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Question

On the superposition of the two waves represented by equation,
y1=Asin(ωtkx)
y2=Acos(ωtkx+π6)
The resultant angular frequency of the oscillation will be

A
ω
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B
2ω
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C
ω2
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D
3ω
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Solution

The correct option is A ω
Given: y1=Asin(ωtkx)
y2=Acos(ωtkx+π6)
ynet=y1+y2
ynet=Asin(ωtkx)+Acos(ωtkx+π6)
ynet=Asin(ωtkx)+Acos(ωtkx)cos(π6)Asin(ωtkx)sin(π6)
ynet=Asin(ωtkx)(1sin(π6))+Acos(ωtkx)cos (π6)
ynet=A2sin (ωtkx)+Acos(ωtkx)cos (π6)
ynet=Asin(ωtkx)sinπ6+Acos(ωtkx)cos π6
ynet=Acos(ωtkxπ6)
The angular frequency of resultant oscillation is ω

Note: When two waves having same ω, k and propagating in the same direction are superimposed, the resultant oscillation will have the same angular frequency.

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