Three waves y 1 - 2 A sin - t - - 3 y 2 - 2 A sin - t - - 3 and y 3 - - A sin - t interfere each other- The amplitude of the resultant wave is

The correct option is A AAmplitude of resultant wave y=y_1+y_2+y_3 y=2Asin(ω t π3)+2Asin(ω t+π3) Asinω t y=2Asinω tcosπ3 2Acosω tsinπ3+2Asinω tcos ...

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Byju's Answer

Standard XII

Physics

Reflection from a Fixed End

Three waves ...

Question

Three waves $y_{1} = 2 A sin (ω t - \frac{π}{3})$ $y_{2} = 2 A sin (ω t + \frac{π}{3})$ and $y_{3} = - A sin (ω t)$ interfere each other. The amplitude of the resultant wave is

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2 A

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3 A

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Solution

The correct option is A A
Amplitude of resultant wave
$y = y_{1} + y_{2} + y_{3}$
$y = 2 A sin (ω t - \frac{π}{3}) + 2 A sin (ω t + \frac{π}{3}) - A sin ω t$
$y = 2 A sin ω t cos \frac{π}{3} - 2 A cos ω t sin \frac{π}{3} + 2 A sin ω t cos \frac{π}{3} + 2 A cos ω t sin \frac{π}{3} - A sin ω t$
$y = 4 A sin ω t cos \frac{π}{3} - A sin ω t$
$y = 2 A sin ω t - A sin ω t$
$y = A sin ω t$
Thus, the resultant amplitude is A.

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Three waves y1=2Asin(ωt−π3) y2=2Asin(ωt+π3) and y3=−Asin(ωt) interfere each other. The amplitude of the resultant wave is

The correct option is A AAmplitude of resultant wavey=y1+y2+y3y=2Asin(ωt−π3)+2Asin(ωt+π3)−Asinωty=2Asinωtcosπ3−2Acosωtsinπ3+2Asinωtcosπ3+2Acosωtsinπ3−Asinωty=4Asinωtcosπ3−Asinωty=2Asinωt−Asinωty=AsinωtThus, the resultant amplitude is A.

Three waves $y_{1} = 2 A sin (ω t - \frac{π}{3})$ $y_{2} = 2 A sin (ω t + \frac{π}{3})$ and $y_{3} = - A sin (ω t)$ interfere each other. The amplitude of the resultant wave is