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When the waves y(1) = A sin omega t and ...

When the waves `y_(1) = A sin omega t and y_(2) = A cos omega t ` are superposed, then resultant amplitude will be

A

`sqrt(2) ` A

B

`(1)/(sqrt(2))A`

C

A

D

2A

Text Solution

Verified by Experts

The correct Answer is:
A
Rrsultant wave,
` y = y_(1) + y_(2) = A sin omega t + A cos omega t `
` = sqrt(2) A (sin omega t * (1)/(sqrt(2)) + cos omega t * (1)/(sqrt(2)))`
`= sqrt(2) A (sin omega t "cos" (pi)/(4) + cos omega t "sin" (pi)/(4))`
`= sqrt(2) A sin (omega t + (pi)/(4))`
Hence, resultant amplitude ` = sqrt(2) A` .
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