Two waves y1-A1sin- t-1 and y2-A2sin- t-2superimpose to form a resultant wave whose amplitude is

The correct option is D √(A^2_1+A^2_2+2A_1A_2cos(β_1 β_2)) The phase difference the two waves y_1 and y_2 , #160; δ= |β_1 β _2| #16 ...

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YDSE Problems II

Two waves y...

Question

Two waves
$y_{1} = A_{1} sin (ω t - β_{1})$ and
$y_{2} = A_{2} sin (ω t - β_{2})$
superimpose to form a resultant wave whose amplitude is

\sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos (β_{1} - β_{2})}

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\sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} sin (β_{1} - β_{2})}

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A_{1} + A_{2}

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| A_{1} + A_{1} |

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Solution

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y_{1} = A_{1} s i n (ω t - β_{1}), y_{2} = A_{2} s i n (ω t - β_{2})

Two waves $y_{1} = A_{1} sin (ω t - β_{1}) y_{2} = A_{2} sin (ω t - β_{2})$ superimpose to form a resultant wave whose amplitude is

a_{1}, a_{2}, a_{3}, . . . . . a_{2 n}

a_{1}^{2} - a_{2}^{2} + a_{3}^{2} - . . . . + a_{2 n - 1}^{2} - a_{2 n}^{2}

(a_{1}, a_{2}, . . . . . . ., a_{10})

| a_{1} | \leq 1

a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + . . . . . . . . + a_{10}^{2} - a_{1} a_{2} - a_{2} a_{3} - a_{3} a_{4} - . . . . . . - a_{9} a_{10} - a_{10} a_{1} = 2

x_{1} = A_{1} s i n ω t

x_{2} = A_{2} (ω t + \frac{π}{4})

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