Chapter 8

1. Chapter 8 Reflection, refraction and diffraction

2. 8.1 reflection of sound • In every day life we come across many acoustic phenomena e.g., • echoes, • roaring of thunder, • reverberation in buildings etc. [All these phenomena are based on the reflection of sound waves.] • Reflection of sound plays an important role in many acoustic applications e.g., • speaking tubes, • horns and trumpets, • sounding boards etc. طافواالرعد صدى فى المبانى الأبواق

3. 8.2. Reflection of a plane wave at a plane surface All the particles on AB will be vibrating in phase In the time the disturbance atAreachesCthe secondary waves from the pointBmust have traveled a distanceBDequal toAC. In the ΔS BAC and BDC BC is common BD = AC and The angle of incidence is equal to the angle of reflection.

4. Reflection Medium 1 Θi= Θr Θr Θi Transmission Medium 2 8.2. Reflection of a plane wave at a plane surface What happens when a wave “hits” a change in the medium? The angle of incidence is equal to the angle of reflection.

5. X Y A B O 8.3. Experimental demonstration of reflection of sound An alarm clock is placed at the top end of the tube X and the ear is placed near the top end of the tube Y. Keeping X fix the position of the tube Y is gradually changed. At one position maximum sound is heard. It is noticed that the tube X and Y equally inclined to the normal at O i.e. the angle of incidence is equal to the angle of reflection. Θin = Θout

6. S L 8-4Whispering galleries • S is the position of a speaker and L is the position of an observer (Fig.8.3.) Even a very low intensity sound made by S (i.e.,a whisper ) can be heard by the observer at L when he keeps his ear close to the wall . This is due to the multiple reflections of the sound waves from the curved wall of the gallery.

7. 8-5 echo • The repetition of the sound produced due to reflection by a distant extended surface like a cliff, hill, well, building etc. is called an echo. • the effect of sound on the human ear remains for ( 1/10) of second , if the sound is reflected back in a time less than ( 1/10 ) of a second no echo in heard suppose , • a person produces sound and this sound reflected from an obstacle at distance X. the time taken by the sound to travel to the obstacle and back is T . • It means that if the distance between the source of sound and the obstacle is less than 17 meters (56 ft) no echo (repetition) is heard . But echo is heard if the distance more than 17 meters. • If a person is standing in between two hills and produces a sound the sound is reflected again and again from two hills and successive echoes are heard.

8. 8-6Application of reflection of sound • 1.The principle of reflection of sound is used in an auditorium. A large plan sounding board (cylindrical or parabolic) is placed behind the speaker (Fig. 8.4). The speaker stands at the focus of the board. When the speaker speaks, the sound waves get reflected from the sounding board and the reflected sound travels towards the audience. This enables the increase in the intensity of sound and also uniform distribution of sound. • 2. Speaking tube or megaphone. The speaking tube or megaphone consists of a conical metal horn (Fig 8.5). At the narrow end of the tube, the speaker speaks. The sounds waves get reflected from the inside wall of the tube and are propagated practically along the axis of the tube. This provides higher intensity of sound in a particular direction. Here, the sound energy is not spread in all direction but it is concentrated in a desired direction. • 3.Ear trumpet. An ear trumpet is a use full device for persons who are heard of hearing the sound waves that inter the wide end of the trumpet suffer multiple reflections the sound entering the ear has large amplitude and thus higher intensity. This enables the person to hear even low intensity sound. Auditorium:قاعة مكبر الصوت megaphone

9. 8.7 phase change on reflection • According to the laws of reflection and refraction, the velocity in each medium is independent of the direction Here and are the angles of incidence, reflection and refraction respectively (Fig. 8.6). Here C1 is the velocity of sound in the first medium and C2 the velocity of sound in the second medium.

10. It is also necessary that at the boundary of the two media • (i) the component of particle velocity v, normal to the surface must be continuous and • (ii) the pressure, variation ∂p must be continuous . • Accordingly, considering i,r and t as the incident , reflected and transmitted waves , to satisfy the first condition, • to satisfy the second condition c1ρ1 = R1 and c2ρ2 = R2 Where R1 and R2 represent the radiation resistances of the first and second medium respectively.

12. (3) If It means that the phase of the particle velocity remains unchanged. However the phase of the condensation is reversed. • Also incident energy must be equal to the sum of the reflected and the transmitted energy (4) From equations (7) and (8) . Thismeans that the phase of the transmitted wave remains unchanged in all cases. (1) from equation (7) , if R1 = R2 It means that there is no reflected wave and the whole of the energy is transmitted to the second medium. (5) If the velocity of sound C1 in the first medium is less than the velocity of sound C2 in the second medium , there will be a critical angle of incidence When Is equal to In this case. (2)If R2> R1(i.e. wave traveling from water to air) It means that particle velocity of the reflected wave is in reversed phase. However, the quantity the phase of the condensation in the reflected wave remains unaltered because both vr and C are reversed in sign.

13. 8.8. Transmission of sound from air to water It indicates that the incident wave is totally internally reflected almost completely the phase of the condensation is not changed but the particle velocity is reversed (i.e. nodal condition) To conclude, in general, in all cases of sound transmission, from gaseous to a solid or liquid medium orvice versa, i.e. when the radiation resistanceR1 and R2 are widely different, there is almost complete total internal reflection.

14. 8.9. Refraction of a plane wave front at a plane surface From the Δs ACD and MCL Similarly from the Δs ACE and MCN From the Δs ABC and ACD Thus the bending or refraction of sound waves will depend upon the velocities of sound in the two media.

15. air Lower density Higher velocity CO2 Higher density Slower velocity for entering a medium where velocity slows down, “ray” bends towards the normal Since velocity slows but the frequency is the same 8.9. Refraction of a plane wave front at a plane surface Incoming sound wave From Faster to Slower Medium

16. air CO2 Slower velocity Normal incidence, no refraction Wavelength still changes to conserve frequency Incoming sound wave Normal Incidence

17. rubber balloon in the shape of a convex lens Air The sound converges to the point B just similar to light waves. source ofsound The refracted spherical wave front EQF The incident spherical waves front CPD filled with carbon dioxide 8.10. Experimental demonstration of refraction of sound ρair <ρCarbon dioxidetherefore, velocity of sound in carbon dioxide is less than in air. the ear placed at B receives of maximum intensity.

18. 8.11 Diffraction of sound • It is a matter of common experience that the sound is heard behind an obstacle placed in the path of sound. This bending of sound round an obstacle is called diffraction of sound. In the case of light, for a very small obstacle, a shadow is observed and it is difficult to observer theillumination in the geometrical shadow. Both sound and light are propagated as waves in the medium and are diffracted.