lecture21

# lecture21 - Phys 2101 Gabriela Gonzlez If we have two waves...

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Phys 2101 Gabriela González

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2 If we have two waves traveling in the same string, they will overlap and add up to a resultant wave. Overlapping waves do not in any way alter the travel of each other !!
3 Two waves traveling in the same string, in the same direction, with the same frequency, will add up to a single resultant wave with the same frequency, but different amplitude and phase: y(x,t)= y 1 sin(kx- ω t+ φ 1 ) + y 2 sin(kx- ω t+ φ 2 ) = y m sin(kx- ω t+ φ ) with y m 2 =y 1 2 +y 2 2 +2y 1 y 2 cos( φ 1 - φ 2 ) and tan φ =(y 1 sin φ 1 + y 2 sin φ 2 )/ (y 1 cos φ 1 + y 2 cos φ 2 ) Interference term!

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4 Total amplitude: y m 2 =y 1 2 +y 2 2 +2y 1 y 2 cos( φ 1 - φ 2 ) If φ 1 - φ 2 =0, 2 π ,…, y m =y 1 +y 2 : constructive interference If φ 1 - φ 2 = π , 3 π ,…, y m =y 1 -y 2 : destructive interference
5 Waves traveling in opposite directions can also be added. If they have the same frequency, they will produce a standing wave . Waves in strings reaching the

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## This note was uploaded on 12/01/2011 for the course PHYS 2101 taught by Professor Grouptest during the Fall '07 term at LSU.

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lecture21 - Phys 2101 Gabriela Gonzlez If we have two waves...

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