavefront Red wavefront

7. Reflection of a longitudinal pulse compressionrarefaction compression

8. Explanation rarefactioncompression Equilibrium positions + ve slope- ve slope displacement distance Direction of wave displacement distance Direction of wave With a phase change of  (compression  compression)

9. Explanation rarefactioncompression Equilibrium positions + ve slope- ve slope displacement distance Direction of wave displacement distance Direction of wave No phase change (compression  rarefaction)

10. Application of reflection Radar (radio detection and ranging) Employs microwaves (e.g. 3 cm microwaves ) The distance d of the object can be calculated from the time lag t between the transmitted pulse P 1 and the reflected pulse P 2 by the equation d = 2ct where c is the speed of light. Distance of the object is determined form the time lag t Size of the object is determined by the strength of reflected waves. Radar aerial P 1 P 2 t

11. Sonar (sound navigation and ranging) Employs ultrasonic waves. i.e. waves with f > f audible (20kHZ) Submarines use sonar to keep track of water depth. Fishing vessels use sonar to spot shoals of fish. transmitter ultrasound waves produced by a sonar echo

12. Reasons for using ultrasound rather than audible sound Less diffraction so that the wave is more concentrated and can penetrate to a greater depth. Not be interfered by the audible sound in the sea. Smaller objects can be located.

13. Reflection of transverse waves video

14. Refraction Refraction Example 2 If i = 70 o, find the angle of deviation d. By symmetry, i = r, a = b. By geometry, d = a + b --- (1) and (i – a) + (r – b) = 60 o --- (2) By Snell’s law, sin i = n sin (i – a) --- (3) Sub (1), (2) and (3) sin i = n sin 30 o sin 70 o = n sin 30 o n = sin 70 o / sin 30 o = 1.879 a + 30 o = 70 o a = 40 o angle of deviation d = 2a = 80 o i r 60 o d ab

15. Real depth and apparent depth Suppose a fish is at A but it is image is at B which is nearer to water surface. AC is called the real depth and BC is the apparent depth. i i r r A B CO objec t image real depth D apparent depth D’

16. Superposition Two pulses on a string approaching each other. The resultant displacement of the string is the sum of the individual displacements. i.e. the pulses superpose( 疊置 ). A large pulse is produced. After crossing, each pulse travels along the string as if nothing had happened and it has its original shape.

17. Principle of Superposition Pulses (and waves), unlike particles, pass through each other unaffected. The resultant displacement is the vector sum of individual displacements due to each pulse at that point

18. Superposition can be used to find the resultant (solid line) of two waves (dotted line) of different wavelength and amplitude. A B C D P Q R S distance displacement

19. Example 2 Two pulses are traveling toward each other, each at 10 cm s -1 on a long string. Sketch the shape of the string in the following at t = 0.6 s. Solution: Distance travelled by each pulse = vt = (10)(0.6) = 6 cm 1 cm