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Find the resultant amplitude and the pha...

Find the resultant amplitude and the phase difference between the resultant wave and the first wave , in the event the following waves interfere at a point , ` y_(1) = ( 3 cm) sin omega t`,
`y_(2) = ( 4 cm) sin (omega t + (pi)/( 2)), y_(3) = ( 5 cm ) sin ( omega t + pi)`

Text Solution

Verified by Experts

The amplitudes can be added vectorially , with angle between them as their phase difference .
All these are shown in Fig . S 7 .1(a). The resultant amplitude `'A'` due to the interference of three waves is evidently from Fig. S7.1(b) given by
`A = sqrt( 4^(2) + 2^(2)) = 2 sqrt(5) cm`
Also , `tan theta = (2)/(4) = (1)/(2)`
`theta = tan^(-1) ((1)/(2))`
Therefore , the resultant wave leads the first wave by an angle
`(pi)/(2) + tan^(-1) ((1)/(2))`
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