principle of superposition of waves pdf

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The waves pass through each other without being disturbed. 3 Constructive and Destructive Interference A. Superposition of waves. Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with the study of wave motion. LECTURE 27: Superposition of waves Select LEARNING OBJECTIVES: • Understand the principle of superposition. bL��`� &�"�ք��E �|Y��T�03 Q,�2�]/qUsdbq��NIQ�uٴ�BȔPd�`B�%��s�R^��\O[h��s�5��x��}ǡ��Z4�bf�$/SvL㉠֌'��'Ay��Ĵ�+OQ�����HD�4�'���7ji7�l=��ě#B���.�X^0D�C�dqd9ʀ���}��!�r1�:e$�T'?Ң�j�H[�%Bp���e�v�9n:扴�6]������!a�>t�'HG\��� 2Y�\Q���b��,XjUP�T��h��-�a��`�N���!�Z.���e��\�m��;~��m�

Therefore, the wave function (y) labeling the disturbance in the medium can be denoted as: Hence, the superposition of waves can lead to the … :v�"л"� h�vy'��;a���TvƇS:;Aj��[���^0��:���8�I�3���؝#����g��,�_�p̮� Their crests arrive at exactly the same time. (B(�L6Di�"��LR�d�"�u���A���82Qq������OU���L�A���H�8�ŚiT���S4(.%����R��d!�Up���,B�.-˸եe�� .b{uA��Ő��&���l3q���).����"��..R�r���(�����a�)-�z����R��!�e�piY� ���XeJ�"���R*T�ŐK� -�SH�B��nua�:e�r9��-��Hk���S0���[����G@tYI�'�Bu $���O $��HPt ��d� ,Yџ�ҒO �v $��4Q��bc!Ʃ��bW�;9S��~j���!��\ ʧB5AQ�ȑ �TP��~�O ��u $u����Ƈ��9mi>{}>JI��2�Ce3A����K�1���FZ�s� 4 0 obj ���$el�]|�,�{7�Y�Y���(HY�mK�:� �� ]Rd�nz0ƲA�JV.�o^��4�!�� �Y�+��)E=n���?�PИ�Şg@�`[t:R;F�Z�����'ծɶQ��d=��p�7�A}��!5$1w$�a��/�т�/F�p��ނ���8��ݷ�p5�0�u�,u���H��3T�Sn��n#d �����1K(Fրj�\�8V�B���!���5�u�! Consider two waves that arrive in phase as shown in Figure 1. Based on the principle, the overlapping waves (with the frequencies f 1,f 2 ….,f n) do not hamper the motion or travel of each other. aw�&h�ݽ�����.���>h>+J��>�!��!? Understand the definitions of constructive versus destructive interference and how they relate to perceived loudness. D�֣e�"g �#^��Ó�#3�����ؙ�����d�:O�jT87����Gl��XLʬ�b��&W���c T�Ǜ"��Zd��kW�͡��W�}��1�.|�v;�E�y�]��ư���AK�hP�! Constructive Interference distance → Wave 1 Wave 2 Superposition The two waves have the same phase Destructive Interference Wave 1 Wave 2 Superposition The two waves are out of phase (by 180o, or π) Distance -> Noise canceling headphones Noise Anti-noise Wave 1 Wave 2 <> ���P�}\���Vw-�57c��73@�}���Ρ���1O���n�Ɵ�䦋�ըD�Ō,!p�M��l����IÜy�m x��]]�e9q}o���� q��Ҩ�4(�i���M�I�=���W�Ue�{�%�m3RsW���.�]�r�~�������O�����W_�=����_?���?|��{��o�����Fr���o������~%���?������w7���Oo��"�b��v{���7���Vf��[������7��Q���ӛ�B����xz�������>$���_�+��z��I������~?�m�o3�G�;|?���o����/��s���������:�=����g���~�᧿��J��p��_���B�=��(�>���Oo��'��ޔ�i��K��q+}�k�Օo��U���~���n�����V����K�_��e�6�y���:n����%+!���v��P���K^��W�F\(�g=Ѫ03��&�QT㼏��Ԏ�힧r��%q���~��3k���E��-4�d���79K-�=Ks�d8�Ui�6ZP�Ua���Va��>�Х*���M�*E����������|&ϡ��O�tOU�ħ�MnH�6-֍�Q�Z2�ʽ%MnE�=��8�I�j1��7t�E��;[����}��s*-��8�"U!��~p��)�q(�)A�+�C5�¬;Y>HF ��`��0F�9�q�����ҟ6c��7�S0��J#y�ΐY��Tof��h�PULȬ��`g �Y�0�3+H���;���Z�>w�-i�Z�ēY�0�3+LHd�!g��,���j�\^-��jU�5o����N�[��8.��h,��!�Ekd�X_��H賺&��ֱabX����kr�LW6�"�LB̚��JQx����Mͫ�]��� endobj endobj Particle motion will be studied later in the next semester. Principle of Superposition When two or more waves are simultaneously present at a single point in space, the displacement of the medium at that point is the sum of the displacement due to each individual wave. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 595.32 841.92] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> HЃ:��~���8O$�_{����������g���V�T@��$W@ZIW@��֯� U���F@�[��Y�� �};�`Rs�,Ԣ�AsyflY�|i���>h�^e��;>Vtɲ����V̩�� �. )�Vl�>�_#FSW�&-�I�c&�ځ�� ��FվD �"K ����4���{�w�cV��6M���fMv�dܲ�N�ʫ��.LJi�WL�v,���K��g� �>hZ���x��P��F�>hn_�f@�e�ڽZU�؝� �9��%;aZ�Nh��Q��`. �.EJ� Z�Pb0��NSb�JlZr)��EjQ����;���)�)�zUv�{j���)�� � �&f(�\6J�����&�Z��m�L�E4N�"���`�m{�ZK ���u�B�GHZH>z��dq9|ʐ�%$��d��oe���N0T�މ���:uA-A�0�Y��c�yH% h���X,X(��� ra�}�*�;��O�0j�n*�� " ��X������D �\`C�vq>*�8�a���������� This is true of waves which are finite in length (wave pulses) or which are continuous sine waves. H�V@q� @�9��w'�f*F� j�C��ß��ΐ���i��^3e૭���A�$�� n�H�B��ǟR����̈́�-�#2*xU(f}j�V��)���j����U��d*y�Y�b���p��L� ^� �iF�i$Z��2r��ͪcF��e��1��%�Uٟ��g�R3i�����]p&r}"�z�>Q�w���4&�_Ľ�1�q�6v2��u�h!���n�#�.s��YNkNѴB�+w��;���@;x�{>@IV]�Pvm5�A�Ŗ��c����8�H"�)M9E���v2��姐����aBK�CDw����7B�y\� !��AM�؆!���4�Y�&X}�q-�ZP놘�����H�!cs`���$�0p�?��V���.��n[��$DN4�v#{3����#���H�а�Z�̊��L��8����CL�Y�=�E�=����8� �c��I�m �)VG (v�;Րg�nGgv�ʫw���J^\ipKC�-�J>l>'M��J�Y�0' �Ʌ��[�L�e�=���V!����Y+!$h(Y�H�T�W��y�3lO6�G,_���]Ǟ�`զ��_�F�"��N�65�F����jg�-�'�7\������e�A����n�������� �[�wC�dۘ��>�Iʾ����̓:c$���Ѥ��Zo�өr�,�P�����~��TG_��T�"�'b�}��b!_�Od���q�� �@+Ua'3+� 紟8�:���濆'js���s�"�1���/��l�%�ż[�=Z��-R��ϔu�e�'�'��D̐x9�eTԛu Superposition Principle • When two waves overlap in space the displacement of the wave is the sum of the individual displacements. The principle of superposition is expressed by affirming that overlapping waves add algebraically to create a resultant wave. (��3X1��qG� �kSD^��d�[�7�d>�.G�sF�y�ܫu�Qƒ�,̲���Xo�ˆ_�&�$+18J�&W�Na��jy��Q�>���C$8K��Z����R� �l!'�(e���ir���:�ULI�@L���%&��db��CL�У���i��h��!'ڢfrb��$(3�! ���6���s`p��[�Ex1D��B=S���L�d,�Á��Dma�G��Қ����5/ M���A�ԅ���Mˢm/�:��z���3+juʾ��=�G�3O��+���hAt'h`������ۇ$��C�B)g�_֧��.i ڂA҆V,,k��LT�j��lS~Z:�N��~՞��>1êc�k endobj The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time.

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