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Five sinusoidal waves have the same freq...

Five sinusoidal waves have the same frequency 500 Hz but their amplitudes are in the ratio `2 : (1)/(2) : (1)/(2) : 1 : 1` and their phase angles `0, (pi)/(6), (pi)/(3), (pi)/(2)` and `pi` respectively. The phase angle of resultant wave obtained by the supersposition of these five waves is

A

` 30^@ `

B

` 45^@ `

C

` 60 ^@ `

D

`90^@ `

Text Solution

Verified by Experts

The correct Answer is:
B

`y_(t)=2Asin omegat, y_(2)=A/2sin(omega+pi/2)`
`y_(3)=(A)/(2)sin(omegat=(pi)/(3)),y_4=A sin (omegat+(pi)/(2))`
`y_(s)=A sin (omegat+pi)`
By phasor diagram. `tan phi=(PQ)/(OQ)=1`
`Rightarrow phi=45^(@)`
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