Two waves y 1- A 1sin- t -1- y 2- A 2sin- t -2 Superimpose to form a resultant wave whose amplitude isA- -A12-A22-2 A1 A2sin-1-2B- - A 1- A 2-C- -A12-A22-2 A1 A2cos-1-2D- A 1- A 2

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YDSE Problems II

Two waves y 1...

Question

Two waves $y_{1} = A_{1} s i n (ω t - β_{1}), y_{2} = A_{2} s i n (ω t - β_{2})$ Superimpose to form a resultant wave whose amplitude is

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A₁ + A₂

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| A₁ + A₂|

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y_{1} = A_{1} sin (ω t - β_{1})

y_{2} = A_{2} sin (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 particle is subjected to two simple harmonic motions given as $x_{1} = A_{1} s i n ω t$ and $x_{2} = A_{2} s i n (ω t + \frac{π}{3})$

Find A. the displacement at t = 0

B. the maximum speed of the particle and

C. the maximum acceleration of the particle

x_{1} = A_{1} s i n ω t

x_{2} = A_{2} (ω t + \frac{π}{4})

a_{1}, a_{2}, a_{3}, a_{4}

a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} = 1

(a_{1} - a_{2})^{2} + (a_{2} - a_{2})^{2} + (a_{3} - a_{4})^{2} + (a_{4} - a_{1})^{2}

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