X1-A sin - t-0-1x and x2-A sin - t-0-1 x - -2 - Resultant amplitude of combined wave is

X_1=A sin (ω t 0.1x) nbsp;x_2=A sin ( ω t 0.1 x ϕ2 ) x_1+x_2=A [ sin ( ω t 0.1x )+sin ( ω t 0.1x ϕ2 ) ] =A [ 2 sin ( ω t 0.1x+ω t 0.1x ϕ22 ). cos ( ω t ...

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Byju's Answer

Standard XII

Physics

KE & PE Graph

x1=A sin ω t-...

Question

$x_{1} = A sin (ω t - 0.1 x)$ and $x_{2} = A sin (ω t - 0.1 x - \frac{ϕ}{2})$ . Resultant amplitude of combined wave is

2 A cos \frac{ϕ}{4}

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A \sqrt{2 cos ϕ / 2}

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2 A cos \frac{ϕ}{2}

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A \sqrt{2 (1 + cos \frac{ϕ}{4})}

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Solution

The correct option is A $2 A cos \frac{ϕ}{4}$
$x_{1} = A sin (ω t - 0.1 x)$
$x_{2} = A sin (ω t - 0.1 x - \frac{ϕ}{2})$
$x_{1} + x_{2} = A [sin (ω t - 0.1 x) + sin (ω t - 0.1 x - \frac{ϕ}{2})]$
$= A ⎡ ⎢ ⎢ ⎢ ⎣ 2 sin ⎛ ⎜ ⎜ ⎜ ⎝ \frac{ω t - 0.1 x + ω t - 0.1 x - \frac{ϕ}{2}}{2} ⎞ ⎟ ⎟ ⎟ ⎠ . cos ⎛ ⎜ ⎜ ⎜ ⎝ \frac{ω t - 0.1 x - ω t + 0.1 x + \frac{ϕ}{2}}{2} ⎞ ⎟ ⎟ ⎟ ⎠ ⎤ ⎥ ⎥ ⎥ ⎦$
$= 2 A cos \frac{ϕ}{4} . sin (ω t - 0.1 x - \frac{ϕ}{4})$
So, amplitude will be $= 2 A cos \frac{ϕ}{4}$

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x1=Asin(ωt−0.1x) and x2=Asin(ωt−0.1x−ϕ2). Resultant amplitude of combined wave is

$x_{1} = A sin (ω t - 0.1 x)$ and $x_{2} = A sin (ω t - 0.1 x - \frac{ϕ}{2})$ . Resultant amplitude of combined wave is