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Question: x<sub>1</sub> = A sin (wt – 0.1x) and x<sub>2</sub> = A sin\(\left( \omega t - 0.1x - \frac{\varphi}...

x1 = A sin (wt – 0.1x) and x2 = A sin(ωt−0.1x−φ2)\left( \omega t - 0.1x - \frac{\varphi}{2} \right).

resultant amplitude of combined wave is –

A

2A cosφ4\frac{\varphi}{4}

B

A2cos⁡φ2A\sqrt{2\cos\frac{\varphi}{2}}

C

2A cosφ2\frac{\varphi}{2}

D

A2(1+cos⁡φ4)A\sqrt{2\left( 1 + \cos\frac{\varphi}{4} \right)}

Answer

2A cosφ4\frac{\varphi}{4}

Explanation

Solution

R = A2+A2+2 A2cos⁡ϕ2=A2(1+cos⁡ϕ2)\sqrt { \mathrm { A } ^ { 2 } + \mathrm { A } ^ { 2 } + 2 \mathrm {~A} ^ { 2 } \cos \frac { \phi } { 2 } } = \mathrm { A } \sqrt { 2 } \sqrt { \left( 1 + \cos \frac { \phi } { 2 } \right) }

= 2A cos ϕ4\frac { \phi } { 4 }