Why must traveling waves have the same amplitude to form a standing wave?












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I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?






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    2












    $begingroup$


    I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?






    waves







    share|cite|improve this question









    $endgroup$















      2












      2








      2


      2



      $begingroup$


      I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?






      waves







      share|cite|improve this question









      $endgroup$




      I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?






      waves




      waves






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      asked 3 hours ago









      Julia KimJulia Kim

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          If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.



          In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.



          enter image description here



          If the travelling waves are of unequal amplitude then there is a net transfer of energy.

          If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.



          In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
          enter image description here



          If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.



          The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.



          enter image description here






          share|cite|improve this answer











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            1 Answer
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            $begingroup$

            If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.



            In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.



            enter image description here



            If the travelling waves are of unequal amplitude then there is a net transfer of energy.

            If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.



            In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
            enter image description here



            If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.



            The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.



            enter image description here






            share|cite|improve this answer











            $endgroup$


















              7












              $begingroup$

              If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.



              In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.



              enter image description here



              If the travelling waves are of unequal amplitude then there is a net transfer of energy.

              If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.



              In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
              enter image description here



              If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.



              The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.



              enter image description here






              share|cite|improve this answer











              $endgroup$
















                7












                7








                7





                $begingroup$

                If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.



                In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.



                enter image description here



                If the travelling waves are of unequal amplitude then there is a net transfer of energy.

                If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.



                In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
                enter image description here



                If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.



                The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.



                enter image description here






                share|cite|improve this answer











                $endgroup$



                If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.



                In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.



                enter image description here



                If the travelling waves are of unequal amplitude then there is a net transfer of energy.

                If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.



                In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
                enter image description here



                If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.



                The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.



                enter image description here







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited 2 hours ago

























                answered 2 hours ago









                FarcherFarcher

                50.8k338106




                50.8k338106






























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